Student
Handbook
TEKS
TAKS Practice
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S4
Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S4
Application Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S28
Problem-Solving Handbook . . . . . . . . . . . . . . . . . . . . . . . S40
Draw a Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Make a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Guess and Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Work Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Find a Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Make a Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Solve a Simpler Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Use Logical Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Use a Venn Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Make an Organized List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S40
S41
S42
S43
S44
S45
S46
S47
S48
S49
Skills Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S50
Number and Operations
Place Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Compare and Order Rational Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . .
Times Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inverse Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Translate from Words to Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mental Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S50
S50
S51
S51
S52
S52
Measurement
Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S53
Precision, Accuracy, and Significant Digits . . . . . . . . . . . . . . . . . . . . . . . . S54
Absolute and Relative Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S55
Geometry
Points, Lines, Planes, and Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S56
Complementary and Supplementary Angles . . . . . . . . . . . . . . . . . . . . . . S57
Vertical Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S57
S2
Student Handbook
Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Geometric Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Classify Triangles and Quadrilaterals . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Draw Three-Dimensional Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Surface Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pythagorean Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Midpoint Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transformations in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . .
Dilations in the Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S58
S58
S59
S59
S60
S61
S62
S63
S64
S65
S66
S67
S68
S68
S69
S70
Data Analysis
Line Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Measures of Central Tendency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Standard Deviation and the Normal Curve . . . . . . . . . . . . . . . . . . . . . . . .
S71
S72
S73
S73
S74
Algebra
Cubic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S75
Step Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S75
Logic and Set Theory
Conditional Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Counterexamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inductive and Deductive Reasoning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Set Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Field Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
S76
S76
S77
S78
S78
Selected Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S79
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S107
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S149
Symbols and Formulas
. . . . . . . . . . . . . . inside back cover
S3
TEKS
Chapter 1
Lesson
1-1
TAKS Practice
Skills Practice
Give two ways to write each algebraic expression in words.
1. x + 8
2. 6(y)
3. g - 4
12
4. _
h
Evaluate each expression for a = 4, b = 2, and c = 5.
a
7. c - a
8. ab
5. b + c
6. _
b
Write an algebraic expression for each verbal expression. Then evaluate the
algebraic expression for the given values of y.
Verbal
9.
Lesson
1-2
Lesson
1-3
Algebraic
y=9
y=6
y reduced by 4
10.
the quotient of y and 3
11.
5 more than y
12.
the sum of y and 2
Add or subtract using a number line.
13. -7 - 9
14. -2.2 + 4.3
1 - 2_
1
15. -5 _
2
2
Subtract.
17. 12 - 47
18. 1.3 - 9.2
Compare. Write <, >, or =.
20. -5 - (-8)
-4 - 9
21. ⎪-6 - (-2)⎥
2 for y = 1 _
1
19. y - 4 _
3
3
7-4
Evaluate the expression g - (-7) for each value of g.
2
23. g = 121
24. g = 1.25
25. g = - _
5
Find the value of each expression.
27. -24 ÷ (-8)
28. 5(-9)
( )
6
2 ÷ -_
30. _
7
7
16. 3.4 - 6.5
( )
22. -2 - 5
7 - 14
1
26. g = -8 _
3
29. -5.2 ÷ y for y = -1.3
9 ÷0
32. _
10
4
31. 0 ÷ - _
5
Evaluate each expression for x = -8, y = 6, and z = -4.
y
33. xy
34. yz
35. _
z
z
36. _
x
Let a represent a positive number, b represent a negative number, and z represent
zero. Tell whether each expression is positive, negative, zero, or undefined.
a
ab
37. ab
38. -bz
39. - _
40. _
z
b
Lesson
1-4
Write each expression as repeated multiplication. Then simplify the expression.
41. 3 3
42. -2 4
43. (-5)3
44. (-1) 5
Write each expression using a base and an exponent.
45. 5 · 5 · 5 · 5 · 5
46. 4 · 4 · 4
47. 2 · 2 · 2 · 2
Write the exponent that makes each equation true.
48. 2 ■ = 16
S4
TEKS
TAKS Practice
49. 4 ■ = 256
50. (-3)■ = 81
51. -5 ■ = -125
Chapter 1
Lesson
1-5
Skills Practice
Find each square root.
52. - √
64
53. √
144
Compare. Write <, >, or =.
55. √
118
11
56. 6
√
35
54. √
25
57. 14
√
196
58. √
50
Write all classifications that apply to each number.
59. -44
60. √
49
61. 15.982
Lesson
1-6
1
62. _
9
Evaluate each expression for the given value of the variable.
63. 22 - 3g + 5 for g = 4
64. 12 - 30 ÷ h for h = 6
65.
Simplify each expression.
66. 4 + 12 ÷ ⎪3 - 9⎥
67. -36 - √
4 + 15 ÷ 3
Translate each word phrase into an algebraic expression.
69. the quotient of 8 and the difference of a and 5
7
(11j + j) + 6 for j = 3
√
5 - √
12(3)
68. __
-4 + √
2(8)
70. the sum of -9 and the square root of the product of 7 and c
Lesson
1-7
Simplify each expression.
71. -5 + 38 + 5 + 62
1 - 42 + 7 _
2
1 · 4 · 25
72. 2 _
73. _
5
3
3
Write each product using the Distributive Property. Then simplify.
74. 12(108)
75. 7(89)
76. 11(33)
Simplify each expression by combining like terms.
77. 7a - 3a
78. -2b - 12b
79. 4c + 5c 2 - c
Simplify each expression. Justify each step with an operation or property.
80. 6(p - 2) + 3p
81. 8q - 3 + 5q(2 + q)
82. -4 + 3r - 7(2s - r)
Lesson
1-8
Graph each point.
83. A(2, 3)
84. B(-4, 1)
85. C (0, -2)
86. D (-4, -1)
Name the quadrant in which each point lies.
87. J
88. K
89. L
90. M
91. N
92. P
*
Ó
{
Þ
{ Ý
Ó
ä
Ó
Ó
{
{
Generate ordered pairs for each function for x = -2, -1, 0, 1, and 2.
Graph the ordered pairs and describe the pattern.
93. y = x - 3
94. y = -2x
95. y = -x 2
96. y = ⎪3x⎥
Write an equation for each rule. Use the given values for x to generate ordered
pairs. Graph the ordered pairs and describe the pattern.
97. y is equal to the sum of one-third of x and -2; x = -6, -3, 0, 3, and 6.
98. y is equal to 4 less than x squared; x = -2, -1, 0, 1, and 2.
TEKS
TAKS Practice
S5
Chapter 2
Lesson
2-1
Skills Practice
Solve each equation. Check your answer.
1. x - 9 = 5
2. 4 = y - 12
3 =7
3. a + _
5
4. 7.3 = b + 3.4
5. -6 + j = 5
6. -1.7 = -6.1 + k
Write an equation to represent each relationship. Then solve the equation.
7. A number decreased by 7 is equal to 10.
8. The sum of 6 and a number is -3.
Lesson
2-2
Solve each equation. Check your answer.
n = 15
9. _
5
k
10. -6 = _
4
r =5
11. _
2.6
12. 3b = 27
13. 56 = -7d
14. -3.6 = -2f
1z=3
15. _
4
4g
16. 12 = _
5
1 a = -5
17. _
3
Write an equation to represent each relationship. Then solve the equation.
18. A number multiplied by 4 is -20.
19. The quotient of a number and 5 is 7.
Use the equation 9y = -3x to find y for each value of x.
Lesson
2-3
x
-3x
9y = -3x
20.
-6
-3(-6) = 18
9y = 18
21.
0
22.
3
y
Solve each equation. Check your answer.
23. 2k + 7 = 15
24. 11 - 5m = -4
2 b + 6 = 10
26. _
5
f
27. _ - 4 = 2
3
1 y.
29. If 5(y - 2) = 30, find the value of _
4
25. 23 = 9 - 2d
28. 6n + 4 = 22
30. If 4 - 3b = 19, find the value of -2b.
Write an equation to represent each relationship. Solve each equation.
31. The difference of 11 and 4 times a number equals 3.
32. Thirteen less than 5 times a number is equal to 7.
Lesson
2-4
Solve each equation. Check your answer.
33. 5b - 3 = 4b + 1
34. 3g + 7 = 11g - 17
35. -8 + 4y = y - 6 + 3y - 2
36. 7 + 3d - 5 = -1 + 2d - 12 + d
Write an equation to represent each relationship. Then solve the equation.
37. Three more than one-half a number is the same as 17 minus three times the number.
38. Two times the difference of a number and 4 is the same as 5 less than the number.
S6
TEKS
TAKS Practice
Chapter 2
Skills Practice
Solve each equation for the indicated variable.
5 - c = d - 7 for c
39. q - 3r = 2 for r
40. _
6
y
42. 2fgh - 3g = 10 for h
41. 2x + 3 _ = 5 for y
4
Lesson
2-5
Find each unit rate.
43. A long-distance runner ran 9000 meters in 30 minutes.
Lesson
2-6
44. A hummingbird flapped its wings 770 times in 14 seconds.
Solve each proportion.
h =_
5
45. _
4
6
2x
2
_
_
48. =
3
8
5
2
_
46. _
m=5
5 =_
3
49. _
x - 3 10
Find the value of x in each diagram.
51. ABCD ∼ EFGH
Lesson
2-7
nʓ
{ÊvÌ
52. JKL ∼ MNO
ÝÊvÌ
r =_
10
47. _
7
3
7
b
2
_
=_
50.
4
12
£äÊvÌ
£äÊvÌ
Èʓ
Ýʓ
£{ʓ
"
Lesson
53. Find 25% of 60.
54. Find 40% of 95.
2-8
55. What percent of 75 is 15?
56. What percent of 60 is 33?
57. 91 is what percent of 65?
58. 35% of what number is 24.5?
Write each decimal or fraction as a percent.
9
4
59. _
60. 0.55
61. _
5
6
Write each percent as a decimal and as a fraction.
63. 32%
64. 24%
65. 37.5%
62. 0.0375
66. 118.75%
Write each list in order from least to greatest.
9 , 8.8%
6 , 0.19
5 , 9.2, 117%, _
2 , 0.28, 1.9%, _
67. _
68. _
17
25
3
11
Lesson
69. Estimate the tax on a $2438.00 clarinet when the sales tax is 7.9%.
2-9
70. Estimate the tip on a $21.32 check using a tip rate of 20%.
Lesson
Find each percent change. Tell whether it is a percent increase or decrease.
71. 10 to 25
72. 40 to 2
73. 800 to 160
2-10
74. 4 to 14
75. 8 to 30
76. 60 to 36
77. Find the result when 45 is increased by 40%.
78. Find the result when 120 is decreased by 70%.
TEKS
TAKS Practice
S7
Chapter 3
Lesson
3-1
Skills Practice
Describe the solutions of each inequality in words.
1. 3 + v < -2
2. 15 ≤ k + 4
3. -3 + n > 6
4. 1 - 4x ≥ -2
Graph each inequality.
5. f ≥ 2
6. m < -1
8. (-1 -1)2 ≤ p
2
7. √4
+ 32 > c
Write the inequality shown by each graph.
9.
10.
ä
£
Ó
Î
{
x
È
ä
Ó
{
È
n £ä £Ó
Î Ó £
ä
£
11.
Î Ó £
ä
£
Ó
Î
È { ÓÊ
ä
Ó
{
È
Î
{
x
È
12.
13.
14.
Ó
Î
ä
£
Ó
Write each inequality with the variable on the left. Graph the solutions.
15. 14 > b
16. 9 ≤ g
17. -2 < x
18. -4 ≥ k
Lesson
3-2
Solve each inequality and graph the solutions.
19. 8 ≥ d - 4
20. -5 < 10 + w
21. a + 4 ≤ 7
22. 9 + j > 2
Write an inequality to represent each statement. Solve the inequality and graph
the solutions.
23. Five more than a number v is less than or equal to 9.
24. A number t decreased by 2 is at least 7.
25. Three less than a number r is less than -1.
26. A number k increased by 1 is at most -2.
Use the inequality 4 + z ≤ 11 to fill in the missing numbers.
27. z ≤
28. z ≤4
29. z - 3 ≤
Lesson
Solve each inequality and graph the solutions.
3-3
30. 24 > 4b
31. 27g ≤ 81
34. 4p < -2
3s > 3
35. _
8
-2e ≥ 4
39. _
5
38. -3k ≤ -12
h
42. 9 > _
-2
43. 49 > -7m
x <3
32. _
5
3d
36. 0 ≥ _
7
33. 10y ≥ 2
40. 8 < -12y
41. -3.5 > 14c
44. 60 ≤ -12c
1 q < -6
45. - _
3
a ≥_
3
37. _
4
8
Write an inequality for each statement. Solve the inequality and graph the
solutions.
1 and a number is not more than 6.
46. The product of _
2
47. The quotient of r and -5 is greater than 3.
48. The product of -11 and a number is greater than -33.
49. The quotient of w and -4 is less than or equal to -6.
S8
TEKS
TAKS Practice
Chapter 3
Lesson
3-4
Skills Practice
Solve each inequality and graph the solutions.
50. 3t - 2 < 5
51. 4p + 4 ≥ 12
52. 10 > 4 - 3g
53. -6 < 5b - 4
2f + 3
57. 4 < _
2
m - 2 < -2
54. _
4
10x - 4
55. -1 > _
56. 9a + 6 ≥ 3
12
3h<_
2 +_
4
1 (10k - 2) > 1
59. _
60. _
58. 10 ≤ 3(4 - r)
5
3 4
3
3 8q - 2 2 < -3
3
2
2
√
61. -n - 3 < -2
62. 37 - 4d ≤ 3 + 4
63. - _
)
(
4
Use the inequality -6 - 2w ≥ 10 to fill in the missing numbers.
64. w ≤
65. w - 3 ≤
66.
+w≤1
Write an inequality for each statement. Solve the inequality and graph the solutions.
67. Twelve is less than or equal to the product of 6 and the difference of 5 and a number.
68. The difference of one-third a number and 8 is more than -4.
69. Seven more than a number is less than or equal to the square root of the sum of
9 and 7.
70. One-fourth of the sum of 2x and 4 is more than 5.
Lesson
3-5
Solve each inequality and graph the solutions.
71. 4v - 2 ≤ 3v
72. 9e > 7 - 2e
73. 6j ≥ 2j + 8
74. 3z - 5 < 7z
75. 2(7 - s) > 4(s + 2)
76. -3(3 + 2y) - 1 ≤ 2(1 - 4y)
77. 3n < 3(6 - 2n)
5 ≥_
1u-_
1u
78. _
3
2 6
Solve each inequality.
79. 3 + 3c < 6 + 3c
80. 4(k + 2) ≥ 4k + 5
81. 2(5 - b) ≤ 3 - 2b
Write an inequality to represent each relationship. Solve your inequality.
82. The difference of three times a number and 5 is more than the number times 4.
83. Seven more than the product of four and a number is less than or equal to the
number increased by 3.
84. one less than a number is greater than the product of 3 and the difference of 5 and
the number.
Lesson
3-6
Solve each compound inequality and graph the solutions.
85. 6 < 3 + x < 8
86. -1 ≤ b + 4 ≤ 3
87. k + 5 ≤ -3 OR k + 5 ≥ 1
88. r - 3 > 2 OR r + 1 < 4
Write the compound inequality shown by each graph.
89.
90.
Î Ó £
ä
£
Ó
Î
È { Ó
ä
Ó
{
È
Write and graph a compound inequality for the numbers described.
91. all real numbers less than 2 and greater than or equal to -1
92. all real numbers between -3 and 1
Solve each compound inequality and graph the solutions.
93. 2r + 3 ≥ 1 AND 3r - 4 ≤ 5
94. f - 2 > 6 OR f + 2 < 6
TEKS
TAKS Practice
S9
Chapter 4
Lesson
4-1
Skills Practice
Choose the graph that best represents each situation.
1. A person blows up a balloon with a steady airstream.
2. A person blows up a balloon steadily and then lets it deflate.
3. A person blows up a balloon slowly at first and then uses more and more air.
À>«…Ê
6œÕ“i
/ˆ“i
Lesson
4-2
À>«…Ê
6œÕ“i
6œÕ“i
À>«…Ê
/ˆ“i
/ˆ“i
Express each relation as a table, as a graph, and as a mapping diagram.
⎧
⎫
⎧
⎫
4. ⎨(0, 2), (-1, 3), (-2, 5)⎬
5. ⎨(2, 8), (4, 6), (6, 4), (8, 2)⎬
⎩
⎭
⎩
⎭
Give the domain and range for each relation. Tell whether the relation is a function.
Explain.
⎧
⎫
⎧
⎫
6. ⎨(3, 4), (-1, 2), (2, -3), (5, 0)⎬
7. ⎨(5, 4), (0, 2), (5, -3), (0, 1)⎬
⎩
⎭
⎩
⎭
Þ
8.
9.
x
2
0
1
2
-1
y
1
0
-1
-2
-3
n
È
{
Ó
Ó
Lesson
4-3
{
È
n
Ý
Determine a relationship between the x- and y-variables. Write an equation.
⎧
⎫
10. ⎨(1, 3), (2, 6), (3, 9), (4, 12)⎬
11.
x
1
2
3
4
⎩
⎭
y
1
4
9
16
Identify the independent and dependent variables. Write a rule in function
notation for each situation.
12. A science tutor charges students $15 per hour.
13. A circus charges a $10 entry fee and $1.50 for each pony ride.
Evaluate each function for the given input values.
14. For f (a) = 6 - 4a, find f (a) when a = 2 and when a = -3.
2 d + 3, find g (d) when d = 10 and when d = -5.
15. For g (d) = _
5
16. For h (w) = 2 - w 2, find h (w) when w = -1 and when w = -2.
17. Complete the table for f (t ) = 7 + 3t.
t
f(t)
S10
TEKS
TAKS Practice
0
1
2
3
18. Complete the table for h(s) = 2s + s 3 - 6.
s
h(s)
-1
0
1
2
Chapter 4
Lesson
4-4
Skills Practice
Graph each function for the given domain.
⎧
⎧
⎫
⎫
19. 2x - y = 2; D: ⎨-2, -1, 0, 1⎬
20. f(x) = x 2 - 1; D: ⎨-3, -1, 0, 2⎬
⎩
⎭
⎩
⎭
Graph each function.
21. f(x) = 4 - 2x
22. y + 3 = 2x
23. y = -5 + x 2
5 - 2x to find the value of f(x) when x = _
1.
24. Use a graph of the function f(x) = _
2
2
Check your answer.
25. Find the value of x so that (x, 4) satisfies y = -x + 8.
26. Find the value of y so that (-3, y) satisfies y = 15 - 2x 2.
Lesson
For each function, determine whether the given points are on the graph.
x + 4; -3, 3 and 3, 5
27. y = _
28. y = x 2 - 1; (-2, 3) and (2, 5)
)
(
( )
3
Describe the correlation illustrated by each scatter plot.
4-5
29.
30.
Þ
31.
Þ
Ý
Þ
Ý
Ý
Identify the correlation you would expect to see between each pair of data sets.
32. the number of chess pieces captured and the number of pieces still on the board
33. a person’s height and the color of the person’s eyes
Choose the scatter plot that best represents the described situation.
34. the number of students in a class and the
À>«…Ê
Þ
grades on a test
Þ
À>«…Ê
35. the number of students in a class and the
number of empty desks
Ý
Lesson
4-6
Ý
Determine whether each sequence appears to be an arithmetic sequence. If so, find
the common difference and the next three terms.
36. -10, -7, -4, -1, …
37. 8, 5, 1, -4, …
38. 1, -2, 3, -4, …
39. -19, -9, 1, 11, …
Find the indicated term of each arithmetic sequence.
40. 15th term: -5, -1, 3, 7, …
41. 20th term: a 1 = 2; d = -5
42. 12th term: 8, 16, 24, 32, …
43. 21st term: 5.2, 5.17, 5.14, 5.11, …
Find the common difference for each arithmetic sequence.
7, _
10 , …
1 , 1, _
44. 0, 7, 14, 21, …
45. 132, 121, 110, 99, …
46. _
4
4 4
47. 1.4, 2.2, 3, 3.8, …
48. -7, -2, 3, 8, …
49. 7.28, 7.21, 7.14, 7.07, …
Find the next four terms in each arithmetic sequence.
50. -3, -6, -9, -12, …
51. 2, 9, 16, 23, …
5, …
1, _
1 , 1, _
52. - _
53. -4.3, -3.2, -2.1, -1, …
3 3
3
TEKS
TAKS Practice
S11
Chapter 5
Lesson
5-1
Skills Practice
Identify whether each graph represents a function. Explain. If the graph does
represent a function, is the function linear?
1.
{
2.
Þ
3.
Þ
{
Þ
È
Ó
Ó
Ý
È
{
ä
Ó
{
Ý
{
Ó
Ó
ä
Ó
{
Ó
Ó
{
Ý
{
{
Ó
ä
Tell whether the given ordered pairs satisfy a linear function. Explain.
4.
5.
x
2
5
8
x
-4
-2
0
2
4
y
7
6
5
4
y
3
12
8
7
{
11
14
3
3
Lesson
Tell whether each equation is linear. If so, write the equation in standard form and
give the values of A, B, and C.
x = 4 - 2y
6. y = 8 - 3x
7. _
8. -3 + xy = 2
9. 4x = -3 - 3y
3
Find the x- and y-intercepts.
5-2
10.
{
11.
Þ
Þ
{
Ó
Ý
{
Ó
ä
Ý
Ó
ä
Ó
{
{
Ó
È
{
n
12. -4x = 2y - 1
13. x - y = 3
14. 2x - 3y = 12
15. 2.5x + 2.5y = 5
Use intercepts to graph the line described by each equation.
16. 15 = -3x - 5y
17. 4y = 2x + 8
18. y = 6 - 3x
Lesson
Find the slope of each line.
5-3
20.
{
{
Ó
Ó
21.
Þ
19. -2y = x + 2
Þ
n
Ó
{
Ý
{
Lesson
5-4
Ó
ä
Ó
{
Ý
n
TEKS
{
ä
Ó
{
{
n
{
n
Find the slope of the line that contains each pair of points.
22. (-1, 2) and (-4, 8)
23. (2, 6) and (0, 1)
24. (-2, 3) and (4, 0)
Find the slope of the line described by each equation.
25. 2y = 42 - 6x
26. 3x + 4y = 12
S12
Ó
TAKS Practice
27. 3x = 15 + 5y
Chapter 5
Lesson
5-5
Skills Practice
Tell whether each equation represents a direct variation. If so, identify the constant
of variation.
28. x - 2y = 0
29. x - y = 3
30. 3y = 2x
31. The value of y varies directly with x, and y = 2 when x = -3. Find y when x = 6.
32. The value of y varies directly with x, and y = -3 when x = 9. Find y when x = 12.
Each ordered pair is a solution of a direct variation. Write the equation of direct
variation.
1 , -3
33. (1, 4)
34. (-2, 12)
35. _
36. (5, 2)
2
(
37. (8, 12)
Lesson
5-6
Lesson
5-7
38. (7, -2)
)
39. (12, -3)
40. (5, 15)
Write the equation that describes each line in slope-intercept form.
41. slope = 2, y-intercept = -2
42. slope = 0.25, y-intercept = 4
1 , y-intercept = 2
43. slope = -2, y-intercept = 3
44. slope = _
3
Write each equation in slope-intercept form. Then graph the line described by the
equation.
1x=2
45. 2y = x - 3
46. -3x - 2y = 1
47. 2y - _
2
Write an equation in point-slope form for the line with the given slope that
contains the given point.
1 ; 2, 4
48. slope = 2; (0, 3)
49. slope = -1; (1, -1)
50. slope = _
( )
2
1 ; 1, 2
51. slope = _
52. slope = -2; (3, 1)
53. slope = 3; (-2, -5)
( )
3
Write an equation in slope-intercept form for the line through the two points.
54. (-1, 1) and (1, -2)
55. (3, 1) and (2, -3)
56. (4, -5) and (2, -1)
Lesson
5-8
57. Identify which lines are parallel: y = 3x - 2; y = -2; y = 3x + 7; y = 0
1 (x + 3); y = _
1 (x + 8);
58. Identify which lines are perpendicular: y = -2(2x - 1); y = _
4
2
y - 4 = 2(3 - 2x)
Write an equation in slope-intercept form for the line that is parallel to the given
line and that passes through the given point.
59. y = -2x + 3; (1, 4)
60. y = x - 5; (2, -4)
61. y = 3x; (-1, 5)
Write an equation in slope-intercept form for the line that is perpendicular to the
given line and that passes through the given point.
62. y = x + 1; (3, -2)
63. y = -4x - 1; (-1, 0)
64. y = 4x + 5; (2, -1)
Lesson
5-9
Graph f (x) and g(x). Then describe the transformation(s) from the graph of f (x) to
the graph of g(x).
1
65. f(x) = x, g(x) = x + 2
66. f(x) = x, g(x) = x - _
2
67. f(x) = 6x + 1, g(x) = 2x + 1
68. f(x) = 3x - 1, g(x) = 9x - 1
1x
69. f(x) = x, g(x) = 2x - 1
70. f(x) = x + 1, g(x) = - _
2
Graph f (x). Then reflect the graph of f (x) across the y-axis. Write a function g(x) to
describe the new graph.
71. f (x) = 2x + 3
72. f (x) = -3x - 1
73. f (x) = -4x
TEKS
TAKS Practice
S13
Chapter 6
Lesson
6-1
Skills Practice
Tell whether the ordered pair is a solution of the given system.
⎧ 2x - 3y = -7
⎧4x + 3y = -2
⎧ -2x - 3y = 1
1. (1, 3); ⎨
2. (-2, 2); ⎨
3. (4, -3); ⎨
⎩ -5x + 3y = 4
⎩ -2x - 2y = 2
⎩ x + 2y = -2
Use the given graph to find the solution of each system.
⎧
1
_
y = 2 x - 1
⎧y = x + 1
4. ⎨
5. ⎨
1x+3
⎩ y = -x + 1
y = - _
2
⎩
{
Þ
Þ
{
Ó
Ó
Ý
{
ä
Ó
Ó
{Ý
{
Ó
ä
Ó
Ó
{
{
Ó
{
Solve each system by graphing. Check your answer.
⎧y = x + 1
6. ⎨
⎩ y = -2x - 2
Lesson
6-2
⎧3x + y = -8
7. ⎨
1
⎩ 3y = _ x - 5
2
Solve each system by substitution.
⎧2x + y = -6
⎧y = 12 - 3x
10. ⎨
9. ⎨
⎩ y = 2x - 3
⎩ -5x + y = 1
⎧2x + 3y = 2
12. ⎨
1
⎩ - _ x + 2y = -6
2
⎧3x - 2y = -3
13. ⎨
⎩ y = 7 - 4x
⎧x = 2 - 2y
8. ⎨
⎩ -1 = -2x - 3y
⎧y = 11 - 3x
11. ⎨
⎩ -2x + y = 1
⎧4y - 2x = -2
14. ⎨
⎩ x + 3y = -4
Two angles whose measures have a sum of 90° are called complementary angles.
For Exercises 15–17, x and y represent complementary angles. Find the measure of
each angle.
⎧x + y = 90
15. ⎨
⎩ y = 9x - 10
Lesson
6-3
S14
TEKS
⎧x + y = 90
16. ⎨
⎩ y - 4x = 15
⎧x + y = 90
17. ⎨
⎩ y = 2x + 15
Solve each system by elimination.
⎧x - 3y = -1
⎧-3x - y = 1
18. ⎨
19. ⎨
⎩ -x + 2y = -2
⎩ 5x + y = -5
⎧-x - 3y = -1
20. ⎨
⎩ 3x + 3y = 9
⎧3x - 2y = 2
21. ⎨
⎩ 3x + y = 8
⎧5x - 2y = -15
22. ⎨
⎩ 2x - 2y = -12
⎧-4x - 2y = -4
23. ⎨
⎩ -4x + 3y = -24
⎧-3x - 3y = 3
24. ⎨
⎩ 2x + y = -4
⎧4x - 3y = -1
25. ⎨
⎩ 2x - 2y = -4
⎧3x + 6y = 0
26. ⎨
⎩ 7x + 4y = 20
TAKS Practice
Chapter 6
Lesson
6-4
Skills Practice
Solve each system of linear equations.
⎧y = 2x + 4
⎧-y = 3 - 5x
27. ⎨
28. ⎨
⎩ -2x + y = 6
⎩ y - 5x = 6
⎧y + 2 = 3x
29. ⎨
⎩ 3x - y = -1
⎧y - 1 = -3x
31. ⎨
⎩ 12x + 4y = 4
⎧2y = 6 - 6x
30. ⎨
⎩ 3y + 9x = 9
⎧4x - 2y = 4
32. ⎨
⎩ 3y = 6 (x - 1)
Classify each system. Give the number of solutions.
⎧2y = 2 (4x - 3)
33. ⎨
⎩ y - 1 = 4x
⎧3y + 6x = 9
34. ⎨
⎩ 2(y - 3) = -4x
⎧3x - 13 = 2y
35. ⎨
⎩ -3y = 2x
Lesson
Tell whether the ordered pair is a solution of the given inequality.
6-5
36. (3, 6); y > 2x + 4
37. (-2, -8); y ≤ 3x - 2
38. (-3, 3); y ≥ -2x + 5
Graph the solutions of each linear inequality.
39. y > 2x
40. y ≤ -3x + 2
41. y ≥ 2x - 1
42. -y < -x + 4
43. y ≥ -2x + 4
44. y > -x - 3
1 x + 1_
1
45. y < _
2
2
46. y ≤ 4x - (-1)
Write an inequality to represent each graph.
47.
n
48.
Þ
Þ
n
{
{
Ý
n
Lesson
6-6
{
ä
{
Ý
n
n
{
ä
{
{
n
n
{
n
Tell whether the ordered pair is a solution of the given system.
⎧y > 3x - 3
⎧y > -3x - 2
⎧y > 2x
49. (2, 5); ⎨
50. (3, 9); ⎨
51. (2, 3); ⎨
⎩y ≥ x + 1
⎩ y < 2x + 3
⎩y ≤ x - 3
Graph each system of linear inequalities. Give two ordered pairs that are solutions
and two that are not solutions.
⎧x + 4y < 2
52. ⎨
⎩ 2y > 3x + 8
⎧y ≤ 6 - 2x
53. ⎨
⎩ x - 2y < -2
⎧2x - 2 > -3y
54. ⎨
⎩ -x + 3y ≥ -10
Graph each system of linear inequalities.
⎧y > 2x + 1
55. ⎨
⎩ y < 2x - 2
⎧y < 3x - 1
56. ⎨
⎩ y > 3x - 4
⎧y ≥ -x + 2
57. ⎨
⎩ y ≥ -x + 5
⎧y ≥ 2x - 3
58. ⎨
⎩ y ≥ 2x + 3
⎧y > -4x - 2
59. ⎨
⎩ y ≤ -4x - 5
⎧y ≥ -2x + 1
60. ⎨
⎩ y < -2x + 6
TEKS
TAKS Practice
S15
Chapter 7
Skills Practice
Lesson
Simplify.
7-1
1. 3 -4
2. 5 -3
3. -4 0
4. -2 -5
6. (-2)-4
7. 1-7
8. (-4)-3
9. (-5)0
5. 6 -3
10. (-1)-5
Evaluate each expression for the given value(s) of the variable(s).
11. x -4 for x = 2
12. (c + 3)-3 for c = -6
13. 3j -7k -1 for j = -2 and k = 3
14. (2n - 2)-4 for n = 3
Simplify.
15. b 4g -5
k -3
16. _
r5
17. 5s -3c 0
z -4
18. _
5t -2
f2
19. _
3a -4
-3t 4
20. _
q -5
a 0k -4
21. _
p2
22. 3f -1y -5
25. 10 6
26. 10 -8
Lesson
Find the value of each power of 10.
7-2
23. 10 -7
24. 10 9
Write each number as a power of 10.
27. 10,000,000
28. 0.00001
29. 10,000,000,000,000
Find the value of each expression.
30. 72.19 × 10 -2
31. 0.096 × 10 -7
32. 7384.5 × 10 6
Write each number in scientific notation.
33. 3,605,000
34. 0.0063
35. 100,500,000
38. (k 4)
Lesson
Simplify.
7-3
36. 3 4 · 3 2
37. r 7 · r 0
39. (b 4)
40. (c 3d 2) · (cd 2)
4
41. (-3q 3)
-2
3
3
-2
Find the missing exponent in each expression.
a
43. (a 3b ■) = _
b6
3
42. a ■a 6 = a 9
Lesson
Simplify.
7-4
3 11
45. _
38
44 · 53
46. _
2
3 · 43 · 53
9
4
■
b
44. (a 4b -2) · a 3 = _
a5
6h 4
47. _
12h 3
r 6s 5
48. _
r 5s 6
Simplify each quotient and write the answer in scientific notation.
49. (4 × 10 7) ÷ (1.6 × 10 5)
Simplify.
( )
2
52. _
3
S16
TEKS
4
TAKS Practice
50. (10 × 10 4) ÷ (2 × 10 7)
( )
x 2y 2
53. _
y3
2
()
4
54. _
5
-3
51. (2.5 × 10 8) ÷ (5 × 10 3)
( )
2xy 2
55. _2
3(xy)
-3
Chapter 7
Skills Practice
Lesson
Find the degree of each monomial.
7-5
56. 4 7
57. x 3y
r 6st 2
58. _
2
59. 9 0
62. 3 g 4h + h 2 + 4j 6
63. 4no 7 - o 6p 3 + p
Find the degree of each polynomial.
60. a 2b + b - 2 2
61. 5x 4y 2 - y 5z 2
Write each polynomial in standard form. Then give the leading coefficient.
1 t3 + t - _
1 t5 + 4
64. 4r - 5r 3 + 2r 2
65. -3b 2 + 7b 6 + 4 - b
66. _
2
3
Classify each polynomial according to its degree and number of terms.
67. 3x 2 + 4x - 5
Lesson
7-6
Lesson
7-7
68. -4x 2 + x 6 - 4 + x 3
69. x 3 - 7 2
Add or subtract.
70. 4y 3 - 2y + 3y 3
71. 9k 2 + 5 - 10k 2 - 6
72. 7 - 3n 2 + 4 + 2n 2
73. 3a 2 + 4a 3 - 2a 2
74. (2 + x 2) + (5x 2 + 6)
75. (9x 6 - 5x 2 + 3) + (6x 2 - 5)
76. (2y 5 - 5y 2) + (3y 5 - y 3 + 2y 2)
77. (5y 3 - 6y + 2) + (2y 7 + y)
78. (r 3 + 2r + 1) - (2r 3 - 4)
79. (4r 4 - 3r 2 + 4) - (2r 4 - r 2)
80. (10s 2 + 5) - (5s 2 + 3s - 2)
81. (2s 7 - 6s 3 + 2) - (3s 7 + 2)
Multiply.
( )
82. (3a 7)(2a 4)
3 r 5 (12r 2)
83. _
4
84. (-3xy 3)(2x 2z)(yz 4)
85. (4kl 3m)(-2k 2m 2)
86. (-6c 2e)(-2de 2)
87. 3jk 2(2j 2 + k)
88. 4q 3r 2 (2qr 2 + 3q)
89. -2c 3 (c 3 + 3c - 2)
90. 3xy 2(2x 2y - 3y)
91. (x - 3)(x + 1)
92. (x - 2)(x - 3)
93. (x - 4)(x - 4)
94. (2x 2 - 3y)(3x - y 2)
95. (x 2 + 2xy)(3x 2y - 2)
96. (x 2 - 3x)(2xy - 3y)
97. (x - 2)(x 2 + 3x - 4)
98. (2x - 1)(-2x 2 - 3x + 4) 99. (x + 3)(2x 4 - 3x 2 - 5)
100. (2a + 3)(a 2 + 2ab - b)
101. (3a + b)(2a 2 + ab - 2b 2) 102. (a 2 - b)(3a 2 - 2ab + 3b 2)
Lesson
Multiply.
7-8
103. (x + 3) 2
104. (3 + 2x) 2
105. (4x + 2y)2
106. (3x - 2)2
107. (5 - 2x) 2
108. (3x - 5y)2
109. (3 + x)(3 - x)
110. (x - 5)(x + 5)
111. (2x + 1)(2x - 1)
112. (x 2 + 4)(x 2 - 4)
113. (2 + 3x 3)(2 - 3x 3)
114. (4x 3 - 3y)(4x 3 + 3y)
TEKS
TAKS Practice
S17
Chapter 8
Lesson
8-1
Skills Practice
Write the prime factorization of each number.
1. 24
2. 78
3. 88
4. 63
5. 128
6. 102
7. 71
8. 125
Find the GCF of each pair of numbers.
9. 18 and 66
10. 24 and 104
11. 30 and 75
12. 24 and 120
13. 36 and 99
14. 42 and 72
Find the GCF of each pair of monomials.
15. 4a 3 and 9a 4
16. 6q 2 and 15q 5
17. 6x 2 and 14y 3
18. 4z 2 and 10z 5
19. 5g 3 and 9g
20. 12x 2 and 21y 2
Lesson
Factor each polynomial. Check your answer.
8-2
21. 6b 2 - 15b 3
22. 11t 4 - 9t 3
23. 10v 3 - 25v
24. 12r + 16r 3
25. 17a 4 - 35a 2
26. 9f + 18f 5 + 12f 2
27. 3(a + 3) + 4a(a + 3)
28. 5(k - 4) - 2k (k - 4)
29. 5(c - 3) + 4c 2(c - 3)
30. 3(t - 4) + t (t - 4)
31. 5(2r - 1) - s(2r - 1)
32. 7(3d + 4) - 2e(3d + 4)
Factor each expression.
Factor each polynomial by grouping. Check your answer.
33. x 3 + 3x 2 - 2x - 6
34. 2m 3 - 3m 2 + 8m - 12
35. 3k 3 - k 2 + 15k - 5
36. 15r 3 + 25r 2 - 6r - 10
37. 12n 3 - 6n 2 - 10n + 5
38. 4z 3 - 3z 2 + 4z - 3
39. 2k 2 - 3k + 12 - 8k
40. 3p 2 - 2p + 8 - 12p
41. 10d 2 - 6d + 9 - 15d
42. 6a 3 - 4a 2 + 10 - 15a
43. 12s 3 - 2s 2 + 3 - 18s
44. 4c 3 - 3c 2 + 15 - 20c
Lesson
Factor each trinomial. Check your answer.
8-3
45. x 2 + 15x + 36
46. x 2 + 13x + 40
47. x 2 + 10x + 16
48. x 2 - 9x + 18
49. x 2 - 11x + 28
50. x 2 - 13x + 42
51. x 2 + 4x - 21
52. x 2 - 5x - 36
53. x 2 - 7x - 30
54. Factor c 2 - 2c - 48. Show that the original polynomial and the factored form
describe the same sequence of values for c = 0, 1, 2, 3, and 4.
Complete the table.
S18
TEKS
x 2 + bx + c
Sign of c
Binomial factors
Sign of Numbers
in Binomials
x 2 + 9x + 20
Positive
(x + 4)(x + 5)
Both positive
55.
x - x - 20
?
(x + ?)(x + ?)
?
56.
x - 2x - 8
?
(x + ?)(x + ?)
?
57.
x - 6x + 8
?
(x + ?)(x + ?)
?
2
2
2
TAKS Practice
Chapter 8
Skills Practice
Lesson
Factor each trinomial. Check your answer.
8-4
58. 2x 2 + 13x + 15
59. 3x 2 + 14x + 16
60. 8x 2 - 16x + 6
61. 6x 2 + 11x + 4
62. 3x 2 - 11x + 6
63. 10x 2 - 31x + 15
64. 6x 2 - 5x - 4
65. 8x 2 - 14x - 15
66. 4x 2 - 11x + 6
67. 12x 2 - 13x + 3
68. 6x 2 - 7x - 10
69. 6x 2 + 7x - 3
70. 2x 2 + 5x - 12
71. 6x 2 - 5x - 6
72. 8x 2 + 10x - 3
73. 10x 2 - 11x - 6
74. 4x 2 - x - 5
75. 6x 2 - 7x - 20
76. -2x 2 + 11x - 5
77. -6x 2 - x + 12
78. -8x 2 - 10x - 3
79. -4x 2 + 16x - 15
80. -10x 2 + 21x + 10
81. -3x 2 + 13x - 14
Lesson
8-5
Determine whether each trinomial is a perfect square. If so, factor. If not,
explain why.
82. x 2 - 8x + 16
83. 4x 2 - 4x + 1
84. x 2 - 8x + 9
85. 9x 2 - 14x + 4
86. 4x 2 + 12x + 9
87. x 2 + 8x - 16
88. 9x 2 - 42x + 49
89. 4x 2 + 18x + 25
90. 16x 2 - 24x + 9
Determine whether each trinomial is the difference of two squares. If so, factor. If
not, explain why.
91. 4 - 16x 4
92. -t 2 - 35
93. c 2 - 25
94. g 5 - 9
95. v 4 - 64
96. x 2 - 120
97. x 2 - 36
98. 9m 2 - 15
99. 25c 2 - 16
Find the missing term in each perfect-square trinomial.
100. 4x 2 - 20x +
101. 9x 2 +
103. 9b 2 -
104.
+ 25
+1
+ 28a + 49
102.
- 56x + 49
105. 4a 2 + 4a +
Lesson
Tell whether each polynomial is completely factored. If not, factor.
8-6
106. 5(16x 2 + 4)
107. 3r (4x 2 - 9)
108. (9d - 6)(2d - 7)
109. (5 - h)(6 - 5h)
110. 12y 2 - 2y - 24
111. 3f (2f 2 + 5fg + 2g 2)
Factor each polynomial completely. Check your answer.
112. 12b 3 - 48b
113. 24w 4 - 20w 3 - 16w 2
114. 18k 3 - 32k
115. 4a 3 + 12a 2 - a 2b - 3ab 116. 3x 3y - 6x 2y 2 + 3xy 3
117. 36p 2q - 64q 3
118. 32a 4 - 8a 2
119. m 3 + 5m 2n + 6mn 2
120. 4x 2 - 3x 2 - 16x + 48x
121. 18d 2 + 3d - 6
122. 2r 2 - 9r - 18
123. 8y 2 + 4y - 4
124. 81 - 36u 2
125. 8x 4 + 12x 2 - 20
126. 10j 3 + 15j 2 - 70j
127. 27z 3 - 18z 2 + 3z
128. 4b 2 + 2b - 72
129. 3f 2 - 3g 2
TEKS
TAKS Practice
S19
Chapter 9
Lesson
9-1
Skills Practice
Tell whether each function is quadratic. Explain.
1. y + 4x 2 = 2x - 3
2. 4x - y = 3
4.
5.
x
-6
-4
-2
-0
2
y
-5
-6
-4
2
11
3. 3x 2 - 4 = y + x
x
0
1
2
3
4
y
-5
-5
-3
1
7
Tell whether the graph of each quadratic function opens upward or downward.
Then use a table of values to graph each function.
2 x2
6. y = -3x 2
7. y = _
8. y = x 2 + 2
9. y = -4x 2 + 2x
3
Identify the vertex of each parabola. Then find the domain and range.
10.
11.
Y
12.
Y
X
X
Y
X
Lesson
9-2
Find the zeros of each quadratic function and the axis of symmetry of each
parabola from the graph.
13.
14.
Y
15.
Y
Y
X
X
X
Lesson
9-3
For each quadratic function, find the vertex of its graph.
16. y = 3x 2 - 6x + 2
17. y = -2x 2 + 8x - 3
18. y = x 2 + 2x - 4
Graph each quadratic function.
19. y = x 2 - 4x + 1
20. y = -x 2 - x + 4
21. y = 3x 2 - 3x + 1
22. y - 2 = 2x 2
24. y - 4 = x 2 + 2x
23. y + 3x 2 = 3x - 1
Lesson
Order the functions from narrowest to widest.
9-4
25. f (x) = 2x 2, g(x) = -4x 2, h(x) = -x 2
1 x 2, h(x) = -2x 2
26. f (x) = 3x 2, g(x) = _
2
1 x2
27. f (x) = 4x 2, g(x) = x 2, h(x) = - _
28. f (x) = 2x 2, g(x) = 5x 2, h(x) = -3x 2
4
Compare the graph of each function with the graph of f (x) = x 2.
1 x2
29. g(x) = 2x 2 - 2
30. g(x) = - _
31. g(x) = -3x 2 + 1
2
S20
TEKS
TAKS Practice
Chapter 9
Lesson
9-5
Lesson
9-6
Skills Practice
Solve each quadratic equation by graphing the related function.
32. x 2 - x - 2 = 0
33. x 2 - 2x + 8 = 0
34. 2x 2 + 4x - 6 = 0
35. 2x 2 + 9x = -4
36. 2x 2 + 3 = 0
37. 2x 2 - 2x - 12 = 0
38. 3x 2 = -3x + 6
39. x 2 = 4
40. 2x 2 + 6x - 20 = 0
41. -3x 2 - 2 = 0
42. x 2 = -2x + 8
43. x 2 - 2x = 15
Use the Zero Product Property to solve each equation. Check your answer.
44. (x + 3)(x - 2) = 0
45. (x - 4)(x + 2) = 0
46. (x)(x - 4) = 0
47. (2x + 6)(x - 2) = 0
48. (3x - 1)(x + 3) = 0
49. (x)(2x - 4) = 0
Solve each quadratic equation by factoring. Check your answer.
50. x 2 + 5x + 6 = 0
51. x 2 - 3x - 4 = 0
52. x 2 + x - 12 = 0
Lesson
9-7
Lesson
9-8
Lesson
9-9
53. x 2 + x - 6 = 0
54. x 2 - 6x + 5 = 0
55. x 2 + 4x - 12 = 0
56. x 2 = 6x - 9
57. 2x 2 + 4x = 6
58. x 2 + 2x = -1
59. 3x 2 = 3x + 6
60. x 2 = x + 12
61. 4x 2 + 8x + 4 = 0
Solve using square roots. Check your answer.
62. x 2 = 169
63. x 2 = 121
64. x 2 = 289
65. x 2 = -64
66. x 2 = 81
67. x 2 = -441
68. 4x 2 - 196 = 0
69. 0 = 3x 2 - 48
70. 24x 2 + 96 = 0
71. 10x 2 - 75 = 15
72. 0 = 4x 2 + 144
73. 5x 2 - 105 = 20
Solve. Round to the nearest hundredth.
74. 4x 2 = 160
75. 0 = 3x 2 - 66
76. 250 - 5x 2 = 0
77. 0 = 9x 2 - 72
79. 6x 2 = 78
78. 48 - 2x 2 = 42
Complete the square to form a perfect square trinomial.
80. x 2 - 8x +
81. x 2 + x +
82. x 2 + 10x +
83. x 2 - 5x +
85. x 2 - 7x +
84. x 2 + 6x +
Solve by completing the square.
86. x 2 + 6x = 91
87. x 2 + 10x = -16
88. x 2 - 4x = 12
89. x 2 - 8x = -12
90. x 2 - 12x = -35
91. -x 2 - 6x = 5
92. -x 2 - 4x + 77 = 0
93. -x 2 = 10x + 9
94. -x 2 + 63 = -2x
Solve using the quadratic formula.
95. x 2 + 3x - 4 = 0
96. x 2 - 2x - 8 = 0
98. x 2 - x - 10 = 0
99. 2x 2 - x - 4 = 0
97. x 2 + 2x - 3 = 0
100. 2x 2 + 3x - 3 = 0
Find the number of solutions of each equation using the discriminant.
101. x 2 + 4x + 1 = 0
102. 2x 2 - 3x + 2 = 0
103. x 2 - 5x + 2 = 0
104. 2x 2 - 4x + 2 = 0
105. x 2 + 2x - 5 = 0
106. 2x 2 - 2x - 3 = 0
TEKS
TAKS Practice
S21
Use the circle graph for Exercises 5–7.
5. Which candidate received the fewest votes?
äÈ
äx
Óä
6œÌˆ˜}ʜÀÊ-ÌÕ`i˜Ì‡œ`ÞÊ*ÀiÈ`i˜Ì
7. A total of 400 students voted in the election.
How many votes did Velez receive?
10-2
ä{
9i>À
6. Which two candidates received approximately
the same number of votes?
Lesson
Óä
Óä
ä£
4. Estimate the amount by which the population
decreased from 2005 to 2006.
äÎ
3. During which one-year period did the
population increase by the greatest amount?
Óä
£x
£ä
x
ä
Óä
2. Estimate the population in 2005.
*œ«Õ>̈œ˜Êœvʈ`ۈi
äÓ
10-1
Use the line graph for Exercises 1–4.
1. In what year was the population the greatest?
Óä
Lesson
Skills Practice
Óä
Chapter 10
The daily high temperatures in degrees Celsius
during a two-week period in Madison, Wisconsin,
are given at right.
8. Use the data to make a stem-and-leaf plot.
9. Use the data to make a frequency table with intervals.
10. Use the frequency table from Exercise 9 to make a
histogram for the data.
>À˜iÃ
£ä¯
6iiâ
În¯
>VŽÃœ˜
Óx¯
9>˜}
Óǯ
High Temperatures (oC)
22 25 28 33 29 24 19
19
18
25
32
30
32
25
11. Use the data to make a cumulative frequency table.
Lesson
10-3
Find the mean, median, mode, and range of each data set.
12. 42, 45, 48, 45
13. 66, 68, 68, 62, 61, 68, 65, 60
14. The numbers of customers who attended a reading at a bookstore on five different
nights are 15, 23, 92, 15, 25. Use the mean, median, and mode of the data to answer
each question.
Mean = 34
Median = 23
Mode = 15
a. Which value describes the average number of customers at the readings?
b. Which value best describes the number of customers at the readings? Explain.
Use the data set to make a box-and-whisker plot.
15. 7, 8, 10, 2, 5, 1, 10, 8, 5, 5
16. 54, 64, 50, 48, 53, 55, 57
Lesson
10-4
17. The graph shows the ages of people who listen to a radio program.
a. Explain why the graph is misleading.
}iÃʜvÊ,>`ˆœÊ*Àœ}À>“ʈÃÌi˜iÀÃ
b. What might someone believe because of the
graph?
ÓxÊ̜ÊÎÈ
c. Who might want to use this graph?
18. A researcher surveys people at the Elmwood
library about the number of hours they spend
reading each day. Explain why the following
statement is misleading: “People in Elmwood
read for an average of 1.5 hours per day.”
S22
TEKS
TAKS Practice
Îä¯
1˜`iÀÊ£n
£x¯
£nÊ̜ÊÓ{
£x¯
Chapter 10
Lesson
10-5
Skills Practice
19. Identify the sample space and the outcome shown for the spinner at right.
Write impossible, unlikely, as likely as not, likely, or certain to describe
each event.
20. Two people sitting next to each other on a bus have the same birthday.
21. Dylan rolls a number greater than 1 on a standard number cube.
An experiment consists of randomly choosing a fruit snack from
a box. Use the results in the table to find the experimental
probability of each event.
22. choosing a blueberry fruit snack.
Cherry
8
Peach
6
23. choosing a cherry fruit snack
Blueberry
6
Outcome
Frequency
24. not choosing a cherry fruit snack
Lesson
10-6
Find the theoretical probability of each outcome.
25. rolling an even number on a number cube
26. flipping two coins and both landing tails up
27. randomly choosing a prime number from a bag that contains ten slips of paper
numbered 1 through 10
28. The probability of choosing a green marble from a bag is __37 . What is the probability of
not choosing a green marble?
29. The odds against winning a game are 8 : 3. What is the probability of winning the game?
Lesson
10-7
Tell whether each set of events is independent or dependent. Explain your answer.
30. You pick a bottle of orange juice from a basket containing chilled drinks, and then
your friend chooses a bottle of apple juice.
31. You roll a 6 on a number cube and a coin lands heads up.
32. A number cube is rolled three times. What is the probability of rolling three numbers
greater than 4?
33. An experiment consists of randomly selecting a marble from a bag, replacing it, and
then selecting another marble. The bag contains 3 blue marbles, 2 orange marbles,
and 5 yellow marbles. What is the probability of selecting a blue marble and then a
yellow marble?
34. Madeleine has 3 nickels and 5 quarters in her pocket. She randomly chooses one
coin and does not replace it. Then she randomly chooses another coin. What is the
probability that she chooses two quarters?
Lesson
10-8
Tell whether each situation involves combinations or permutations. Then give the
number of possible outcomes.
35. How many different ways can three photographs be arranged in a row on a wall?
36. How many different smoothies can be made by blending two of the following fruits:
oranges, bananas, strawberries, and peaches?
37. There are 6 entrants in a livestock competition at a county fair. How many different
ways can the first-place, second-place, and third-place ribbons be awarded?
38. An amusement park has 7 roller coasters. How many different ways can Jacinto
choose 4 different roller coasters to ride?
TEKS
TAKS Practice
S23
Chapter 11
Lesson
11-1
Skills Practice
Find the next three terms in each geometric sequence.
1. 1, 5, 25, 125 …
2. 736, 368, 184, 92, …
3. -2, 6, -18, 54, …
1
1
1, _
1 , 1, 3, …
_
_
4. 8, 2, , , …
5. 7, -14, 28, -56, …
6. _
2 8
9 3
7. The first term of a geometric sequence is 2, and the common ratio is 3. What is the
8th term of the sequence?
8. What is the 8th term of the sequence 600, 300, 150, 75, …?
Lesson
11-2
Tell whether each set of ordered pairs satisfies an exponential function. Explain
your answer.
⎧
⎧
1 , 0, 2 , 1, 8 , 2, 32 ⎫⎬
1 , 0, 0 , 1, _
1 , 2, 4 ⎫⎬
9. ⎨ -1, _
10. ⎨ -1, - _
)
( ) ( ) (
( )
( )
2
2
2
⎩
⎭
⎩
⎭
(
(
)
( )(
)
⎧
1 , 2, _
1 ⎫⎬
11. ⎨(-1, 4), (0, 1), 1, _
4
16 ⎭
⎩
⎧
⎫
12. ⎨(0, 0), (1, 3), (2, 12), (3, 27)⎬
⎩
⎭
Graph each exponential function.
x
1 (4)x
13. y = 3(2)
14. y = _
2
x
x
1
1
_
16. y = - (2)
17. y = 5 _
2
2
()
Lesson
11-3
( )
)
15. y = -3 x
18. y = -2(0.25)
x
Write an exponential growth function to model each situation. Then find the value
of the function after the given amount of time.
19. The rent for an apartment is $6600 per year and increasing at a rate of 4% per year;
5 years.
20. A museum has 1200 members and the number of members is increasing at a rate of
2% per year; 8 years.
Write a compound interest function to model each situation. Then find the balance
after the given number of years.
21. $4000 invested at a rate of 4% compounded quarterly; 3 years
22. $5200 invested at a rate of 2.5% compounded annually; 6 years
Write an exponential decay function to model each situation. Then find the value of
the function after the given amount of time.
23. The cost of a stereo system is $800 and is decreasing at a rate of 6% per year; 5 years.
24. The population of a town is 14,000 and is decreasing at a rate of 2% per year; 10 years.
Lesson
11-4
S24
TEKS
Graph each data set. Which kind of model best describes the data?
⎧
⎫
25. ⎨(0, 3), (1, 0), (2, -1), (3, 0), (4, 3)⎬
⎭
⎧⎩
⎫
26. ⎨(-4, -4), (-3, -3.5), (-2, -3), (-1, -2.5), (0, -2), (1, -1.5)⎬
⎩⎧
⎭
⎫
27. ⎨(0, 4), (1, 2), (2, 1), (3, 0.5), (4, 0.25)⎬
⎩
⎭
Look for a pattern in each data set to determine which kind of model best describes
the data.
⎧
⎫
28. ⎨(-1, -5), (0, -5), (1, -3), (2, 1), (3, 7)⎬
⎧⎩
⎫ ⎭
29. ⎨(0, 0.25), (1, 0.5), (2, 1), (3, 2), (4, 4)⎬
⎩⎧
⎭ ⎫
30. ⎨(-2, 11), (-1, 8), (0, 5), (1, 2), (2, -1)⎬
⎩
⎭
TAKS Practice
Chapter 11
Lesson
11-5
Skills Practice
Find the domain of each square-root function.
31. y = √
x+1
32. y = √
x-2+4
x
34. y = √
3x - 6
35. y = 1 + _
3
Graph each square-root function.
37. y = √
x+2
38. y = √
x-3
√
40. y = - √
x
Lesson
Simplify each expression.
11-6
43.
46.
128
√_
2
3
_
√ 48
33. y = √
4+x
36. y = √
4x - 1
39. y = √
3x + 1
41. y = 2 √
x+1
42. y = 3 √
x-2
2
+ 24 2
44. √7
45.
47.
y 2 + 4y + 4
√
(4 - x)2
√
48. √
52 - 42
Simplify. All variables represent nonnegative numbers.
72
49. √
50.
75x 4y 3
√
51.
64
√_
x
53.
16a
_
√
25b
54.
52.
Lesson
11-7
Lesson
11-8
6
4
2
11
_
√
81
18x
_
√
49x
4
3
Add or subtract.
+ 3 √7
55. 5 √7
56. 6 √
2 + √
2
57. 5 √
3 - 2 √3
- 9 √
58. √
5 + 7 √5
5
59. 2 √
y + 4 √
y - 3 √
y
- 3 √
60. 5 √
3 + 4 √2
3
Simplify each expression.
61. √
75 + √
27
62. √
45 - √
20
63. 2 √
12 + √
18
64. 3 √
27x + √
48x
65. 5 √
20y - 2 √
80y
66. √
28a + 2 √
63a - √
175a
67. √
50y - 2 √
18y + 3 √
8y
68. √
12x - √
27x - √
5x
69. 5 √
180s - 6 √
80s
Multiply. Write each product in simplest form.
70. √
5 √
10
71. √
6 √
12
73. (2 √
7)
2
( √
76. 2 √5
20 + 3)
)(8 - √
79. (3 + √5
5)
74. √
6x √
15x
77. √
2x (3 + √
8x )
80. (4 + √
2)
2
72. (3 √
3)
2
)
75. √
3 (2 + √27
78. (4 + √
3 )(1 - √
3)
81. (5 - √
3)
2
Simplify each quotient.
√
5
82. _
√
3
√
5
7
85. _
√
50
Lesson
11-9
2 √
7
83. _
√
5
√
12a
86. _
√
32
Solve each equation. Check your answer.
88. √
x = 11
89. √
3x = 9
√
3
84. _
√
20
√
200x
87. _
√
28
90. √
-2x = 10
91. 5 = √
-4x
92.
94. √
3x + 1 = 4
95. √
2x + 5 = 3
96. √
x-4+1=7
97. √
6 - 3x - 2 = 4
98. √
6 - x - 5 = -3
99. 4 √
x = 20
√
x
+ 5 = 12
93.
√
x
-4=1
TEKS
TAKS Practice
S25
Chapter 12
Lesson
12-1
Skills Practice
Tell whether each relationship is an inverse variation. Explain.
1.
x
y
4
2.
x
y
8
2
8
16
16
32
3.
x
y
6
-1
24
3
4
2
-12
32
6
2
4
-6
64
12
1
8
-3
4. 3xy = 10
5. y - x = 6
6. 6xy = -1
7. Write and graph the inverse variation in which y = 4 when x = 3.
1 when x = 6.
8. Write and graph the inverse variation in which y = _
2
9. Let x 1 = 6, y 1 = 8, and x 2 = 12. Let y vary inversely as x. Find y 2.
10. Let x 1 = -4, y 1 = -2, and y 2 = 16. Let y vary inversely as x. Find x 2.
Lesson
12-2
Identify the excluded values for each rational function.
16
11. y = _
x
3
13. y = - _
x+5
20
14. y = _
x + 20
8
16. y = _
x+5
7
17. y = _
-6
3x - 2
3
18. y = _
+4
2x - 2
1
19. y = _
x+3
1
20. y = _
x-2
1 +4
21. y = _
x
3
22. y = _
x-2
1 +2
23. y = _
x-3
1 -6
24. y = _
x-5
1 +5
25. y = _
x+2
1 +1
26. y = _
x+5
1
12. y = _
x-1
Identify the asymptotes.
2
15. y = _
x-4
Graph each function.
Lesson
Find the excluded value(s) of each rational expression.
12-3
3
27. _
7x
-2
28. _
x2 - x
6
29. __
x 2 + x - 12
p+1
30. __
2
p + 4p - 5
Simplify each rational expression, if possible. Identify excluded values.
4m 2
31. _
12m
7x 5
32. _
28x
4x 2 - 8x
33. _
x-2
2y
34. _
y-1
5x 3 + 20x 2
35. _
x+4
a+1
36. _
a-2
3y 3 + 3y
37. _
y2 + 1
x 3 + 4x
38. _
x2 + 4
Simply each rational expression, if possible.
S26
TEKS
b+2
39. __
b 2 + 5b + 6
x-3
40. __
x 2 - 6x + 9
y 2 - 4y - 5
41. __
y 2 - 2y - 3
(m + 2)2
42. __
m 2 - 6m - 16
x2 - 9
43. __
2
x + x - 12
2-m
44. _
3m 2 - 6m
x-4
45. _
12x 2 - 3x 3
6 - 3x
46. __
x 2 - 6x + 8
TAKS Practice
Chapter 12
Skills Practice
Lesson
Multiply. Simplify your answer.
12-4
ab
4a 3 · _
47. _
3
b
6a 2
2x - 10
x-2 ·_
50. _
x-5
3
1 (x 2 - 2x - 8)
53. _
2x + 4
4r 3 + 8r _
· 2r
56. _
r3
3r + 6
4b 2 + 4 b 2 - 1
59. _ · _
b-1
8b 2 + 8
6x 3y _
8x 2yz 2
48. _
·
4y 4
3xz 5
x-3 ·_
8
49. _
2
4x - 12
9b 2
a 2b 3 · _
51. _
6a 3c 12b 5c 2
3x (x 2 + x - 30)
54. _
4x - 20
3x + 6
3x · _
52. _
2x + 4
9
2y
55. _ (y 2 + 10y + 25)
3y + 15
x2 + x
x-3
57. _
·_
2
x - x - 6 6x 2 + 6x
pq + 2q
3pq + 3
60. _ · _
pq + 1 pq 2 + 2q 2
a 2 - 3a - 10 · __
a 2 - 2a - 3
58. __
2
a-5
a -a-6
x 2 + 4x + 3 ( 2
63. __
÷ x - 1)
3x 3 + 9x 2
p 2 - 2p
p-1
__
÷
64. __
p 2 + 4p - 5
p 2 + 3p - 10
x2 + 1
1 - 3x
66. _ + _
x-1
x-1
2x
2x 2
+ __
67. __
2
x - 2x - 3 x 2 - 2x - 3
r 2 + 3r + 2
2r + 6
61. _ · _
4r + 4
r 2 - 2r - 8
Divide. Simplify your answer.
6y 4
3x 2y 3 _
÷
62. _
x 2z 5
x 3z 2
Lesson
Add. Simplify your answer.
12-5
5x
3x + _
65. _
4x 3 4x 3
Subtract. Simplify your answer.
5 -_
2
68. _
6y 4 6y 4
Lesson
12-6
15a + 1
m 2 + 2m _
m + 12
5a 2 + 1
69. _
-_
70. _
- 2
2
2
a -a-6
a -a-6
m2 - 9
m -9
Find the LCM of the given expressions.
71. 8x 5y 8, 6x 4y 9
72. x 2 - 4, x 2 + 7x + 10
73. d 2 - 2d - 3, d 2 + d - 12
Add or subtract. Simplify your answer.
3
5
5 -_
1
75. _
+_
74. _
y 2 4y 2
x2 - x - 6 x + 2
3x - _
x
76. _
x-2 2-x
Divide.
77. (12y 5 - 16y 2 + 4y) ÷ 4y 2 78. (6m 4 - 18m + 3) ÷ 6m 2 79. (16x 4 + 20x 3 - 4x) ÷ -4x 3
b 2 - 4b - 5
80. __
b+1
2x 2 + 9x + 4
81. __
x+4
Divide using long division.
83. (a 2 - 5a - 6) ÷ (a + 1)
84. (2x 2 + 10x + 8) ÷ (x + 4) 85. (3y 2 - 11y + 10) ÷ (y - 2)
6a 2 - 13a - 5
82. __
3a + 1
86. (3x 2 - 2x - 7) ÷ (x - 2) 87. (2x 2 + 2x - 9) ÷ (x + 3) 88. (5x 3 + 2x 2 - 4) ÷ (x - 2)
Lesson
12-7
Solve. Check your answer.
5 =_
10
4
4 =_
89. _
90. _
t
x+1 x-1
t+9
8
3
4 =_
1
92. _
93. _
=_
y
a-2 a+1
2y + 4
x
3
3
1
1
2
96. _ + _ = _
95. _ + _ = - _2
x
2 2m
2 2
m
Solve. Identify any extraneous solutions.
x+2
3 =_
x-5
2=_
98. _
99. _
x
x+4
x+4
x2 - 4
8
6
_
91. _
m = m+1
5
6
94. _
=_
4w - 2 5w - 2
3 _
10
97. 1 - _
a = a2
4x - 7 = _
16
100. _
x-4
x-4
TEKS
TAKS Practice
S27
TEKS
Chapter 1
TAKS Practice
Applications Practice
Biology Use the following information for
Exercises 1 and 2.
In general, every cell in the human body contains
46 chromosomes. (Lesson 1-1)
1. Write an expression for the number of
chromosomes in c cells.
2. Find the number of chromosomes in 8, 15, and
50 cells.
3. On a winter day in Fairbanks, Alaska, the
temperature dropped from 12°F to -16°F.
How many degrees did the temperature
drop? (Lesson 1-2)
4. Geography The elevation of the Dead Sea in
Jordan is -411 meters. The greatest elevation
on Earth is Mt. Everest, at 8850 meters. What is
the difference in elevation between these two
locations? (Lesson 1-2)
5. Jeremy is raising money for his school
by selling magazine subscriptions. Each
subscription costs $16.75. During the first
week, he sells 12 subscriptions. How much
money does he raise? (Lesson 1-3)
6. As a service charge, Nadine’s checking account
is adjusted by -$3 each month. What is the
total amount of the adjustment over the
course of one year? (Lesson 1-3)
7. To go from one figure to the next in the
sequence of figures, each square is split into
four smaller squares. How many squares will
be in Figure 5? (Lesson 1-4)
10. An art museum exhibits a square painting
that has an area of 75 square feet. Find its side
length to the nearest tenth. (Lesson 1-5)
11. Travel The base of the Washington
Monument in Washington, D.C., is a square
with an area of 336 yards. Find the length
of one side of the monument’s base to the
nearest tenth. (Lesson 1-5)
12. The toll to cross a bridge is $2 for cars, $5 for
trucks, and $10 for buses. The total amount
of money collected can be found using the
expression 2C + 5T + 10B. Use the table to
find the total amount of money collected
between 10 A.M. and 11 A.M. (Lesson 1-6)
Bridge Tolls, 10 A.M. to 11 A.M.
Type of Vehicle
Car C
Truck T
Bus B
Number
104
20
3
13. The expression __59 (F - 32) converts a
temperature F in degrees Fahrenheit to a
temperature in degrees Celsius. Convert 77°F
to degrees Celsius. (Lesson 1-6)
Use the following information for Exercises 14
and 15.
An airplane has 12 rows of seats in first class and
35 rows of seats in coach. Each row has the same
number of seats. (Lesson 1-7)
14. The total number of seats in the plane is
12x + 35x, where x is the number of seats in a
row. Simplify the expression.
ˆ}ÕÀiÊä
S28
ˆ}ÕÀiÊ£
ˆ}ÕÀiÊÓ
15. Find the total number of seats in a plane that
has 6 seats per row.
8. When you fold a sheet of paper in half and
then open it, the crease creates 2 regions.
Folding the paper in half 2 times creates 4
regions. How many regions do you create
when you fold a sheet of paper in half 5
times? (Lesson 1-4)
Use the following information for Exercises 16
and 17.
A sales representative earns $680 per week plus a
$40 commission for each sale. (Lesson 1-8)
9. Dan began his stamp collection with just 5
stamps in the first year. Every year thereafter,
his collection grew 5 times as large as the
year before. How many stamps were in Dan’s
collection after 4 years? (Lesson 1-4)
17. Write ordered pairs for the amount the sales
representative earns for 5, 8, and 10 sales.
TEKS
TAKS Practice
16. Write a rule for the sales representative’s
weekly earnings.
Chapter 2
Applications Practice
1. Economics In 2004, the average price of an
ounce of gold was $47 more than the average
price in 2003. The 2004 price was $410. Write
and solve an equation to find the average price
of an ounce of gold in 2003. (Lesson 2-1)
2. During a renovation, 36 seats were removed
from a theater. The theater now seats 580
people. Write and solve an equation to find
the number of seats in the theater before the
renovation. (Lesson 2-1)
10. A cheetah can reach speeds of up to
103 feet per second. What is the cheetah’s
speed in miles per hour? Round to the nearest
tenth. (Lesson 2-6)
11. Write and solve a proportion to find the height
of the flagpole. (Lesson 2-7)
3. A case of juice drinks contains 12 bottles and
costs $18. Write and solve an equation to find
the cost of each drink. (Lesson 2-2)
4. Astronomy Objects weigh about 3 times
as much on Earth as they do on Mars. A
rock weighs 42 kg on Mars. Write and solve
an equation to find the rock’s weight on
Earth. (Lesson 2-2)
¶
x°{ÊvÌ
n°£ÊvÌ
ÓÇÊvÌ
5. The county fair’s admission fee is $8 and each
ride costs $2.50. Sonia spent a total of $25.50.
How many rides did she go on? (Lesson 2-3)
12. Paul has 8 jazz CDs. The jazz CDs are 5%
of his collection. How many CDs does Paul
have? (Lesson 2-8)
6. At the beginning of a block party, the
temperature was 84°. During the party, the
temperature dropped 3° every hour. At the end
of the party, the temperature was 66°. How
long was the party? (Lesson 2-3)
13. Sports During the 2004 season, the Texas
Rangers baseball team had 32 players on their
active roster, 3 of whom were catchers. To the
nearest percent, what percent of the players
were catchers? (Lesson 2-8)
7. Consumer Economics A health insurance
policy costs $700 per year, plus a $15 payment
for each visit to the doctor’s office. A different
plan costs $560 per year, but each office
visit is $50. Find the number of office visits
for which the two plans have the same total
cost. (Lesson 2-4)
14. Miguel earns an annual salary of $38,000 plus
a 3.5% commission on sales. His sales for one
year were $90,000. Find his total salary for the
year. (Lesson 2-9)
8. Geometry The formula A = __12 bh gives the
area A of a triangle with base b and height
h. (Lesson 2-5)
a. Solve A = __12 bh for h.
b. Find the height of a triangle with an area of
30 square feet and a base of 6 feet.
9. The ratio of students to adults on a school
camping trip is 9 : 2. There are 6 adults on the
trip. How many students are there?
(Lesson 2-6)
15. How long would it take $3600 to earn simple
interest of $450 at an annual interest rate of
5%? (Lesson 2-9)
16. At the end of summer, a store offers swimsuits
at a 30% discount. What is the final price of a
swimsuit that originally sold for $28?
(Lesson 2-10)
17. Mei sells strawberry jam at a farmer’s market
for $4.20 per jar. Each jar costs Mei $3 to make.
What is the markup as a percent?
(Lesson 2-10)
TEKS
TAKS Practice
S29
Chapter 3
Applications Practice
1. At a food-processing factory, each box of
cereal must weigh at least 15 ounces. Define
a variable and write an inequality for the
acceptable weights of the cereal boxes. Graph
the solutions. (Lesson 3-1)
8. The admission fee at an amusement park is
$12, and each ride costs $3.50. The park also
offers an all-day pass with unlimited rides for
$33. For what numbers of rides is it cheaper to
buy the all-day pass? (Lesson 3-4)
2. In order to qualify for a discounted entry fee at
a museum, a visitor must be less than 13 years
old. Define a variable and write an inequality
for the ages that qualify for the discounted
entry fee. Graph the solutions. (Lesson 3-1)
9. Geometry The perimeter of a rectangle with
length and width w is given by 2( + w). The
length of a rectangle is 18 inches. What must
the width of the rectangle be in order for
its perimeter to be at least 50 inches?
(Lesson 3-4)
3. A restaurant can seat no more than 102
customers at one time. There are already
96 customers in the restaurant. Write and
solve an inequality to find out how many
additional customers could be seated in the
restaurant. (Lesson 3-2)
4. Meteorology A hurricane is a tropical
storm with a wind speed of at least 74 mi/h.
A meteorologist is tracking a storm whose
current wind speed is 63 mi/h. Write and solve
an inequality to find out how much greater the
wind speed must be in order for this storm to
be considered a hurricane. (Lesson 3-2)
Hobbies Use the following information for
Exercises 5–7.
When setting up an aquarium, it is recommended
that you have no more than one inch of fish per
gallon of water. For example, in a 30-gallon tank,
the total length of the fish should be at most
30 inches. (Lesson 3-3)
Freshwater Fish
Name
Length (in.)
Red tail catfish
3.5
Blue gourami
1.5
5. Write an inequality to show the possible
numbers of blue gourami you can put in a 10gallon aquarium.
6. Find the possible numbers of blue gourami
you can put in a 10-gallon aquarium.
7. Find the possible numbers of red tail catfish
you can put in a 20-gallon aquarium.
S30
TEKS
TAKS Practice
10. The table shows the cost of Internet access at
two different cafes. For how many hours of
access is the cost at Cyber Station less than the
cost at Web World? (Lesson 3-5)
Internet Access
Cafe
Cost
Cyber
Station
$12 one-time membership fee
$1.50 per hour
Web
World
No membership fee
$2.25 per hour
11. Larissa is considering two summer jobs. A
job at the mall pays $400 per week plus $15
for every hour of overtime. A job at the movie
theater pays $360 per week plus $20 for every
hour of overtime. How many hours of overtime
would Larissa have to work in order for the
job at the movie theater to pay a higher salary
than the job at the mall? (Lesson 3-5)
12. Health For maximum safety, it is
recommended that food be stored at
a temperature between 34°F and 40°F
inclusive. Write a compound inequality
to show the temperatures that are within
the recommended range. Graph the
solutions. (Lesson 3-6)
13. Physics Color is determined by the
wavelength of light. Wavelengths are
measured in nanometers (nm). Our eyes see
the color green when light has a wavelength
between 492 nm and 577 nm inclusive.
Write a compound inequality to show the
wavelengths that produce green light. Graph
the solutions. (Lesson 3-6)
Chapter 4
Applications Practice
1. Donnell drove on the highway at a constant
speed and then slowed down as she
approached her exit. Sketch a graph to show
the speed of Donnell’s car. Tell whether the
graph is continuous or discrete. (Lesson 4-1)
7. The function y = 3.5x describes the number
of miles y that the average turtle can walk in
x hours. Graph the function. Use the graph to
estimate how many miles a turtle can walk in
4.5 hours. (Lesson 4-4)
2. Lori is buying mineral water for a party. The
bottles are available in six-packs. Sketch a
graph showing the number of bottles Lori
will have if she buys 1, 2, 3, 4, or 5 six-packs.
Tell whether the graph is continuous or
discrete. (Lesson 4-1)
8. Earth Science The Kangerdlugssuaq glacier
in Greenland is flowing into the sea at the
rate of 1.6 meters per hour. The function
y = 1.6x describes the number of meters y
that flow into the sea in x hours. Graph the
function. Use the graph to estimate the
number of meters that flow into the sea in
8 hours. (Lesson 4-4)
3. Health To exercise effectively, it is important
to know your maximum heart rate. You can
calculate your maximum heart rate in beats
per minute by subtracting your age from
220. (Lesson 4-2)
a. Express the age x and the maximum heart
rate y as a relation in table form by showing
the maximum heart rate for people who are
20, 30, 35, and 40 years old.
9. The scatter plot shows a relationship between
the number of lemonades sold in a day and
the day’s high temperature. Based on this
relationship, predict the number of lemonades
that will be sold on a day when the high
temperature is 96°F. (Lesson 4-5)
i“œ˜>`iÊ->iÃ
b. Is this relation a function? Why or why not?
Season Statistics
Wins
Home Runs
95
185
93
133
80
140
93
167
5. Michael uses 5.5 cups of flour for each loaf
of bread that he bakes. He plans to bake a
maximum of 4 loaves. Write a function rule
to describe the number of cups of flour used.
Find a reasonable domain and range for the
function. (Lesson 4-3)
6. A gym offers the following special rate. New
members pay a $425 initiation fee and then
pay $90 per year for 1, 2, or 3 years. Write
a function rule to describe the situation.
Find a reasonable domain and range for the
function. (Lesson 4-3)
nä
Õ«ÃÊ܏`
4. Sports The table shows the number of games
won by four baseball teams and the number
of home runs each team hit. Is this relation a
function? Explain. (Lesson 4-2)
Èä
{ä
Óä
ä
Óä
{ä
Èä
nä
ˆ}…ÊÌi“«iÀ>ÌÕÀiÊ­c®
10. The Elmwood Public Library has 85 Spanish
books in its collection. Each month, the
librarian plans to order 8 new Spanish books.
How many Spanish books will the library have
after 15 months? (Lesson 4-6)
11. Nikki purchases a card that she can use to ride
the bus in her town. The card costs $45, and
each time she rides the bus $1.50 is deducted
from the value of the card. How much money
will be left on the card after Nikki has taken
12 bus rides? (Lesson 4-6)
TEKS
TAKS Practice
S31
Chapter 5
Applications Practice
1. Jennifer is having prints made of her
photographs. Each print costs $1.50. The
function f (x) = 1.50x gives the total cost of
the x prints. Graph this function and give its
domain and range. (Lesson 5-1)
2. Rolando is serving on jury duty. He is paid
$40, plus $15 for each day that he serves. The
function f (x) = 15x + 40 gives Rolando’s total
pay for x days. Graph this function and give its
domain and range. (Lesson 5-1)
7. A bicycle rental costs $10 plus $1.50 per hour.
The cost as a function of the number of hours
is shown in the graph. (Lesson 5-6)
a. Write an equation that represents the cost
as a function of the number of hours.
b. Identify the slope and y-intercept and
describe their meaning.
c. Find the cost of renting a bike for 6 hours.
ˆVÞViÊ,i˜Ì>Ê
œÃÌÃ
3. The Chang family lives 400 miles from Denver.
They drive to Denver at a constant speed of 50
mi/h. The function f (x) = 400 - 50x gives their
distance in miles from Denver after x hours.
(Lesson 5-2)
œÃÌÊ­f®
Îä
Óä
£ä
a. Graph this function and find the intercepts.
ä
b. What does each intercept represent?
4. History The table shows the number of
nations in the United Nations in different
years. Find the rate of change for each time
interval. During which time interval did the
U.N. grow at the greatest rate? (Lesson 5-3)
Year
1945
1950
1960
1975
51
60
99
144
5. The graph shows the temperature of an oven
at different times. Find the slope of the line.
Then tell what the slope represents.
(Lesson 5-4)
/i“«iÀ>ÌÕÀiÊ­c®
"Ûi˜Ê/i“«iÀ>ÌÕÀi
{xä
È
8. A hot-air balloon is moving at a constant rate.
Its altitude is a linear function of time, as
shown in the table. Write an equation in
slope-intercept form that represents this
function. Then find the balloon’s altitude
after 25 minutes. (Lesson 5-7)
Time (min)
Altitude (m)
0
250
7
215
12
190
9. Geometry Show that the points A(2, 3),
B(3, 1), C (-1, -1), and D(-2, 1) are the
vertices of a rectangle. (Lesson 5-8)
­£ä]Ê{£ä®
Îxä
­{ä]Êәä®
Óxä
ä
Óä
{ä
/ˆ“iÊ­“ˆ˜®
6. Sports Competitive race-walkers move at
a speed of about 9 miles per hour. Write a
direct variation equation for the distance y
that a race-walker will cover in x hours. Then
graph. (Lesson 5-5)
TEKS
{
/ˆ“iÊ­…®
Balloon’s Altitude
Number of
Nations
S32
Ó
TAKS Practice
10. A phone plan for international calls costs
$12.50 per month plus $0.04 per minute. The
monthly cost for x minutes of calls is given by
the function f (x) = 0.04x + 12.50. How will the
graph change if the phone company raises the
monthly fee to $14.50? if the cost per minute is
raised to $0.05? (Lesson 5-9)
Chapter 6
Applications Practice
1. Net Sounds, an online music store, charges $12
per CD plus $3 for shipping and handling. Web
Discs charges $10 per CD plus $9 for shipping
and handling. For how many CDs will the cost
be the same? What will that cost be?
(Lesson 6-1)
2. At Rocco’s Restaurant, a large pizza costs $12
plus $1.25 for each additional topping. At
Pizza Palace, a large pizza costs $15 plus $0.75
for each additional topping. For how many
toppings will the cost be the same? What will
that cost be? (Lesson 6-1)
Use the following information for Exercises 3
and 4.
The coach of a baseball team is deciding between
two companies that manufacture team jerseys.
One company charges a $60 setup fee and $25 per
jersey. The other company charges a $200 setup fee
and $15 per jersey. (Lesson 6-2)
3. For how many jerseys will the cost at the two
companies be the same? What will that cost be?
4. The coach is planning to purchase 20 jerseys.
Which company is the better option? Why?
5. Geometry The length of a rectangle is
5 inches greater than the width. The sum of
the length and width is 41 inches. Find the
length and width of the rectangle. (Lesson 6-2)
6. At a movie theater, tickets cost $9.50 for
adults and $6.50 for children. A group of
7 moviegoers pays a total of $54.50. How many
adults and how many children are in the
group? (Lesson 6-3)
7. Business A grocer is buying large quantities
of fruit to resell at his store. He purchases
apples at $0.50 per pound and pears at $0.75
per pound. The grocer spends a total of $17.25
for 27 pounds of fruit. How many pounds of
each fruit does he buy? (Lesson 6-3)
8. Bricks are available in two sizes. Large bricks
weigh 9 pounds, and small bricks weigh 4.5
pounds. A bricklayer has 14 bricks that weigh a
total of 90 pounds. How many of each type of
brick are there? (Lesson 6-3)
9. Sports The table shows the time it took two
runners to complete the Boston Marathon
in several different years. If the patterns
continue, will Shanna ever complete the
marathon in the same number of minutes as
Maria? Explain. (Lesson 6-4)
Marathon Times (min)
2003
2004
2005
2006
Shanna
190
182
174
166
Maria
175
167
159
151
10. Jordan leaves his house and rides his bike at
10 mi/h. After he goes 4 miles, his brother
Tim leaves the house and rides in the same
direction at 12 mi/h. If their rates stay the
same, will Tim ever catch up to Jordan?
Explain. (Lesson 6-4)
11. Charmaine is buying almonds and cashews for
a reception. She wants to spend no more than
$18. Almonds cost $4 per pound, and cashews
cost $5 per pound. Write a linear inequality to
describe the situation. Graph the solutions.
Then give two combinations of nuts that
Charmaine could buy. (Lesson 6-5)
12. Luis is buying T-shirts to give out at a school
fund-raiser. He must spend less than $100 for
the shirts. Child shirts cost $5 each, and adult
shirts cost $8 each. Write a linear inequality
to describe the situation. Graph the solutions.
Then give two combinations of shirts that Luis
could buy. (Lesson 6-5)
13. Nicholas is buying treats for his dog. Beef
cubes cost $3 per pound, and liver cubes
cost $2 per pound. He wants to buy at least
2 pounds of each type of treat, and he wants
to spend no more than $14. Graph all possible
combinations of the treats that Nicholas could
buy. List two possible combinations.
(Lesson 6-6)
14. Geometry The perimeter of a rectangle is
at most 20 inches. The length and the width
are each at least 3 inches. Graph all possible
combinations of lengths and widths that
result in such a rectangle. List two possible
combinations. (Lesson 6-6)
TEKS
TAKS Practice
S33
Chapter 7
Applications Practice
1. Biology The eye of a bee is about 10 -3 m in
diameter. Simplify this expression.
(Lesson 7-1)
2. A typical stroboscopic camera has a shutter
speed of 10 -6 seconds. Simplify this expression.
(Lesson 7-1)
3. Space Exploration During a mission that
took place in August, 2005, the Space Shuttle
Discovery traveled a total distance of
9.3 × 10 6 km. The Space Shuttle’s velocity
was 28,000 km/h. (Lesson 7-2)
a. Write the total distance that the Space
Shuttle traveled in standard form.
b. Write the Space Shuttle’s velocity in
scientific notation.
4. There are approximately 10,000,000 grains in
a pound of salt. Write this number in scientific
notation. (Lesson 7-2)
5. A high-speed centrifuge spins at a speed of
2 × 10 4 rotations per minute. How many
rotations does the centrifuge make in one
hour? Write your answer in scientific notation.
(Lesson 7-3)
6. Astronomy Earth travels approximately
5.8 × 10 8 miles as it makes one orbit of
the Sun. How far does Earth travel in
50 years? (Note: One year is one orbit of
the Sun.) Write your answer in scientific
notation. (Lesson 7-3)
7. Geography In 2005, the population of
Indonesia was 2.4 × 10 8. This was 8 times
the population of Afghanistan. What was the
population of Afghanistan in 2005? Write your
answer in standard form. (Lesson 7-4)
8. The Golden Gate Bridge weighs about
8 × 10 8 kg. The Eiffel Tower weighs about
1 × 10 7 kg. How many times heavier is the
Golden Gate Bridge than the Eiffel Tower?
Write your answer in standard form.
(Lesson 7-4)
9. A rock is thrown off a 220-foot cliff with an
initial velocity of 50 feet per second. The
height of the rock above the ground is given by
the polynomial -16t 2 - 50t + 220, where t is
the time in seconds. What is the height of the
rock after 2 seconds? (Lesson 7-5)
10. The sum of the first n natural numbers is
given by the polynomial __12 n 2 + __12 n. Use this
polynomial to find the sum of the first 9
natural numbers. (Lesson 7-5)
11. Biology The population of insects in a
meadow depends on the temperature. A
biologist predicts the population of insect A
with the polynomial 0.02x 2 + 0.5x + 8 and the
population of insect B with the polynomial
0.04x 2 - 0.2x + 12, where x is the temperature
in degrees Fahrenheit. (Lesson 7-6)
a. Write a polynomial that represents the
total population of both insects.
b. Write a polynomial that represents the
difference of the populations of insect B
and insect A.
12. Geometry The length of the rectangle shown
is 1 inch longer than 3 times the width.
a. Write a polynomial that represents the area
of the rectangle.
b. Find the area of the rectangle when the
width is 4 inches. (Lesson 7-7)
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ÎÝÊÊ£
13. A cabinet maker starts with a square piece
of wood and then cuts a square hole from
its center as shown. Write a polynomial that
represents the area of the remaining piece of
wood. (Lesson 7-8)
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ÝÊÊÈ
S34
TEKS
TAKS Practice
Chapter 8
Applications Practice
1. Ms. Andrews’s class has 12 boys and 18 girls.
For a class picture, the students will stand in
rows on a set of steps. Each row must have the
same number of students, and each row will
contain only boys or girls. How many rows will
there be if Ms. Andrews puts the maximum
number of students in each row? (Lesson 8-1)
2. A museum director is planning an exhibit of
Native American baskets. There are 40 baskets
from North America and 32 baskets from
South America. The baskets will be displayed
on shelves so that each shelf has the same
number of baskets. Baskets from North and
South America will not be placed together
on the same shelf. How many shelves will
be needed if each shelf holds the maximum
number of baskets? (Lesson 8-1)
3. The area of a rectangular painting is (3x 2 + 5x)ft 2.
Factor this polynomial to find expressions for
the dimensions of the painting. (Lesson 8-2)
4. Geometry The surface area of a cylinder with
radius r and height h is given by the expression
2πr 2 + 2πrh. Factor this expression.
(Lesson 8-2)
5. The area of a rectangular classroom in square
feet is given by x 2 + 9x + 18. The width of the
classroom is (x + 3) ft. What is the length of
the classroom? (Lesson 8-3)
8. A rectangular poster has an area of
(6x 2 + 19x + 15) in 2. The width of the poster
is (2x + 3) in. What is the length of the
poster? (Lesson 8-4)
9. Physics The height of an object thrown
upward with a velocity of 38 feet per second
from an initial height of 5 feet can be modeled
by the polynomial -16t 2 + 38t + 5, where t is
the time in seconds. Factor this expression.
Then use the factored expression to find the
object’s height after __12 second. (Lesson 8-4)
10. A rectangular pool has an area of
(9x 2 + 30x + 25) ft 2. The dimensions of the
pool are of the form ax + b, where a and b are
whole numbers. Find an expression for the
perimeter of the pool. Then find the perimeter
when x = 5. (Lesson 8-5)
11. Geometry The area of a square is
9x 2 - 24x + 16. Find the length of each side of
the square. Is it possible for x to equal 1 in this
situation? Why or why not? (Lesson 8-5)
Architecture Use the following information for
Exercises 12–14.
An architect is designing a rectangular hotel room.
A balcony that is 5 feet wide runs along the length
of the room, as shown in the figure. (Lesson 8-6)
ÓÝÊvÌ
xÊvÌ
Gardening Use the following information for
Exercises 6 and 7.
A rectangular flower bed has a width of (x + 4) ft.
The bed will be enlarged by increasing the length,
as shown. (Lesson 8-3)
­ÝÊÊ{®ÊvÌ
12. The area of the room, including the balcony,
is (4x 2 + 12x + 5) ft 2. Tell whether the
polynomial is fully factored. Explain.
6. The original flower bed has an area of
(x 2 + 9x + 20)ft 2. What is its length?
13. Find the length and width of the room
(including the balcony).
7. The enlarged flower bed will have an area of
(x 2 + 12x + 32)ft 2. What will be the new length
of the flower bed?
14. How long is the balcony when x = 9?
TEKS
TAKS Practice
S35
Chapter 9
Applications Practice
1. The table shows the height of a ball at
various times after being thrown into the
air. Tell whether the function is quadratic.
Explain. (Lesson 9-1)
Time (s)
Height (ft)
0
1
2
3
4
200
204
176
116
24
2. The height of the curved roof of a camping
tent can be modeled by f (x) = -0.5x 2 + 3x,
where x is the width in feet. Find the height of
the tent at its tallest point. (Lesson 9-2)
3. Engineering A small bridge passes over
a stream. The height in feet of the bridge’s
curved arch support can be modeled by
f (x) = -0.25x 2 + 2x + 1.5, where the x-axis
represents the level of the water. Find the
height of the arch support. (Lesson 9-2)
4. Sports The height in meters of a football that
is kicked from the ground is approximated
by f (x) = -5x 2 + 20x, where x is the time in
seconds after the ball is kicked. Find the ball’s
maximum height and the time it takes the ball
to reach this height. Then find how long the
ball is in the air. (Lesson 9-3)
5. Physics Two golf balls are dropped, one from
a height of 400 feet and the other from a height
of 576 feet. (Lesson 9-4)
a. Compare the graphs that show the time it
takes each golf ball to reach the ground.
8. A child standing on a rock tosses a ball into the
air. The height of the ball above the ground is
modeled by h = -16t 2 + 28t + 8, where h is
the height in feet and t is the time in seconds.
Find the time it takes the ball to reach the
ground. (Lesson 9-6)
9. A fireworks rocket is shot directly up from
the edge of a rooftop. The height of the
rocket above the ground is modeled by
h = - 16t 2 + 40t + 24, where h is the height in
feet and t is the time in seconds. Find the time
it takes the rocket to hit the ground.
(Lesson 9-6)
10. Geometry The base of the triangle in the
figure is five times the height. The area of
the triangle is 400 in 2. Find the height of the
triangle to the nearest tenth. (Lesson 9-7)
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xÝ
11. The length of a rectangular swimming pool is
8 feet greater than the width. The pool has an
area of 240 ft 2. Find the length and width of
the pool. (Lesson 9-8)
12. Geometry One base of a trapezoid is 4 ft
longer than the other base. The height of the
trapezoid is equal to the shorter base. The
trapezoid’s area is 80 ft 2. Find the height.
Hint: A = __12 h(b 1 + b 2) (Lesson 9-8)
(
)
b. Use the graphs to tell when each golf ball
reaches the ground.
6. A model rocket is launched into the air with
an initial velocity of 144 feet per second. The
quadratic function y = -16x 2 + 144x models
the height of the rocket after x seconds. How
long is the rocket in the air? (Lesson 9-5)
7. A gymnast jumps on a trampoline. The
quadratic function y = -16x 2 + 24x models
her height in feet above the trampoline after
x seconds. How long is the gymnast in the
air? (Lesson 9-5)
S36
TEKS
TAKS Practice
Ý
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13. A referee tosses a coin into the air at the start
of a football game to decide which team will
get the ball. The height of the coin above the
ground is modeled by h = -16t 2 + 12t + 4,
where h is the height in feet and t is the time in
seconds after the coin is tossed. Will the coin
reach a height of 8 feet? Use the discriminant
to explain your answer. (Lesson 9-9)
Chapter 10
Applications Practice
Geography Use the following information for
Exercises 1–3.
The bar graph shows the areas of the Great
Lakes. (Lesson 10-1)
7. Use the data to make a box-and-whisker plot.
8. The weekly salaries of five employees at a
restaurant are $450, $500, $460, $980, and
$520. Explain why the following statement
is misleading: “The average salary is
$582.” (Lesson 10-4)
Ài>ÃʜvÊ̅iÊÀi>ÌÊ>ŽiÃ
9. The graph shows the sales figures for three
sales representatives. Explain why the graph
is misleading. What might someone believe
because of the graph? (Lesson 10-4)
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>ŽiʈV…ˆ}>˜
->iÃÊvœÀÊ"V̜LiÀ
˜
Ã
φ
iÀ
À
1. Estimate the difference in the areas between
the lake with the greatest area and the lake
with the least area.
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“
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£ä]äää
ˆ>
ä
£n]äää
£Ç]äää
£È]äää
£x]äää
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7
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2. Estimate the total area of the five lakes.
3. Approximately what percent of the total area is
Lake Superior?
4. The scores of 18 students on a Spanish exam
are given below. Use the data to make a stemand-leaf plot. (Lesson 10-2)
Exam Scores
65
94
92
75
71
83
77
73
91
82
63
79
80
77
99
76
80
88
5. The numbers of customers who visited a hair
salon each day are given below. Use the data to
make a frequency table with intervals.
(Lesson 10-2)
Number of Customers Per Day
32
35
29
44
41
25
35
40
41
32
33
28
33
34
Sports Use the following information for
Exercises 6 and 7.
The numbers of points scored by a college football
team in 11 games are given below. (Lesson 10-3)
10. A manager inspects 120 stereos that were built
at a factory. She finds that 6 are defective. What
is the experimental probability that a stereo
chosen at random will be defective?
(Lesson 10-5)
Travel Use the following information for
Exercises 11–13.
A row of an airplane has 2 window seats, 3 middle
seats, and 4 aisle seats. You are randomly assigned
a seat in the row. (Lesson 10-6)
11. Find the probability that you are assigned a
window seat.
12. Find the odds in favor of being assigned a
window seat.
13. Find the probability that you are not assigned
a middle seat.
14. A class consists of 19 boys and 16 girls. The
teacher selects one student at random to
be the class president and then selects a
different student to be vice president. What
is the probability that both students are
girls? (Lesson 10-7)
10 17 17 14 21 7 10 14 17 17 21
6. Find the mean, median, mode, and range of
the data set.
TEKS
TAKS Practice
S37
Chapter 11
Applications Practice
1. Scientists who are developing a vaccine track
the number of new infections of a disease each
year. The values in the table form a geometric
sequence. To the nearest whole number, how
many new infections will there be in the 6th
year? (Lesson 11-1)
Year
Number of New
Infections
1
12,000
2
9000
3
6750
a. Find the investment’s value after 5 years.
b. Approximately how many years will it take
for the investment to be worth $3100?
3. Chemistry Cesium-137 has a half-life of
30 years. Find the amount left from a 200-gram
sample after 150 years. (Lesson 11-3)
4. The cost of tuition at a dance school is $300
a year and is increasing at a rate of 3% a year.
Write an exponential growth function to model
the situation and find the cost of tuition after
4 years. (Lesson 11-3)
5. Use the data in the table to describe how the
price of the company’s stock is changing. Then
write a function that models the data. Use your
function to predict the price of the company’s
stock after 7 years. (Lesson 11-4)
Stock Prices
Price ($)
0
1
2
3
10.00
11.00
12.20
13.31
6. Use the data in the table to describe the rate
at which Susan reads. Then write a function
that models the data. Use your function to
predict the number of pages Susan will read in
6 hours. (Lesson 11-4)
Total Number of Pages Read
S38
Time (h)
1
2
3
4
Pages
48
96
144
192
TEKS
TAKS Practice
9. Geometry Given the surface area, S, of a
S
sphere, the formula r = ___
can be used to
4π
find the sphere’s radius. What is the radius of
a sphere with a surface area of 100 m 2? Use
3.14 for π. Round your answer to the nearest
hundredth of a meter. (Lesson 11-5)
√
2. Finance For a savings account that earns
5% interest each year, the function
x
f (x) = 2000(1.05) gives the value of a
$2000 investment after x years. (Lesson 11-2)
Year
gives the
7. The function f (x) = √1.44x
approximate distance in miles to the horizon
as observed by a person whose eye level is x
feet above the ground. Jamal stands on a tower
so that his eyes are 180 ft above the ground.
What is the distance to the horizon? Round
your answer to the nearest tenth.
(Lesson 11-5)
9. Cooking A chef has a square baking pan with
sides 8 inches long. She wants to know if an
11-inch fish can fit in the pan. Find the length
of the diagonal of the pan. Give the answer as
a radical expression in simplest form. Then
estimate the length to the nearest tenth of
an inch. Tell whether the fish will fit in the
pan. (Lesson 11-6)
10. Alicia wants to put a fence around the irregular
garden plot shown. Find the perimeter of the
plot. Give your answer as a radical in simplest
form. (Lesson 11-7)
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е“
ÊȖе
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е“
ÊȖе
ÎÊÊ
“
ÊȖе
ÇxÊÊ
е“
11. Physics The velocity of an object in meters
√2
√
E
per second is given by _____
, where E is kinetic
√
m
energy in Joules and m is mass in kilograms.
What is the velocity of an object that has
40 Joules of kinetic energy and a mass of
10 kilograms? Give the answer as a radical
expression in simplest form. Then estimate
the velocity to the nearest tenth.
(Lesson 11-8)
12. A rectangular window has an area of 40 ft 2.
The window is 8 feet long and its height
is √
x + 2 ft. What is the value of x? What is the
height of the window? (Lesson 11-9)
Chapter 12
Applications Practice
1. The inverse variation xy = 200 relates the
number of words per minute x at which a
person types to the number of minutes y
that it takes to type a 200-word paragraph.
Determine a reasonable domain and range
and then graph this inverse variation. Use the
graph to estimate how many minutes it would
take to type the paragraph at a rate of 60 words
per minute. (Lesson 12-1)
7. A committee consists of five more women than
men. The chairperson randomly chooses one
person to serve as secretary and a different
person to serve as treasurer. Write and simplify
an expression that represents the probability
that both people who are chosen are men.
What is the probability of choosing two men
if there are 6 men on the committee?
(Lesson 12-4)
2. Business The owner of a deli finds that the
number of sandwiches sold in one day varies
inversely as the price of the sandwiches. When
the price is $4.50, the deli sells 60 sandwiches.
How many sandwiches can the owner expect
to sell when the price is $3.60? (Lesson 12-1)
8. Transportation A delivery truck makes a
delivery to a town 150 miles away traveling
r miles per hour. On the return trip, the
delivery truck travels 20% faster. Write and
simplify an expression for the truck’s roundtrip delivery time in terms of r. Then find the
round-trip delivery time if the truck travels 55
mi/h on its way to the delivery. (Lesson 12-5)
3. A gardener has $30 in his budget to buy
packets of seeds. He receives 3 free packets of
seeds with his order. The number of packets
30
y he can buy is y = __
x + 3, where x is the
price per packet. Describe the reasonable
domain and range values. Then graph the
function. (Lesson 12-2)
4. Ashley wants to save $1000 for a trip to Europe.
She puts aside x dollars per month, and her
grandmother contributes $10 per month.
The number of months y it will take to save
1000
$1000 is y = _____
. Describe the reasonable
x + 10
domain and range values. Then graph the
function. (Lesson 12-2)
5. Geometry Find the ratio of the area of a
circle to the circumference of the circle. (Hint:
For a circle, A = πr 2 and C = 2πr). For what
radius is this ratio equal to 1? (Lesson 12-3)
6. Geometry For a cylinder with radius r and
height h, the volume is V = πr 2h, and the
surface area is S = 2πr 2 + 2πrh. What is the
ratio of the volume to the surface area for a
cylinder? What is this ratio when r = h = 1?
(Lesson 12-3)
À
…
9. Recreation Jordan is hiking 2 miles to a vista
point at the top of a hill and then back to his
campsite at the base of the hill. His downhill
rate is 3 times his uphill rate, r. Write and
simplify an expression in terms of r for the
time that the round-trip hike will take. Then
find how long the hike will take if Jordan’s
uphill rate is 2 mi/h. (Lesson 12-5)
10. Geometry The volume of a rectangular prism
is the area of the base times the height. A
rectangular prism has a volume given by
(2x 2 + 7x + 5) cm 3 and a height given by
(x + 1) cm. What is the area of the base of the
rectangular prism? (Lesson 12-6)
11. Tanya can deliver newspapers to all of the
houses on her route in 1 hour. Her brother,
Nick, can deliver newspapers along the
same route in 2 hours. How long will it
take to deliver the newspapers if they work
together? (Lesson 12-7)
12. Agriculture Grains are harvested using a
combine. A farm has two combines—one that
can harvest the wheat field in 9 hours and
another that can harvest the wheat field in
11 hours. How long will it take to harvest the
wheat field using both combines?
(Lesson 12-7)
TEKS
TAKS Practice
S39
Problem Solving Handbook
Draw a Diagram
Problem Solving Strategies
You can draw a diagram to help you visualize what
the words of a problem are describing.
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
EXAMPLE
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
A gardener wants to plant a 2.5-foot-wide border of
flowers around a rectangular herb garden. The herb
garden is 12 feet long and 7.5 feet wide. What is the
area of the border?
1
Understand the Problem
You need to find the area of the garden’s border. You are given the garden’s
dimensions and the width of the border.
2 Make a Plan
Draw and label a diagram of the herb garden with the surrounding border. Find the
dimensions of the outer rectangle. Then find the area of the inner rectangle and
subtract to find the area of the border.
3 Solve
length of outer rectangle: 2.5 ft + 12 ft + 2.5 ft = 17 ft
width of outer rectangle: 2.5 ft + 7.5 ft + 2.5 ft = 12.5 ft
Ó°xÊvÌ
Ó°xÊvÌ
£ÓÊvÌ
Ó°xÊvÌ
Find the area of each rectangle:
area of outer rectangle: 17 ft × 12.5 ft = 212.5
area of inner rectangle: 12 ft × 7.5 ft = 90 ft2
ft2
Ç°xÊvÌ
Subtract:
area of border: 212.5
ft2
- 90
ft2
= 122.5
ft2
4 Look Back
Ó°xÊvÌ
To check your answer, solve the problem in a different way.
Divide the border into four parts and find the area of
each part. Then add the areas.
17 ft × 2.5 ft = 42.5 ft 2
7.5 ft × 2.5 ft = 18.75 ft 2
17 ft × 2.5 ft = 42.5 ft
7.5 ft × 2.5 ft = 18.75 ft
£ÇÊvÌ
Ó°xÊvÌ
Ó°xÊvÌ
2
2
42.5 ft 2 + 42.5 ft 2 + 18.75 ft 2 + 18.75 ft 2 + = 122.5 ft2
PRACTICE
1. A circular fish pond is surrounded by a circular border of stones that is 18 inches wide.
The fish pond is 4 feet in diameter. What is the area of the border? (Use 3.14 for π.)
2. Thirty-two teams are in the first round of a softball tournament. A team is eliminated
as soon as it loses a game. How many games need to be played to determine the
winner? (Hint: Use a tree diagram.)
S40
Problem Solving Handbook
Ç°xÊvÌ
Make a Model
You can make a model, or representation of the
objects in a problem, to help you solve it.
EXAMPLE
Problem Solving Strategies
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
Mr. Duncan is using blue and white square tiles to create a pattern on his kitchen
wall. The entire design will have 8 rows with 15 tiles in each row. The bottom row
alternates colors starting with blue, and the row above that alternates colors
starting with white. He will continue this alternating pattern so that the same two
colors are never next to each other. How many of each color tile does Mr. Duncan
need to complete the entire design?
1
Understand the Problem
You need to find how many of each color tile are needed. You know the number of
rows and the number of tiles in each row. The colors alternate so that the same two
colors are never next to each other.
2 Make a Plan
Use blocks (preferably blue and white, but any two colors would work) to make a
model of the first two rows. Count how many of each color you use. Then multiply to
find how many of each color would be used in the entire design.
3 Solve
Create the bottom row. Start with a blue block and alternate
colors across the row until you have used 15 blocks.
Create the row above the bottom row. Start with a white block.
You could build all 8 rows
and just count the number of
each color, but each group
of two rows will be the
same, so this way is quicker.
There will be a total of 8 rows: 4 that start with blue and 4 that start with white.
Count how many of each color are used above and multiply each number by 4.
blue: 15 × 4 = 60
white: 15 × 4 = 60
Mr. Duncan needs 60 blue tiles and 60 white tiles.
4 Look Back
The grid is 15 units by 8 units, so there are 15 × 8 = 120 squares in the grid. Add the
number of blue and white tiles to see if the sum is 120: 60 + 60 = 120.
PRACTICE
1. Mr. Duncan decides to tile another area of his kitchen wall. This design will have 12 rows
with 10 tiles in each row. The bottom row will repeat this pattern: blue, white, blue, blue,
white. The row above the bottom row will repeat this pattern: white, green, white, white,
green. He will use these two patterns for each of the remaining rows so that the first colors
of each row always alternate. How many of each color tile will Mr. Duncan need?
Problem Solving Handbook
S41
Guess and Test
Problem Solving Strategies
The guess and test strategy can be used when you
cannot think of another way to solve the problem.
Begin by making a reasonable guess, and then test it
to see whether your guess is correct. If not, adjust the
guess accordingly and test again. Keep guessing and
testing until you correctly solve the problem.
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
EXAMPLE
The manager of a college computer lab purchased 24 printers at a total cost of
$3120. Some of the printers were laser, and some were ink jet. The laser printers
cost $250 each, and the ink jet printers cost $70 each. How many of each type of
printer did the manager purchase?
1
Understand the Problem
You know the cost of each type of printer and the total number of printers.
You need to find the number of each type of printer purchased.
2 Make a Plan
Make reasonable first guesses for each type of printer. The sum must be 24. Then
multiply each guess by the cost of each printer. Find the total and compare it to
$3120. Adjust the guess as needed and continue until you find the solution.
3 Solve
Use a table to organize your guesses.
Laser
Printers
Ink Jet
Printers
Total
Priners
1st guess
12
12
24
12($250) + 12($70)
$3000 + $840 = $3840
Too high—try fewer laser
printers.
2nd guess
6
18
24
6($250) + 18($70)
$1500 + $1260 = $2760
Too low—try more laser
printers.
3rd guess
8
16
24
8($250) + 16($70)
$2000 + $1120 = $3120
Correct!
Total Cost
The manager purchased 8 laser printers and 16 ink jet printers.
4 Look Back
The total spent is $3120, and the total number of printers is 24. The solution
is correct.
PRACTICE
1. All 350 seats were sold for a concert in the park. Adult tickets cost $15, and
child tickets cost $5. Ticket sales totaled $4350. How many of each type of
ticket were sold?
2. Jane is 3 times as old as Theo. Luke is 5 years older than Theo. Zoe is 8 years
younger than twice Theo’s age, and Cassie is 6 years younger than Theo. The sum
of their ages is 71. How old is each person?
S42
Problem Solving Handbook
Work Backward
You can work backward to solve a problem when
you know the ending value and are asked to find the
initial value.
EXAMPLE
Problem Solving Strategies
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
Lee Ann is taking a vacation in Paris, France. Her flight arrived in Paris at 9:35 A.M.
on Tuesday. The plane left New York City and flew for 7 hours and 55 minutes to
Nice, France, where there was a layover of 1 hour 12 minutes. From Nice the plane
flew 1 hour and 25 minutes to Paris. Paris time is 6 hours ahead of New York City
time. What time did the plane leave New York City?
1
Understand the Problem
You are asked to find the time that the plane left New York City. You know when the
flight arrived in Paris, the length of the stops that were made along the way, and the
time difference between New York City and Paris.
2 Make a Plan
Work backward from the time the plane arrived in Paris, using inverse operations.
Then apply the time difference between the two cities.
3 Solve
Subtract the length of time it took to fly from Nice to Paris from the time Lee Ann
arrived in Paris.
9:35 A.M. - 1 hour 25 minutes = 8:10 A.M.
Subtract the length of the layover in Nice.
8:10 A.M. - 1 hour 12 minutes = 6:58 A.M.
Subtract the length of the flight from New York to Nice.
6:58 A.M. – 7 hours 55 minutes = 11:03 P.M. Monday
Since Paris time is ahead of New York time, subtract the time difference.
11:03 P.M., Monday - 6 hours = 5:03 P.M. Monday
Lee Ann’s flight left New York City on Monday at 5:03 P.M.
4 Look Back
Work forward to check your answer.
5:03 P.M. Monday + 6 h + 7 h 55 min + 1 h 12 min + 1 h 25 min
= 5:03 P.M. Monday + 16 h 32 min
= 9:35 A.M. Tuesday
This matches the information given in the problem.
PRACTICE
1. A bus arrives in Dallas, Texas, at 10:59 A.M. on Friday. The bus left Atlanta,
Georgia, and took 12 hours and 15 minutes to arrive in Shreveport, Louisiana,
where there was a 45-minute layover. From Shreveport it took 4 hours and 29
minutes to get to Dallas. Dallas time is 1 hour behind Atlanta time. What time did
the bus leave Atlanta?
2. Carolina bought a DVD player that was on sale for 90% of the original price. The
total amount she paid was $135.72, which included a sales tax of $5.22. What was
the original price of the DVD player?
Problem Solving Handbook
S43
Find a Pattern
Problem Solving Strategies
If a problem involves a sequence of numbers or
figures, it is often necessary to find a pattern to
solve the problem.
EXAMPLE
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
Darian created the following sequence of stars:
How many stars will be in the 6th figure?
1
Understand the Problem
You need to find the number of stars in the 6th figure. You can find the number in
the first four figures by counting.
2 Make a Plan
Count the number of stars in each of the first four figures. Use the information to
find a pattern and determine a general rule.
3 Solve
Look for a pattern between the position of each figure in the sequence and the
number of stars in that figure.
Position
1
2
3
4
Stars
2
6
12
20
The number of stars is the square of the
position number plus the position number.
This rule written algebraically is n 2 + n.
Evaluate the expression for n = 6: n 2 + n
6 2 + 6 = 36 + 6 = 42
There will be 42 stars in the 6th figure.
4 Look Back
Look for another pattern. The number of stars in each position increases by 4, then
by 6, then by 8. That is, the amount of increase always increases by 2. So the number
of stars in the 5th position will be 20 + 10, or 30, and the number of stars in the 6th
position will be 30 + 12, or 42.
PRACTICE
1. The first three figures of a pattern are shown.
How many circles will be in the 10th figure?
S44
Problem Solving Handbook
2. Lily drew the first four figures of a pattern.
How many squares will be in the 7th figure?
Make a Table
Problem Solving Strategies
You can make a table to solve problems because
the rows and columns can help you arrange
information. Sometimes this also allows you to discover
relationships that might otherwise be hard to notice.
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
EXAMPLE
A scientist begins a culture with 500 bacteria. The number of bacteria triples every
1
30 minutes. How many bacteria are in the culture after 2 __
hours?
2
1
Understand the Problem
You are asked to find the number of bacteria in the culture after 2 __12 hours.
You know the initial number of bacteria, and you know that the population
triples every half hour.
2 Make a Plan
Make a table with rows for time and number of bacteria. Start with the initial
number in the culture. Increase the time in 30-minute increments and triple the
number of bacteria with each increase. Keep extending the table until the time is
2 __12 hours (150 minutes).
3 Solve
Time (min)
Bacteria
0
30
60
90
120
150
500
1500
4500
13,500
40,500
121,500
There are 121,500 bacteria in the culture after 2 __12 hours.
4 Look Back
Check your answer by solving a simpler problem. The number of bacteria in the
culture triples five times (150 min ÷ 30 min = 5). Start with 5 instead of 500 and triple
the number five times.
5 × 3 = 15
15 × 3 = 45
45 × 3 = 135
135 × 3 = 405
405 × 3 = 1215
Multiply by 100 to find the total if you had started with 500; 1215 × 100 = 121,500
PRACTICE
1. A dietician’s report states that a 125-pound woman needs to eat about 1750
Calories a day to maintain her weight. It also states that a 132-pound woman
needs 1848 Calories and a 139-pound woman needs 1946 Calories a day. Based
on these values, how many Calories does a 160-pound woman need to eat each
day to maintain her weight?
2. Simon opened a savings account with an initial deposit of $200. At the end of
each year, the account earns 4% interest. If he does not deposit or withdraw any
additional money, what would his balance be at the end of 6 years?
Problem Solving Handbook
S45
Solve a Simpler Problem
Sometimes a problem contains numbers that make
it seem difficult to solve. You can solve a simpler
problem by rewriting the numbers so they are easier
to compute.
Problem Solving Strategies
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
EXAMPLE
During a skating competition, Jules skated around the track 35 times. One lap is
0.9 mile. If Jules finished in 1 hour 30 minutes, what was his average speed?
1
Understand the Problem
You are asked to find Jules’s average speed for 35 laps. You know the distance of each
lap and the amount of time it took him to finish the competition.
2 Make a Plan
Solve a simpler problem by using easier numbers to do the computations.
3 Solve
Find the total distance skated.
35(0.9)
There were 35 laps that measured 0.9 mile.
35(1 - 0.1)
Write 0.9 as 1 - 0.1
35(1) - 3.5(0.1)
Use the Distributive Property.
35 - 3.5
31.5
Use the distance formula to find the average speed.
d = rt
1 hour 30 minutes = 1.5 hours
31.5 = r × 1.5
31.5 = r
_
Solve for r.
1.5
315 = r
Multiply the numerator and denominator by 10
_
15
to eliminate the decimals.
1 (315) = r
_
15
1 (300 + 15) = r
_
Write 315 as 300 + 15.
15
1 (300) + _
1 (15) = r
_
Use the Distributive Property.
15
15
20 + 1 = r
21 = r
Jules skated at an average speed of 21 miles per hour.
4 Look Back
Each lap is a little less than 1 mile, so 35 laps is a little less than 35 miles. Round this
distance to 30 miles and use d = rt to find the rate when the time is 1.5 hours:
30 mi = (1.5 h)r r = 20 mi/h. This is close to 21 mi/h.
PRACTICE
1. Diana swam 24 laps in the pool today. One lap is 200 feet. She swam at an
average rate of 4 feet per second. How many minutes did Diana swim?
S46
Problem Solving Handbook
Use Logical Reasoning
Problem Solving Strategies
Use logical reasoning to solve problems when
you are given several facts and can use common sense
to find a missing fact.
EXAMPLE
1
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
Five players on a baseball team wear the numbers 2, 12, 15, 34, and 42. Their
positions are pitcher, catcher, first base, left field, and center field. The pitcher’s
number is less than the left fielder’s number. The center fielder’s number is greater
than 25, and the left fielder wears an even number. The catcher wears number 34.
What is the pitcher’s number?
1
Understand the Problem
You want to find the jersey number of the pitcher. You know there are five positions
and five jersey numbers. Some information about who wears which number is given.
2 Make a Plan
Organize the information in a table. Start with the fact that the catcher wears
number 34 and use logical reasoning to determine the numbers of the other
positions.
3 Solve
The catcher wears number 34. No other player wears 34, and the catcher wears no
other number. Enter Y’s and N’s in the chart as shown.
The center fielder’s number is greater than 25, so he must wear number 42.
The left fielder cannot wear number 15 (because it is odd), and he cannot have the
least number (the pitcher’s number is less than his). The left fielder must wear 12.
The pitcher’s number is less than 12 (the left fielder’s), so he must wear number 2.
2
12
15
34
42
Pitcher
Y
N
N
N
N
Catcher
N
N
N
Y
N
First Base
N
N
Y
N
N
Left Fielder
N
Y
N
N
N
Center Fielder
N
N
N
N
Y
Y = yes; N = no
Once you enter Y in a cell, enter N in the
remaining cells for the row and the
column that include it.
The pitcher wears number 2.
4 Look Back
Complete the chart if needed. Read the problem while looking at the chart to make
sure there are no contradictions.
PRACTICE
1. Rose, Jill, Gaby, and Chloe bowled the scores 110, 125, 144, and 150. Jill did not
bowl the 110. The person who bowled the 150 is Rose’s sister and Jill’s aunt. Chloe
bowled the 125. What score did Jill bowl?
Problem Solving Handbook
S47
Use a Venn Diagram
You can use a Venn diagram to display
relationships among sets of numbers. Circles are used
to represent the individual sets.
EXAMPLE
Problem Solving Strategies
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
At a local supermarket, 194 people were given samples of two brands of orange
juice. Their opinions were as follows: 120 people liked brand A, 101 people liked
brand B, and 15 people did not like either brand. How many people liked only
brand A?
1
Understand the Problem
The total number of people was 194, and 15 of them did not like either brand. The
statement “120 people liked brand A” means some of the 120 people liked only brand A
and some liked brand A and brand B. The statement “101 people liked brand B” means
some of the 101 people liked only brand B and some liked brand A and brand B.
2 Make a Plan
Use a Venn diagram to show the relationship among the groups of people.
3 Solve
Draw and label two intersecting circles to show the sets of
people who liked brand A and brand B. Write 15 in the area
labeled “Neither.”
Out of 194 people, 15 liked neither brand. Subtract 15 from
194 to find how many people liked at least one brand:
194 - 15 = 179.
Add the number of people who liked brand A to the number
of people who liked brand B: 120 + 101 = 221. You know there
are only 179 people who liked at least one brand, so subtract
179 from 221: 221 - 179 = 42. This means 42 people were
counted twice, and that 42 people liked both brands. Write 42
in the area labeled both.
Out of 120 people who liked brand A, 42 also liked brand B.
Subtract 42 from 120 to find the number of people who liked
only brand A: 120 - 42 = 78.
So 78 people liked only brand A.
4 Look Back
À>˜`Ê
À>˜`Ê
œÌ…
iˆÌ…iÀ\Ê£x
À>˜`Ê
À>˜`Ê
œÌ…
Çn
iˆÌ…iÀ\Ê£x
Find the number of people who liked brand B only: 101 - 42 = 59. Add all the
numbers in the Venn diagram. The sum of the number who liked only brand A,
the number who liked only brand B, the number who liked both brands, and the
number who liked neither brand should be the total number of people surveyed:
78 + 59 + 42 + 15 = 194.
PRACTICE
In a group of 138 people, 55 own a cat, 27 own a cat and a dog, and 42 own
neither pet.
1. How many people own only a cat?
2. How many people own a dog?
S48
Problem Solving Handbook
{Ó
x™
Make an Organized List
Problem Solving Strategies
If a problem asks you to find all the possible ways
in which something can happen, you can make an
organized list to keep track of the outcomes.
Draw a Diagram
Make a Model
Guess and Test
Work Backward
Find a Pattern
Make a Table
Solve a Simpler Problem
Use Logical Reasoning
Use a Venn Diagram
Make an Organized List
EXAMPLE
A fair coin is tossed 4 times. What is the probability that it lands heads up at least
3 times?
1
Understand the Problem
You need to find the probability that a coin tossed 4 times lands heads up 3 or 4
times.
2 Make a Plan
The formula for probability is:
number of favorable outcomes
probability = ___
total number of outcomes
The total number of outcomes is the number of items in the list. The number of
favorable outcomes is the number of times the coin lands heads up 3 or 4 times.
Make an organized list of the coin tosses to find the total number of outcomes.
3 Solve
Start with heads for all 4 tosses, then heads for the first 3 tosses, then heads for the
first 2 tosses, and then heads for the first toss. Repeat the pattern for tails.
HHHH
HTHH
TTTT
THTT
HHHT
HTHT
TTTH
THTH
HHTH
HTTH
TTHT
THHT
HHTT
HTTT
TTHH
THHH
There are 16 total
outcomes.
There are 5 favorable
outcomes.
5
The probability that the coin lands heads up 3 or 4 times is __
.
16
4 Look Back
Double-check that each combination is listed and that no combination is written
more than once. You can also use the Fundamental Counting Principle to check
the total number of outcomes. For each of the 4 coin tosses, there are 2 possible
outcomes, so the total number of outcomes is 2 × 2 × 2 × 2 = 16.
PRACTICE
1. A beagle, a fox terrier, an Afghan hound, and a golden retriever are competing in
the finals of a dog show. How many ways can the dogs finish in first, second, and
third place?
2. Two number cubes are rolled. What is the probability that the sum of the
numbers rolled is an odd number?
Problem Solving Handbook
S49
Skills Bank
Place Value
You can use a place-value chart to read and write numbers. The number 5,304,293,087,201.286
is shown below.
Trillions
Billions
Millions
Thousands
Ones
.
Tenths
Hundredths
Thousandths
5,
304,
293,
087,
201
.
2
8
6
EXAMPLE
1
Use the place-value chart to find the place value of the underlined digit.
A 5,304,293,087,201.286
B 5,304,293,087,201.286
billions
C 5,304,293,087,201.286
ten millions
thousandths
Expanded form shows the number as the sum of the values of each digit. The number 1463
written in expanded form is 1000 + 400 + 60 + 3.
EXAMPLE
2
Write 16,752,045.12 in expanded form.
10,000,000 + 6,000,000 + 700,000 + 50,000 + 2,000 + 40 + 5 + 0.1 + 0.02
PRACTICE
Use the place-value chart to find the place value of the underlined digit.
1. 22.38
2. 1,238,400
3. 2,809,354.003
−
−
−
Write each number in expanded form.
4. 899,456
5. 1645.445
6. 3,009,844,002,359
Compare and Order Rational Numbers
You can compare and order rational numbers by graphing them on a number line.
EXAMPLE
1
ÚÚ
Ê{Ê
ÊÎÊ ÚÚ
ä°£ ä°Óx
ä
3
4
Order 0.25, __
, 0.1, and __
from least to greatest.
4
5
{ x
ä°x
£
3
__
= 0.75
4
4
__
= 0.8
5
The values increase from left to right: 0.1, 0.25, __34 , __45 .
PRACTICE
Order each set of numbers from least to greatest.
3, _
2, 2_
1
4
1. 2.6, 2 _
2. 0.45, _
5 2
8 9
3, _
1 , 5.05, 5.5
1 , 0.42
4. 5.25, 5 _
5. 0.4, _
5 4
3
S50
Skills Bank
2 , 0.6
3. 0.55, _
3
5
6
4
6. _, _, 0.6, _
7
8 9
Times Tables
You can use a multiplication table to multiply and write number families. A number family
is a group of related number sentences that use the same numbers.
EXAMPLE
1
Find 8 × 9.
Find where the 8’s row and
the 9’s column intersect.
8 × 9 = 72
EXAMPLE
2
Write a multiplication and division
number family for 8, 9, and 72.
8 × 9 = 72
9 × 8 = 72
72 ÷ 9 = 8
72 ÷ 8 = 9
×
1
2
3
4
5
6
7
8
9
10
11
12
1
1
2
3
4
5
6
7
8
9
10
11
12
2
2
4
6
8
10
12
14
16
18
20
22
24
3
3
6
9
12
15
18
21
24
27
30
33
36
4
4
8
12
16
20
24
28
32
36
40
44
48
5
5
10
15
20
25
30
35
40
45
50
55
60
6
6
12
18
24
30
36
42
48
54
60
66
72
7
7
14
21
28
35
42
49
56
63
70
77
84
8
8
16
24
32
40
48
56
64
72
80
88
96
9
9
18
27
36
45
54
63
72
81
90
99
108
10
10
20
30
40
50
60
70
80
90
100 110 120
11
11
22
33
44
55
66
77
88
99
110 121 132
12
12
24
36
48
60
72
84
96
108 120 132 144
PRACTICE
Find each product. Write a multiplication and division number family for each set of
numbers.
1. 4 × 8
2. 5 × 12
3. 3 × 11
4. 8 × 7
5. 9 × 6
6. 12 × 12
Inverse Operations
Inverse operations “undo” each other. Addition and subtraction are inverse operations.
Multiplication and division are inverse operations.
EXAMPLE
1
Use inverse operations to check each answer.
A 567 - 180 487
487 + 180
667
667 ≠ 557
incorrect
B 110 ÷ 11 10
Use addition
to check
subtraction.
10 × 11
110
110 = 110
correct
Use multiplication
to check division.
PRACTICE
Use inverse operations to check each answer.
1. 51 + 25 = 86
2. 14 × 4 = 48
3. 144 ÷ 4 = 36
5.
134 + 653 = 787
6. 364 ÷ 7 = 52
7. 500 - 428 = 82
4. 345 - 72 = 273
8. 6 × 25 = 150
Skills Bank
S51
Translate from Words to Math
Some words indicate certain math operations. Common math words and phrases are shown
below. Some are listed in more than one column, so always read the problem carefully.
Addition
Subtraction
Multiplication
Division
add, plus, total, sum,
more, more than,
increased by, in all,
combined
subtract, minus,
difference, less, less
than, more, more than,
decreased by
multiply, times, of,
product, per, for each,
total
divide, divided by,
quotient, divide equally,
per, percent
EXAMPLE
A Caroline saved $42 in September, $25 in
October, and $33 in November. How much
money did she save in all?
The words “in all” indicate addition.
42 + 25 + 33 = 100
Caroline saved $100 in all.
B Jamal bought 13 gallons of gas for $1.98 per
gallon. What is the total amount he paid?
The word “per” could mean multiplication
or division. But the word “total” indicates
multiplication.
13 × 1.98 = 25.74.
Jamal paid a total of $25.74.
PRACTICE
1. Sarah worked 15 hours this week and
earned a total of $112.50. How much does
she earn per hour? What words tell you
which operation to use?
2. Lance biked 28.5 miles on Monday. On Thursday
he biked 5.75 miles less than he did on Monday.
How far did he bike on Thursday? What words
tell you which operation to use?
Mental Math
Mental math strategies include using the Distributive Property, using the Commutative
Property, and using facts about powers of 10.
EXAMPLE
Use mental math to solve each problem.
A 6 × 17
B 225 + 78 + 75
C 132 × 100,000
Break 17 into 10 + 7.
Then use the Distributive
Property.
Use the Commutative
Property to add or multiply
numbers in a different order.
Count the number of zeros
in 100,000. Move the decimal
point that many places right.
6 × 17 = 6 (10 + 7)
= 6 (10) + 6 (7)
= 60 + 42
= 102
225 + 78 + 75 = 225 + 75 + 78
= 300 + 78
= 378
132 × 100,000 = 13,200,000
= 13,200,000
PRACTICE
Use mental math to solve each problem.
1. 3987 × 10,000
2. 5 × 29
4. 12 × 41
S52
Skills Bank
5. 25 × 42 × 4
3. 950 + 273 + 50
6. 4.5 × 100 × 2
Measurement
The measurements for time
are the same worldwide.
1 min = 60 s
1 h = 60 min
1 day = 24 h
The customary system of
measurement is used in the
United States.
Length
12 in. = 1 ft
3 ft = 1 yd
5280 ft = 1 mi
The metric system is used
elsewhere and in science
worldwide.
Length
1 mm = 0.001 m
1 cm = 0.01 m
1 km = 1000 m
1 wk = 7 days
1 yr = 12 mo
1 yr = 365 days
1 leap yr = 366 days
Capacity
8 oz = 1 c
2 c = 1 pt
2 pt = 1 qt
Weight
16 oz = 1 lb
2000 lb = 1 ton
Capacity
1 mL = 0.001 L
1 kL = 1000 L
Mass
1 mg = 0.001 g
1 kg = 1000 g
Use the table below to convert from metric to customary measurements.
Length
Capacity
Mass/Weight
Temperature
1 cm ≈ 0.394 in.
1 L ≈ 1.057 qt
1 g ≈ 0.0353 oz
1 m ≈ 3.281 ft
1 L ≈ 0.264 gal
1 kg ≈ 2.205 lb
1 m ≈ 1.094 yd
1 L ≈ 4.227 c
1 kg ≈ 0.001 ton
1 km ≈ 0.621 mi
1 mL ≈ 0.338 fl oz
1 metric T ≈ 1.102 ton
F=
(_59 × C) + 32
Use the table below to convert from customary to metric measurements.
Length
Capacity
Weight/Mass
Temperature
1 in. ≈ 2.540 cm
1 qt ≈ 0.946 L
1 oz ≈ 28.350 g
1 ft ≈ 0.305 m
1 gal ≈ 3.785 L
1 lb ≈ 0.454 kg
1 yd ≈ 0.914 m
1 c ≈ 0.237 L
1 ton ≈ 907.185 kg
1 mi ≈ 1.609 km
1 fl oz ≈ 29.574 mL
1 ton ≈ 0.907 metric ton
C=
_5 × (F - 32)
9
EXAMPLE
A Write <, =, or >.
35 in.
1 yd
B
C Convert 25°C to °F.
Convert 32 km/h to mi/h.
(
)
9 × 25 + 32
F= _
5
1 km/h ≈ 0.621 mi/h
35 in.
3 ft
1 yd = 3 ft
35 in. < 36 in. 3 ft = 36 in. 32 km/h ≈32 0.621 mi/h
35 in. < 1 yd
32 km/h ≈ 19.872 mi/h
F = 45 + 32
F = 77°F
PRACTICE
Write <, >, or =.
1. 3 lb
40 oz
Convert.
4. 15mi/h to km/h
2. 200 cm
5. 2 weeks to hours
2m
3. 6 c
6. 32 fl oz to mL
2 qt
7. 95°F to °C
8. 14 tons to kg
Skills Bank
S53
Precision, Accuracy, and Significant Digits
Significant digits are those digits that are known to be correct in a measurement.
• All nonzero digits are significant.
• Zeros between significant digits are significant.
• Zeros after the last nonzero number after the
• Zeros at the end of a whole number are not
decimal point are significant.
significant
EXAMPLE
1
Determine the number of significant digits in each measurement.
A 272 ft
Three significant digits: 272
All digits are nonzero digits.
B 0.0050 mm
Two significant digits: 0.0050
The last zero is significant.
Accuracy is determined by the exactness of a measurement—that is, how close it is to the
actual or accepted value. Precision describes the level of detail an instrument measures. A
measurement of 200 mm is more precise than a measurement of 20 cm because millimeters are
a smaller unit of measurement. A measurement can be precise, but not accurate, and vice versa.
EXAMPLE
2
Three students measured the width of a dictionary. Their measurements were
21 cm, 8.5 in., and 212 mm. The publisher lists the width of the dictionary as 8.52 in.
A Which measurement is most accurate?
8.5 in.
8.5 in. is closest to the accepted width of the dictionary.
B Which measurement is most precise?
Millimeters are the smallest unit of measurement used.
212 mm
• When adding or subtracting measurements, the answer must have the same number of
decimal places as the measurement with the least number of decimal places.
• When multiplying or dividing measurements, the answer must have the same number
of significant digits as the least precise measurement.
EXAMPLE
3
Perform the indicated operation. Write the answer with the correct number of
significant digits.
A 14 in. + 2.76 in.
B 12.3 cm × 6.4 cm
14 in. + 2.76 in. = 16.76 in.
12.3 cm × 6.4 cm = 78.72 cm 2
14 has zero decimal places.
2.76 has two decimal places.
12.3 has three significant digits.
6.4 has two significant digits.
Round to zero decimal places: 17 in.
Round to two significant digits: 79 cm 2
PRACTICE
Determine the number of significant digits in each measurement.
1. 1,234.55 yd
2. 10,000 mi
3. 0.040 km
4. 102.045 ft
5. Three students measured the length of a classroom. Their measurements were 18.5 ft,
362 in., and 21 ft. A blueprint shows that the length of the classroom is 18.43 ft.
a. Which measurement is most accurate?
b. Which measurement is most precise?
Perform the indicated operation. Write the answer with the correct number of significant digits.
6. 244 in. + 4.58 in.
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Skills Bank
7. 155.02 ft ÷ 0.05 ft
8. 38.33 yd × 2.8 yd
Absolute and Relative Error
It is never possible to measure quantities exactly—all measures are estimates. Accuracy
refers to how close a measurement is to its actual or accepted value. Absolute error is the
difference between the measured value and the actual or accepted value.
absolute error = ⎪measured value - actual value⎥
EXAMPLE
1
Carolyn used her car’s odometer to measure the distance between her house
and her grandmother’s house. Carolyn’s measurement was 1653 miles. The
distance given on a map is 1642.2 miles. Find the absolute error in Carolyn’s
measurement.
absolute error = ⎪measured value - actual value⎥
= ⎪1653 - 1642.2⎥
= 10.8 miles
Use the equation for
absolute error.
Relative error takes into account the size of the measurement by converting the error into
a percent.
absolute error , written as a percent
relative error = __
actual value
EXAMPLE
2
What was the relative error in Carolyn’s measurement?
absolute error
relative error = __
actual value
10.8
=_
1642.2
≈ 0.66%
Use the equation for relative error.
Though the absolute error is 10.8 miles, it is
a relatively small error (less than 1%) when
compared to the total distance measured.
Tolerance is the maximum amount that a measure may vary from an accepted standard.
To find the maximum tolerated value for a measurement, add the tolerance to the
measurement. To find the minimum tolerated value for a measurement, subtract the
tolerance from the measurement. These two values give a tolerance interval.
EXAMPLE
3
A pencil manufacturer specifies that the length of each pencil produced must be
18 cm, with a tolerance of 0.05 cm. What is the tolerance interval?
18 ± 0.05
Add and subtract 0.05.
The tolerance interval ranges from 17.95 cm to 18.05 cm.
PRACTICE
1. Jerome measured the liquid in a filled eye dropper as 0.95 mL. The manufacturer’s label
says the capacity of the eye dropper is 1 mL. What are the absolute and relative errors
in Jerome’s measurement?
2. Julio used a metric ruler to take a measurement of 7.6 cm. The ruler has a precision of
0.1 cm. What is the tolerance interval for Julio’s measurement?
Skills Bank
S55
Points, Lines, Planes, and Angles
A point specifies an exact location in space. A line is a straight path that has no thickness
and extends forever in two directions. A ray is a part of a line that extends forever in one
direction. A plane is a flat surface that has no thickness and extends forever in all directions.
An angle is formed by two rays joined at
their endpoints. Angles are classified by
size and can be measured with a protractor.
Parallel lines are lines in the same plane
that never intersect.
Perpendicular lines intersect to form
right angles.
EXAMPLE
1
Line
Angle
Acute
Obtuse
< 90°
> 90°
Right
Straight
90°
180°
Name a line, angle, ray, or plane. Then name the lines that are parallel or
perpendicular.
Choose two points on the line. Draw a bar with
arrows over the letters.
AB
Use one point on one ray or line, then the vertex,
then a point on the other ray or line.
∠BAC
−−
AC
Ray
Write the endpoint first. Then write another point
the ray passes through.
Plane
Use three points that are not all on the same line
or ray.
plane ABE
Parallel
Choose two lines that will never intersect.
AB
, EG
Perpendicular
Choose two lines that form a right angle.
DF
, EG
EXAMPLE
2
Use a protractor to measure the angle. Then classify the angle.
Align one ray along the base of the protractor, with the
endpoint at the center. Read the protractor where the
second ray crosses it, extending the ray if needed.
120°; obtuse
PRACTICE
Name a line, angle, ray, or plane. Then name the lines that are
parallel or perpendicular.
1. line
2. angle
3. ray
4. plane
5. parallel
6. perpendicular
Use a protractor to measure each angle. Then classify the angle.
7.
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8.
Skills Bank
9.
Complementary and Supplementary Angles
Complementary angles are angles whose measures
add to 90°. ∠1 and ∠2 are complementary.
£
Supplementary angles are angles whose measures
add to 180°. ∠3 and ∠4 are supplementary.
Î {
Ó
Complementary and supplementary angles may or may not be adjacent (have a ray in common).
EXAMPLE
A The angles shown are complementary.
B The two angles that form a draw
Find the unknown angle measure.
¶
bridge are supplementary. One angle
measures 30°. What is the measure of
the other angle?
180 - 30 = 150
The other angle measures 150°.

90 - 20 = 70°
PRACTICE
1. Find the complement and supplement of a 48° angle.
Tell whether each pair of angles is complementary,
supplementary, or neither.
2. ∠1 and ∠4
Ó
3. ∠2 and ∠3
4. ∠1 and ∠2
£
{
5. ∠4 and ∠5
Î
x
Vertical Angles
When two lines intersect, the nonadjacent angles are called vertical
angles. Vertical angles always have the same measure. In the section
of fencing shown, there are two pairs of vertical angles: ∠1 and ∠3, ∠4
and ∠2.
£
{
Ó
Î
EXAMPLE
1
m∠BEC = 70°
m∠AEB = 110°
m∠DEC = 110°
Çä¨
Find the measures of ∠BEC, ∠AEB, and ∠DEC.
∠AED and ∠BEC are vertical.
∠AED and ∠AEB are supplementary.
∠AEB and ∠DEC are vertical.
PRACTICE
1. Name two pairs of vertical angles.
7
6
2. Find m∠PTS, m∠PTQ, and m∠QTR.
*
<
9
+
/
££x¨
8
-
,
Skills Bank
S57
Polygons
A polygon is a closed figure with
three or more sides. The name of a
polygon is determined by its number
of sides.
Number
of Sides
Name
Number
of Sides
Name
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
7
Heptagon
n
n-gon
If all the sides are the same length,
and all the angles have the same
measure, the polygon is a regular
polygon. Sides and angles with the
same measures are marked with the
same symbol.
EXAMPLE
Identify each polygon.
A
The mark on each side indicates that they are
all the same length. The arch inside each angle
indicates that they all have the same measure.
regular hexagon
B
pentagon
PRACTICE
Identify each polygon.
1.
2.
3.
Geometric Patterns
Patterns involving polygons may deal with size, color, position, or shape.
EXAMPLE
Predict the next term:
Each term has one more side than the
previous term. The next term will have
six sides.
hexagon
PRACTICE
1. Predict the next term.
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Skills Bank
2. Describe the missing term.
Congruence
Congruent segments are segments that are the same length.
Congruent angles are angles that have the same measure.
Figures are congruent if all pairs of corresponding angles are congruent and all pairs of
corresponding sides are congruent.
EXAMPLE
Identify the corresponding angles and sides.
∠A ∠D
∠B ∠E
∠C ∠F
−− −−
AB DE
−− −−
BC EF
−− −−
AC DF
The order of the letters in
ABC DEF shows which
angles and sides are congruent.
Congruent sides and angles are also
identified by the same mark.
̱
ÊɁÊ̱ÊÊ
PRACTICE
Identify the corresponding angles and sides.
,
7
1.
2. JKL OPQ
-
/
8
9
Symmetry
A line of symmetry is a line that can be drawn through a plane figure so that the figure on
one side of the line is a reflection of the figure on the other side.
EXAMPLES
A Determine the number of lines of
symmetry.
B The line shown is a line of symmetry.
Draw the reflection.
3 lines of
symmetry
PRACTICE
1. Determine the number
of lines of symmetry.
2. Determine the number
of lines of symmetry.
3. The line shown is a line of
symmetry. Draw the reflection.
Skills Bank
S59
Perimeter
The perimeter of a polygon is the sum of the lengths of its sides. The following formulas can
be used to find the perimeters of rectangles and squares.
Rectangle
2 + 2w
EXAMPLE
1
Square
4s
Find the perimeter of each figure.
A
B
C
nʈ˜°
{ʓ
P = 4s
=4×6
= 24
= 24 ft
EXAMPLE
£Îʈ˜°
Çʓ
ÈÊvÌ
P = 2 + 2w
= (2 × 7) + (2 × 4)
= 14 + 8
= 22
= 22 m
2
£Óʈ˜°
P = 8 + 12 + 13
= 33
= 33 in.
Estimate the perimeter of the figure.
Find the length of the nondiagonal lines.
top: 4 units
left: 4 units
bottom: 9 units
Estimate the length of the diagonal line.
right: ≈ 6 units
Add the lengths of all four sides:
P ≈ 4 + 4 + 9 + 6 ≈ 23 units
PRACTICE
Find the perimeter of each figure.
1.
2.
3.
Îʈ˜°
£xÊvÌ
S60
5.
Skills Bank
ÇÊvÌ
£äÊvÌ
Èʈ˜°
Estimate the perimeter of each figure.
4.
£äÊvÌ
Area
The area of a polygon is the
number of nonoverlapping
square units that will exactly
cover its interior.
1
s2
s: length of one side
Rectangle
w
: length, w: width
Parallelogram
bh
b: base, h: height
1 bh
_
2
b: base, h: height
Triangle
Formulas for the areas of some
polygons are given at right.
EXAMPLE
Square
Trapezoid
1h b + b
_
( 1 2)
2
b 1: top base, b 2: bottom base
h: height
Find the area of each polygon.
A = s2
= 52
= 25
= 25 ft2
A
B
1h b +b
A=_
( 1 2)
2
1 (4)(5 + 7)
=_
2
= 2 × 12
= 24
= 24 in2
xʈ˜°
{ʈ˜°
Çʈ˜°
xÊvÌ
EXAMPLE
2
Estimate the area of the figure.
Count full squares: 21 red squares
Count almost full squares: 8 blue squares
Count squares that are about half full: 6 green squares ≈ 3 full squares
Do not count almost empty purple squares.
Add: 21 + 8 + 3 ≈ 32
A ≈ 32 square units
PRACTICE
Find the area of each polygon.
1.
2.
{ÊvÌ
3.
ȓ
£Óʓ
ʙÊvÌ
£äʈ˜°
nʈ˜°
Estimate the area of each figure.
4.
5.
Skills Bank
S61
Circles
A circle is the set of all points in a plane that are a given distance
from a given point, known as the center. The center names the
circle. The circle shown at right is referred to as circle C.
A diameter is a line segment that passes through the center and
whose endpoints are points on the circle.
ˆ>“iÌiÀ
,>`ˆÕÃ
A radius is a segment whose endpoints are the center of the circle
and a point on the circle. Any radius of a circle is half as long as any
diameter of that circle.
Circumference is the distance around a circle. The ratio of circumference to diameter is the
same for all circles and is denoted by the Greek letter π (pi), which is approximately 3.14.
Circle Formulas
Area: A = πr
Circumference: C = πd or C = 2πr
2
1
EXAMPLE
Find the circumference of each circle. Use 3.14 for π.
C = πd
≈ 3.14(15)
≈ 47.1 ft
A
£xÊvÌ
EXAMPLE
2
A
{ÊvÌ
C = 2πr
≈ 2(3.14)(5)
≈ 31.4 m
B
xʓ
Find the area of each circle. Use 3.14 for π.
A = πr 2
≈ 3.14(4) 2
≈ 3.14(16)
≈ 50.24 ft 2
A = πr 2
≈ 3.14(8) 2
≈ 3.14(64)
≈ 200.96 m 2
B
£Èʓ
PRACTICE
1. The radius of a circle is 13 inches. What is the diameter of the circle? Use 3.14 for π.
2. The diameter of a circle is 22 feet. What is the radius of the circle? Use 3.14 for π.
Find the circumference and area of each circle.
3.
4.
5.
£äʈ˜°
S62
Skills Bank
Îʓ
£ÓÊvÌ
Classify Triangles and Quadrilaterals
A triangle can be classified
according to its angle
measurements or according
to the number of congruent
sides it has.
1
EXAMPLE
Classifying by Angles
Classifying by Sides
Acute
Three acute angles
Scalene
No sides congruent
Right
One right angle
Isosceles
At least 2 sides congruent
Obtuse
One obtuse angle
Equilateral
All sides congruent
Classify each triangle according to its angles and sides.
A
B
£ÓÊV“
C
{ÊV“
™ÊV“
obtuse scalene
acute equilateral
acute isosceles
Quadrilaterals can also be classified according to their sides and angles.
Other Quadrilaterals
Parallelograms
Trapezoid
exactly 1 pair of parallel sides
Parallelogram
2 pairs of parallel,
congruent sides
Isosceles Trapezoid
congruent, nonparallel legs
Rectangle
4 right angles
Kite
2 pairs of adjacent
congruent sides
Rhombus
4 congruent sides
Square
4 right angles and
4 congruent sides
2
EXAMPLE
always
Tell whether the following statement is always, sometimes, or never true:
A square is a rectangle.
A rectangle must have four right angles, and a square always has four right angles.
PRACTICE
Classify each triangle according to its angles and sides.
1.
2.
Îx¨
Îx¨ ££ä¨
3.
{ʈ˜°
Óʈ˜°
{ʈ˜°
Tell whether each statement is always, sometimes, or never true.
4. A rectangle is a square.
5. A trapezoid is a parallelogram.
Name the quadrilaterals that always meet the given conditions.
6. All sides are congruent.
7. Two pairs of sides are congruent.
Skills Bank
S63
Three-Dimensional Figures
>Vi
Polyhedrons are three-dimensional figures made up of polygons
which are called faces. The sides where faces intersect are edges.
Any point where three or more edges intersect is a vertex.
`}i
6iÀÌiÝ
EXAMPLE
1
Tell how many faces, edges, and vertices the figure has.
6 faces
12 edges
8 vertices
ABCD, ABFE, BFHD, DCGH, ACGE, FHGE
−− −− −− −− −− −− −−− −− −− −− −−− −−
AB, BD, DC, AC, AE, BF, DH, CG, EF, FH, HG, EG
A, B, C, D, E, F, G, H
A prism has two faces called bases. The bases are congruent,
parallel polygons. The faces that are not bases are parallelograms.
Pyramids have only one base, and the faces other than the
base are triangles. Both prisms and pyramids are named
according to the polygon that forms the base or bases.
EXAMPLE
2
0YRAMID
>Ãi
Name each figure.
Two congruent bases
Bases are rectangles.
A
0RISM
One base
Base is a pentagon.
B
rectangular prism
Some three-dimensional figures are not polyhedrons
because they are not made up of polygons.
Cones and cylinders have circles as bases. A cone has
one base, and a cylinder has two congruent bases.
pentagonal pyramid
#YLINDER
#ONE
À
…
PRACTICE
Name each figure. If the figure is a polyhedron, tell how
many faces, edges, and vertices the figure has.
1.
2.
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Skills Bank
>Ãi
3.
4.
Draw Three-Dimensional Figures
Three-dimensional figures appear different from different perspectives.
EXAMPLE
1
Side views are shown. Draw each figure as viewed from the bottom.
A
B
Pretend you are directly
below the figure. You
would see only a circle.
EXAMPLE
2
The base would be seen
from a bottom view.
Draw the top, front, and side views of the figure.
Top
Front
Side
From the front, you can
see the faces of 6 cubes
arranged in 3 stacks.
From the side, you can
see the faces of 3 cubes,
one from each stack.
From the top, you can
see the faces of 3 cubes.
PRACTICE
Side views are shown. Draw each figure as viewed from the top.
1.
2.
3.
Side views are shown. Draw each figure as viewed from the top and from the front.
4.
5.
6.
Skills Bank
S65
Volume
The volume of a three-dimensional figure is the
number of nonoverlapping cubic units that will
exactly fill its interior. The formulas for the volumes
of some types of three-dimensional figures are
given in the table.
Notice that a cube is listed in the table. A cube
is a prism, so the formula for a prism can be
used; however, since all sides in a cube are
congruent, the formula s 3 is more convenient.
1
EXAMPLE
{ʈ˜°
Îʈ˜°
Îʈ˜°
2
B: area of base
h: height of prism
Cube
s3
s: length of one side
Pyramid
1
_
Bh
3
B: area of base
h: height of pyramid
Cylinder
πr 2h
r: radius
h: height
1 2
_
πr h
3
r: radius
h: height
Cone
1 Bh
V=_
3
1 ×9×4
=_
3
=3×4
= 12 in 3
Óʓ
B
xʓ
V = πr 2h
≈ 3.14 × (2 2) × 5
≈ 3.14 × 4 × 5
≈ 62.8
62.8 m 3
Estimate the volume of the figure.
xÊvÌ
{ÊvÌ
Bh
Find the volume of each figure. Use 3.14 for π.
A
EXAMPLE
Prism
Find the volume of the rectangular prism (bottom part):
Bh = 21 × 4 = 84
Pretend the top part is a rectangular prism with
w = 3 ft, = 5 ft, and h = 6 ft - 4 ft = 2 ft.
Bh = 15 × 2 = 30.
Add the volumes of the two prisms:
84 + 30 = 114
The volume is approximately 114 ft 3.
ÈÊvÌ
ÎÊvÌ
ÇÊvÌ
PRACTICE
Find or estimate the volume of each figure. Use 3.14 for π.
1.
2.
Îʓ
3.
{ʈ˜°
{ʈ˜°
{ʈ˜°
£äʓ
£äʓ
Çʓ
nʓ
{ʓ
™Ê“
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Skills Bank
Surface Area
The surface area of a three-dimensional
figure is the sum of the areas of its
surfaces.
Prism
Pyramid
Formulas for the surface areas of some
three-dimensional figures are given in
the table.
Cone
1
B: area of base
h: height
1 P
B+_
2
B: area of base
P: perimeter of base
: slant height
6s 2
s: length of one side
Cube
Cylinder
EXAMPLE
2B + Ph
2πr + 2πrh
2
πr 2 + πr
r: radius; h: height
r: radius; : slant height
Find the surface area of each figure. Use 3.14 for π.
A
B
C
Çʈ˜°
™ÊvÌ
ÈÊvÌ
xʈ˜°
xʈ˜°
xÊvÌ
{ʓ
{ÊvÌ
1 P
S=B+_
2
1 (20 × 7)
= 25 + _
2
= 25 + 70
= 95 in 2
S = 2B + Ph
= 2 × 20 + 18 × 9
= 40 + 162
= 202 ft 2
EXAMPLE
2
S = πr 2 + πr
≈ 3.14 × 4 2 + (3.14 × 4 × 6)
≈ 50.24 + 75.36
≈125.6 m 2
The net of a prism is shown below. Estimate the surface area of the prism.
Count full squares: 16 red squares
Count squares that are about half full: 4 blue squares ≈ 2 full squares
Add: 16 + 2 = 18
S ≈ 18 square units
PRACTICE
Find or estimate the surface of each figure. Use 3.14 for π.
1.
2.
ÎÊvÌ
3.
nÊvÌ
™Êˆ˜°
Skills Bank
S67
Pythagorean Theorem
In the right triangle shown, a and b are the lengths of the legs, and c is the
length of the hypotenuse. The Pythagorean Theorem states the following:
If a triangle is a right triangle, then a 2 + b 2 = c 2. The converse of the theorem
is also true: For any triangle, if a 2 + b 2 = c 2, then the triangle is a right triangle.
D Ó
Ó
B
B D
C
Ó
C
1
EXAMPLE
Find the missing measure. Round to the nearest tenth
if necessary.
A
Dʓ
Îʓ
{ʓ
EXAMPLE
2
a2 + b2 = c2 B
32 + 42 = c2
9 + 16 = c 2
25 = c 2
√
25 = c2
5m=c
£äʈ˜°
£Óʈ˜°
Bʈ˜°
a2 + b2 = c2
a 2 + 10 2 = 12 2
a 2 + 100 = 144
Subtract
a 2 = 44
100 from
√
a 2 = √
44
each side.
a ≈ 6.6 in. Round.
a2 + b2 = c2
8 2 + 14 2 20 2
The hypotenuse is always the
longest side.
64 + 196 400
260 400 ✗ The triangle is not a right triangle.
Determine whether a
triangle with side lengths
of 8 cm, 14 cm, and 20 cm
is a right triangle.
PRACTICE
Find the missing measure. Round to the nearest tenth if necessary.
1.
2.
3. A leg is 6 ft long
4. Both legs are
£Óʓ
VÊvÌ
and
the
hypotenuse
20 mm long.
{ÊvÌ
is
10
ft
long.
Bʓ
£Îʓ
ÈÊvÌ
5. Determine whether a triangle with side lengths of 16 ft, 30 ft, and 34 ft is a right triangle.
Midpoint Formula
If a segment in the coordinate plane has endpoints (x 1, y 1) and (x 2, y 2), the coordinates of
(
)
y +y
x 1 + x 2 _____
the midpoint are _____
, 12 2 .
2
EXAMPLE
Find the coordinates of the midpoint of the segment with endpoints A(2, 1) and B(6, 5).
Let (x 1, y 1) = (2, 1).
Let (x 2, y 2) = (6, 5).
y +y
x +x _
2+6 1+5
8, _
6 = 4, 3
,
= _, _ ) = (_
( )
(_
2
2 ) ( 2
2
2 2)
1
2
1
2
PRACTICE
−−
Find the coordinates of the midpoint of segment AB.
1. A(0, 5), B(-4, 3)
2. A(6, -2), B(3, -8)
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Skills Bank
3. A(4, 9), B(-2, -3)
Transformations in the Coordinate Plane
A transformation is a change in the size or position of a figure. If the preimage, or
original figure, is named ABC, then the transformed figure, or image, is named AB C .
Transformations include translations (slides), reflections (flips), and rotations (turns),
for which preimages and images are congruent.
1
EXAMPLE
A Translate ABC 2 units
B Reflect ABC across the
right and 1 unit up.
Þ
{
y-axis.
{
Þ
Þ
Ý
{
Ó
£
about point A.
Ī
Î
Ī
£
Ó
Î
2
Ó
£
{
Ī
Ī
Ó
Ó
Î
Ý
{
£
Ī
Ī
Ī
È
Ó
Ý
{
Move each vertex 2 units
right and 1 unit up.
EXAMPLE
Ó
Ī
C Rotate ABC 90° clockwise
The y-axis is a line of symmetry.
A is the same as A. Maintain the
same side lengths on the image.
Could ABCD be transformed into ABCD ? Explain.
{
The figures are congruent, so a translation, rotation, or reflection is
possible. Study the figures. If A B C D is translated 1 unit right,
both figures would be symmetric about the x-axis.
ABCD can be transformed into AB C D by reflecting it
across the x-axis and translating it 1 unit left.
Þ
Ó
Ó
Ī
Ī
Ó
Ī
{
Ý
{
È
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PRACTICE
1. Translate ABCD 2 units left and 4 units down.
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2. Graph triangle ABC with vertices A(1, -2), B(3, -2), and C(2, -4).
Rotate ABC 90° counterclockwise about A and reflect it across the x-axis.
Use the graph for Exercises 3 and 4.
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3. Could ABCD be transformed into AB C D ? Explain.
Ī
4. Could FGHJKL be transformed into F G H J K L? Explain.
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Skills Bank
S69
Dilations in the Coordinate Plane
A dilation is a transformation that changes the size, but not the shape, of a figure.
A scale factor, k, describes how much a figure is enlarged or reduced.
Every dilation has a fixed point, C, that is the center of dilation.
If a dilation with center C and scale factor k is applied to
the preimage, point P(x, y), then the image will be point (kx, ky).
Ž­
*®
*Ī
*
If k is the scale factor and C is the center of the dilation:
«Àiˆ“>}i
Vi˜ÌiÀʜv
• when ⎪k⎥ > 1, the dilation is an enlargement.
`ˆ>̈œ˜
⎪
⎥
• when 0 < k < 1, the dilation is a reduction.
.
• when k is positive, k(x, y) = (kx, ky) and (kx, ky) lies on CP
.
• when k is negative, ⎪k⎥(x, y) = (kx, ky) and (kx, ky) lies on the ray opposite CP
ˆ“>}i
EXAMPLES
−−
A Sketch the dilation image of AB with center C and scale factor __13 .
k is between 0 and 1, so it is a reduction.
−−− 1
−−
Draw A so that the length of CA is _
the length of CA, and draw B 3
−−− 1
−−
so that the length of CB is _
the length of CB.
3
Ī
Ī
B The preimage is blue. The image is shown in red. What scale factor, with center C,
was used?
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Count the blocks from C to a point on the image and then from
C to a point on the preimage that is on the same ray. Find the ratio.
{
8 = 2.
The scale factor was _
4
n
n
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n
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PRACTICE
1. Sketch the dilation image of MNO with
center C and scale factor 4.
2. The preimage is blue. The image is red.
What scale factor, with center C, was used?
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S70
Skills Bank
{
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Line Plots
How often a data value occurs in a data set is called its frequency. A line plot is a graph
made up of a number line and columns of X’s (or other markers) to show frequency. Line
plots make it easy to identify gaps and clusters in a data set. A gap is a large empty space in
a graph. A cluster is an isolated group of data values bunched together.
EXAMPLE
Twenty people went on a tour. Their
ages are shown in the frequency table.
Create a line plot. Identify any gaps
and clusters.
Draw a number line that includes the minimum and
maximum data values. Use an X to represent each person.
Draw each X the same size.Title the axis and the graph.
Age
Frequency
Age
Frequency
15
2
21
0
16
0
22
3
17
1
23
4
18
1
24
5
19
1
25
1
20
0
26
2
*iœ«iʜ˜Ê̅iÊ/œÕÀ
There is a gap between 19 and 22.
There is a cluster from 22 through 26.
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PRACTICE
Create a line plot for each data set. Identify any gaps and clusters.
1.
High Temperatures for Two Weeks
Temperature
Frequency
Temperature
Frequency
55
2
60
0
56
0
61
2
57
0
62
4
58
0
63
3
59
2
64
1
2. scores on a math test: 75, 81, 82, 84, 92, 76, 77, 77, 81, 75, 95, 83, 84, 90, 84, 76, 76
Use the line plot for Exercises 3–6.
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3. What are the minimum and maximum prices?
4. What is the most common price?
5. Where is the largest cluster?
6. Where is the largest gap?
Skills Bank
S71
Measures of Central Tendency
Measures of central tendency are values that represent the center of a data set and can be
considered typical of the set. These measures are the mean, median, and mode.
It is…
Find by…
Mean
The average.
Adding the data values and dividing by the number of values.
Median
The “middle value.”
First ordering the data values from least to greatest.
If there are an odd number of values, the median is the middle number.
If there are an even number of values, the median is the mean of the
two middle values.
Mode
The value or values that
occur most often. If every
value occurs the same
number of times, the data
set has no mode.
Choosing the value or values that occur more often than any other.
EXAMPLES
Find the mean, median, and mode of each data set.
A 18, 22, 13, 16, 15, 18, 10
B These are the number of people who attended a
seminar each of four days: 102, 96, 88, 109.
mean:
102 + 96 + 88 + 109 395
mean: __ = _
= 98.75
4
4
The mean is 98.75.
median:
18
+ 22 + 13 + 16 + 15 + 18 + 10 _
____
= 112 = 16
7
7
The mean is 16.
median:
Order the data values from least to greatest.
There are an even number of values. Find the
mean of the two middle numbers.
Order the data values from least to greatest.
There are an odd number of values. Choose the
middle number.
88, 96, 102, 109
10, 13, 15, 16, 18, 18, 22
96 + 102 _
_
= 198 = 99
2
2
The median is 99.
mode:
The median is 16.
mode:
Every value occurs once except 18, which
occurs twice.
Every value occurs once.
The mode is 18.
There is no mode.
PRACTICE
Find the mean, median, and mode of each data set.
1.
High Temperatures (°F)
Sun
Mon
Tue
Wed
Thu
Fri
Sat
85
81
83
85
86
82
84
2. These are the ages of the students in an after-school club:
14, 15, 14, 16, 15, 17, 14, 15.
3. Jenny took a survey of her classmates to find out how much they each paid for their
notebooks. Here are their responses: 85¢, 55¢, 80¢, 85¢, 75¢, 95¢, 85¢, 75¢, 67¢.
S72
Skills Bank
Sampling
A population is a group that someone is gathering information about.
A sample is part of a population. For example, if 5 students are chosen to represent a class
of 20 students, the 5 chosen students are a sample of the population of 20 students.
The sample is a random sample if every member of the population had an equal chance of
being chosen.
EXAMPLE
Explain whether each sample is random.
A Carlos wrote the name of each student
in his class on a slip of paper and put the
papers into a hat. Then, without looking
at the slips, he drew the names of the
students who would complete his survey.
Each name is in the hat once, so each has
an equal chance of being selected. The
sample is random.
B Jamal telephoned people on a list of
100 names in the order in which they
appeared. He surveyed the first 20
people who answered their phone.
Names at the beginning of the list have
a greater chance of being selected than
those at the end of the list, so the sample
is not random.
PRACTICE
Explain whether each sample is random.
1. Rebecca surveyed every person in a theater who was sitting in a seat along the aisle.
2. Inez assigned 50 people a number from 1 to 50. Then she used a calculator to generate
10 random numbers from 1 to 50 and surveyed those with matching numbers.
Bias
Bias is error that favors part of a population and/or does not accurately represent the
population. Bias can occur from using sampling methods that are not random or from
asking confusing or leading questions.
EXAMPLE
Explain why each survey is biased.
A Jenn went to a movie theater and asked
people who exited if they agree that the
theater should be torn down to build
office space.
People usually only go to movies if they
enjoy them, so those exiting a movie
theater would not want it torn down.
People who do not use the theater did
not have a chance to answer.
B A student asked, “A new cafeteria would
mean that loud construction would
take place for several weeks. Also, the
hallways would become even more
congested in that area. Do you want a
new cafeteria?”
The question only mentions the bad
things that could come from a new
cafeteria, not the good ones, such as
better food or more seats.
PRACTICE
Explain why each survey is biased.
1. A surveyor asked, “Is it not true that you do not oppose the candidate’s views?”
2. Brendan asked everyone on his track team how they thought the money from the athletic department
fund-raiser should be spent.
Skills Bank
S73
Standard Deviation and the Normal Curve
The standard deviation of a data set is a number that describes how spread out the data
values are from the mean. Suppose two tests are given and both have the same mean
score, but the standard deviations are 2.5 and 6.8. The scores on the test with the standard
deviation of 6.8 are more spread out than the scores on the test with the standard deviation
of 2.5.
EXAMPLE
1
Find the standard deviation of the following data set: 6, 5, 6, 7, 2, 4. Round to the
nearest hundredth.
Step 1 Find the mean. (6 + 5 + 6 + 7 + 2 + 4) ÷ 6 = 5
Step 2 Square the difference between each data value and the mean. Use a table to organize the
information.
Data Value
Data Value – Mean
2
(Data Value – Mean)
6
5
6
7
2
4
6-5=1
5-5=0
6-5=1
7-5=2
2 - 5 = -3
4 - 5 = -1
1 =1
0 =0
1 =1
2 =4
(-3) = 9
(-1)2 = 1
2
2
2
2
2
−
1 + 0 + 1 + 4 + 9 + 1 16
Step 3 Find the mean of the squares of the differences. __ = _
= 2.6
6
6
−
Step 4 Take the square root of the quotient. √
2.6 ≈ 1.63
The standard deviation is approximately 1.63.
Some data sets are normally distributed, which means the
graph of the distribution is a bell-shaped curve with the mean
Èn¯
at the center. In a normal distribution:
• 68% of data fall within one standard deviation of the mean.
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™™°Ç¯
• 95% of data fall within two standard deviations of the mean.
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• 99.7% of data fall within three standard deviations of the mean.
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EXAMPLE
2
The heights of 1000 men are normally distributed,
with a mean of 70 inches and a standard deviation
of 3 inches. Between what heights do the middle 95%
of the men fall?
Sketch a normal curve with 70 at the center.
Label the standard deviations above and below
the mean by repeatedly adding or subtracting 3.
Because 95% of the data fall within two standard
deviations, the heights of the middle 95% of the
men fall between 64 inches and 76 inches.
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PRACTICE
Find the standard deviation of each data set.
1. 12, 15, 20, 16, 32, 25
2. 10, 15, 9, 5, 8, 6, 10
3. A collection of test scores are normally distributed, with a mean of 80 and a standard
deviation of 5. In what range do the middle 68% of the test scores lie?
4. The scores on a certain test are normally distributed, and 99.7% of the test takers
scored between 92 and 128. The standard deviation is 6. What is the mean score?
S74
Skills Bank
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Cubic Functions
A cubic function contains a variable that is raised to the third power.
The parent function is y = x 3. Its graph is shown at right. Cubic equations
such as x 3 - 2 = 0 can be solved by graphing the related function
(y = x 3 - 2). Then the solution is the x-value where y = 0.
EXAMPLE
ÞÊÊÝÎ
Graph the function y = 2x 3. Use the graph to solve the
equation 2x 3 = 0.
Create a table of ordered
pairs. Then plot each
point and connect them
with a smooth curve.
To solve 2x 3 = 0, find
the value of x when y = 0.
The solution is x = 0.
(x, y)
y = 2x 3
x
-2
2(-2)3 = 2(-8) = -16
-1
2(-1) = 2(-1) = -2
3
0
2(0) = 2(0) = 0
1
2(1)3 = 2(1) = 2
2
2(2)3 = 2(8) = 16
3
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(-2, -16)
(-1, -2)
(0, 0)
(1, 2)
(2, 16)
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PRACTICE
Graph each cubic function.
1 x3
1. y = x 3 - 2
2. y = _
3. y = x 3 + 1
4. y = -x 3
2
5. Use a graphing calculator to estimate the solution of 0 = x 3 + 4x - 8 to the nearest tenth.
Step Functions
A step function is a function whose graph looks like a series of steps. The graph of a step
function is made up of unconnected line segments.
At a garage, parking costs $5.50 for each hour or fraction of an hour.
After 4 hours it costs $25.00 to park for any amount of time up to 8 hours.
Graph this step function.
Create a table. Use x-values to
represent time and y-values to
represent the costs for those times.
On the graph, an open circle
indicates a value that is not
included, and a closed circle
indicates a value that is included.
x
y
0<x≤1
$5.50
1<x≤2
$11.00
2<x≤3
$16.50
3<x≤4
$22.00
4<x≤8
$25.00
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EXAMPLE
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PRACTICE
1. A bookseller gives discounts for book purchases made online and the amount of the
discount is based on the cost of the book. A $2 discount is applied to books costing at
least $20 but less than $50. A $5 discount is applied to books costing at least $50 but
less than $100, and a $10 discount is applied to books costing at least $100. No book
costs more than $150. Graph this step function.
Skills Bank
S75
Conditional Statements
If-then statements are called conditional statements. The phrase that follows if is called the
hypothesis, and the phrase that follows then is called the conclusion.
If the hypothesis is true, the conclusion is also true.
If the conclusion is true, the hypothesis may or may not be true.
EXAMPLE
A Identify the hypothesis and conclusion: If it is raining, then Jim will go to the movies.
Hypothesis: It is raining today.
Conclusion: Jim will go to the movies.
B If it is raining, then Jim will go to the movies. It is raining. What can you conclude? Explain.
Jim will go to the movies. The hypothesis is true, so the conclusion is also true.
C If it is raining, then Jim will go to the movies. Jim goes to the movies. What can you conclude? Explain.
Nothing can be concluded. Jim may have gone to the movies for reasons other than rain.
PRACTICE
1. Identify the hypothesis and conclusion: If it is Thursday, then Paulo has soccer practice.
2. If it is Thursday, then Paulo has soccer practice. Paulo has soccer practice today.
What can you conclude? Explain.
3. Identify the hypothesis and conclusion: All dogs have four legs. (Hint: Write in if-then
form first.)
4. All dogs have four legs. Barry is a dog. What can you conclude? Explain.
Counterexamples
Conjectures are guesses and could be either true or false. If a conjecture is true, then it is
always true. Therefore, just one example is enough to prove a conjecture false. An example
that proves a conjecture false is called a counterexample.
EXAMPLE
Find a counterexample for each conjecture.
A If the clock reads 5:55, then it is early in
the morning.
Counterexample: It could be 5:55 P.M.
B If xy is a positive number, then x and
y are both positive.
Counterexample: (-2)(-3) = 6
PRACTICE
Find a counterexample for each conjecture.
1. If an integer is divisible by 2, then it is also divisible by 4.
2. If the DVD recorder did not record the program, then the recorder is broken.
S76
Skills Bank
Inductive and Deductive Reasoning
Inductive reasoning involves examining a set of data to determine a pattern and then
making a conjecture about the data. Sometimes inductive reasoning can lead to different
conclusions. In contrast, deductive reasoning uses logical reasoning based on given
statements that are assumed to be true.
EXAMPLE
1
Use inductive reasoning to predict the value of the 100th term in the sequence 1, 5,
9, 13, 17, … .
Examine the numbers and look for a pattern.
Term
1st
2nd
3rd
4th
5th
Value
1
5
9
13
17
1 + (0)(4)
1 + (1)(4)
1 + (2)(4)
1 + (3)(4)
1 + (4)(4)
Pattern
Each term is 4 more than the previous term. The rule 1 + (n - 1)(4) can be used to find any term n.
So a reasonable prediction for the value of the 100th term is 1 + (99)(4) = 397.
EXAMPLE
2
Use deductive reasoning to make a conclusion based on the given statements.
Given: If it is raining, the grass is wet.
Given: It is raining.
Conclusion: The grass is wet.
Hypothesis: It is raining.Conclusion:
The grass is wet.
If the hypothesis is true, the conclusion
is always true.
PRACTICE
Use inductive reasoning to predict the value of the given term in each sequence.
1. 100th term: 2, 4, 6, 8, 10, …
2. 50th term: 5, 10, 15, 20, 25, ...
3. 28th term: 0, 3, 6, 9, 12, ...
4. 77th term: 12, 8, 4, 0, -4, ...
Use deductive reasoning to make a conclusion based on the given statements.
5. Given: Darla bowls in a bowling league every Tuesday.
Given: Today is Tuesday.
6. Given: A quadrilateral with two pairs of parallel sides is a parallelogram.
Given: A rectangle is a quadrilateral with two pairs of parallel sides.
Determine if the reasoning used was inductive or deductive. Explain.
7. Sandra visited San Diego four times. Each time it was raining. Sandra concludes, “San
Diego is a very rainy city.”
8. Charlie’s mother told him that if he wants to go out Friday night, then he has to clean his
room. Charlie wants to go out Friday night. He concluded that he has to clean his room.
9. Looking at the series 3, 9, 27, 81, ..., Trina concludes that the next number is 243
because each term is three times the previous term.
Skills Bank
S77
Set Theory
A set is a collection of objects. Each object is called an element of the set. A set can have no elements, a
finite number of elements, or an infinite number of elements. A set that contains no elements is called the
⎧⎫
null or empty set. The null set is symbolized by or ⎨ ⎬.
⎩⎭
Set A is a subset of set B (A ⊂ B), if each element of A is also in B.
The intersection of sets A and B (A B), is the set of all elements that are in both A and B.
The union of A and B (A B), is the set of all elements that are in A or B.
EXAMPLE
Tell whether A ⊂ B. Then find A B and A B.
⎧
⎫
⎧
⎫
A = ⎨ 2, 7, 8, 10 ⎬; B = ⎨ 2, 5, 7, 8, 9, 11, 13 ⎬
⎩
⎭
⎩
⎭
AB
10 is an element of A but not an element of B.
⎧
⎫
A B = ⎨ 2, 7, 8 ⎬
2, 7, and 8 are in both sets.
⎩⎧
⎭
⎫
A B = ⎨ 2, 5, 7, 8, 9, 10, 11, 13 ⎬
Elements belonging to both sets are listed only once.
⎩
⎭
PRACTICE
Tell whether A ⊂ B, B ⊂ A, or neither. Then find A B and A B.
⎧
⎫
⎧
⎫
1. A = ⎨ red, blue, yellow ⎬; B = ⎨ green, red ⎬
⎩⎧
⎭⎧
⎩ ⎫
⎭
⎫
2. A = ⎨ 2, 14, 15, 20 ⎬; B = ⎨ 2, 20 ⎬
⎩
⎭
⎩
⎭
Field Properties
The table shows properties of addition and multiplication where a, b, and c are real numbers.
A property is said to hold for a set of numbers if it is true for each element of the set.
EXAMPLE
1
Name the property shown by
25 + (-25) = 0.
Addition
Multiplication
Commutative
a+b=b+a
ab = ba
Associative
(a + b) + c =
a + (b + c)
(ab)c = a(bc)
Inverse
a + (-a) = 0
1
a×_
a = 1, a ≠ 0
Identity
a+0=a
a×1=a
Closure
a + b is a real
number.
ab is a real number.
Inverse Property of Addition
EXAMPLE
2
Does the Closure Property
hold for the set of negative
integers under multiplication?
Justify your answer.
No; (-2)(-3) = 6, and since 6 is not an element
of the set of negative integers, the property does
not hold.
Distributive
a(b + c) = ab + ac
PRACTICE
Name the property shown.
1. 7 + 4 = 4 + 7
2. 23 × 1 = 23
3. 2(4 + 7) = 8 + 14 4. (9 × 3)2 = 9(3 × 2)
Tell whether the Closure Property holds for each set under the given operation. Justify your answer.
5. whole numbers; multiplication
⎧
⎫
6. ⎨ 1, 2, 3 ⎬; addition
⎩
⎭
S78
Skills Bank
Selected Answers
Chapter 1
81. c divided by d; the quotient of c
and d 83. __52 85. 280
1-3
Check It Out! 1a. -7 1b. 44
1-1
Check It Out! 1a. 4 decreased by
n; n less than 4 1b. the quotient of
t and 5; t divided by 5 1c. the sum
of 9 and q; q added to 9 1d. the
product of 3 and h; 3 times h
2a. 65t 2b. m + 5 2c. 32d 3a. 6
3b. 7 3c. 3 4. a. 63s, b. 756 bottles;
1575 bottles; 3150 bottles
Exercises 1. variable 3. the
quotient of f and 3; f divided
by 3 5. 9 decreased by y; y less
than 9 7. the sum of t and 12; t
increased by 12 9. x decreased by
3; the difference of x and 3
11. w + 4 13. 12 15. 6 17. the
product of 5 and p; 5 groups
of p 19. the sum of 3 and x; 3
increased by x 21. negative 3
times s; the product of negative 3
and s 23. 14 decreased by t; the
difference of 14 and t 25. t + 20
27. 1 29. 2 31a. h - 40, b. 0; 4; 8;
12 33. 2x 35. y + 10 37. 9w; 9 in 2;
72 in 2; 81 in 2; 99 in 2 39. 13; 14; 15;
16 41. 6; 10; 13; 15 43a. 47.84 + m;
b. 58.53 - s 45. x + 7; 19; 21
47. x + 3; 15; 17 49. F 51. 36
53. 1 55. 45° 57. 90° 59. __12 61. 1
63. Multiply the previous term by 3;
729, 2187, 6561.
1-2
Check It Out! 1a. 4 1b. -10
1c. 1.5 2a. -12 2b. -35.8
2c. -16 3a. -8 3b. 4 3c. -2
4. 13,018 ft
Exercises 1. opposite 3. -8.5
5. 9 __14 7. 1 9. -13 11. -1 __35
13. 4 15. -11 __34 17. -30 19. 14
21. - __12 23. 23°F 25. 0.75
27. -12 __25 29. -12 31. 37 33. 0
1
35. __
37. > 39. > 41. <
10
43. 11,331 ft 45. always 47. A
51. F 53. -9 55. 2 57. Subtract 4;
-2, -6, -10. 59. 12,660.5 ft
61. 44 in2 63. 13 cm 65. 12 67. 4
1
1c. -42 2a. __
2b. - __14 2c. - __12
12
3a. 0 3b. undefined 3c. 0 4. 7.875 mi
Exercises 3. -121 5. 7 7. -2
9. undefined 11. 0 13. about
$210,000,000 15. -32 17. - __35
19. 3 21. 0 23. 0 25. -15°F
27. -4 29. -62 31. 18.75
33. 1 35. -12 37. 6 39. negative
41. negative 43. positive
45. undefined 47. 1 49. __12
51. - __15 53. __98 55. 15 h per
semester 57. < 59. < 61. =
63a. positive b. negative c. The
product of two negative numbers
is positive. The product of that
positive number and a negative
1
number is negative. d. no 65. 75 __
15
1
67. -121 __
69. sometimes
11
25
73. B 75. 16 quarter notes 77. __
49
27
__
79. 5 81. 1 83. - 64 85. Multiply by
-2; -16, 32, -64. 87. The numbers
are alternating positive and
negative multiples of 5; 30,
-35, 40. 89. $85 91. hexagon
93. triangle 95. -6 97. 8
( )
( )
1-4
Check It Out! 1a. 2 2 1b. x 3
27
2a. -125 2b. -36 2c. __
3a. 8 2
64
3
3b. (-3) 4. 2 8 = 256
Exercises 1. the number of times
to use the base as a factor 3. 2 3
5. 49 7. -32 9. 9 2 11. (-4)3
13. 3 4 15. 3 5 = 243 17. 3 3 19. 27
21. -16 23. 7 2 25. (-2) 3 27. 4 3
29. 2 4 = 16 31. < 33. = 35. =
1
37. > 39. 8 41. -64 43. -1 45. __
27
2
2
2
47a. 36 in b. 9 in c. 27 in 49. 6 2
3
4
51. (-1) 53. __19
55. between
( )
8000 cm3 and 15,625 cm 3 57. 2
59. 4 61. 2 63. 4 65a. 100, 1000,
10,000 b. The exponent is the
same as the number of zeros in
the number. 67. C 69. B 71. 64
73. 65,536 75a. 4 · 4; 4 · 4 · 4
b. 4 · 4 · 4 · 4 · 4 = 4 5 c. 2 + 3 = 5;
the sum of the exponents in 4 2 and
4 3 is the exponent in the product 4 5.
77. 5 79. 5 minus x; x less than 5
1-5
Check It Out! 1a. 2 1b. -5
2. about 6.2 3a. rational number,
repeating decimal 3b. rational
number, terminating decimal,
integer 3c. irrational number
Exercises 1. any negative
integer 3. 15 5. 13 7. rational
number, terminating decimal,
integer 9. irrational number
11. 11 13. -10 15. 14.9 yd
17. rational number, terminating
decimal, integer, whole number,
natural number 19. irr. 21. >
23. = 25. 6 in. 27. 45; rational
number, terminating decimal,
integer, whole number, natural
number 29. 34.625; rational
number, terminating decimal
31. always 33. always
35. whole numbers 37. positive
rational numbers 39. positive
rational numbers 41. irrational
numbers 43a. c 2 = 169; c = 13
b. 130 ft 45. A 47. B 49. 0.5 51. 1.5
53. no 55. 168 in 3 57. __12 59. -81
61. 196
1-6
Check It Out! 1a. 48 1b. 2.6
1c. 2 2a. 15 2b. 3 3a. 1 3b. -3
3c. 21 4. 6.2(9.4 + 8) 5. 400
Exercises 3. 15 5. -9
7. 14 9. 1 11. 14 13. 92 15. 1.5
17. -3 19. -22 21. 12(-2 + 6)
23. 188.4 ft2 25. 19 27. -15 29. 3
31. -5 33. 24 35. 17 37. -9
39. 17 41. -7 43. 0 45. __14 47. 1
49. 6 51. 3 - __25 53. 8 - ⎪3 · 5⎥
55a. 55 b. 498 c. 250 d. 10 e. 30
√7
f. 70 57. 2⎡⎣9 + (-x)⎤⎦ 59. ____
3 · 10
63. 3 · 5 - 6 · 2 = 3 69. H 71. -3
73. 6 77. 20 79. acute 81. 100
83. -11 85. 8 87. __67
1-7
Check It Out! 1a. 21 1b. 560
1c. 28 2a. 9(50) + 9(2) = 468
2b. 12(100) - 12(2) = 1176
Selected Answers
S79
2c. 7(30) + 7(4) = 238 3a. 100p
3b. -28.5t 3c. 3m 2 + m 3
4a. 6x - 15 4b. 3a - 16x
Exercises 1. Associative Property of
Addition 3. 24 5. 56 7. 118,000 9. 304
11. 456 13. 763 15. 20x 17. -9r
19. 7.9x 21. 9a - 31 23. 7x - 3x 2
25. 2a + 2 39. -3x - 14
43. 13y - 10 45a. Amy: 98:21;
Julie: 81:12; Mardi: 83:39; Sabine:
63:47 b. Sabine, Julie, Mardi, Amy
47. Commutative Property of
Addition 49. Distributive Property
51. Distributive Property 53. 6p + 9
57a. equal b. 96π c. 2(16π) + 96π
= 128π 59. J 61. 12x + 116
63. -3b - 7 65a. Commutative
Property of Addition b. Associative
Property of Addition c. Distributive
Property d. Rule for subtraction
67. 36 ft 2 69. 64
1-8
T y
S
x
R
2a. none 2b. I 2c. III 2d. II
3. y = 10 + 20x; (1, 30), (2, 50),
(3, 70), (4, 90) 4a. (-4, -6),
(-2, -5), (0, -4), (2, -3), (4, -2);
line 4b. (-3, 30), (-1, 6), (0, 3),
(1, 6), (3, 30); U shape 4c. (0, 2),
(1, 1), (2, 0), (3, 1), (4, 2); V shape
Exercises 7. none 9. none 11. I
13. (-2, 0), (-1, 1), (0, 2), (1, 3),
(2, 4); line 15. (-2, -4), (-1, -2),
(0, 0), (1, -2), (2, -4); V shape
21. none 23. none 25. II
27. y = 500 + 0.10x; (500, 550),
(3000, 800), (5000, 1000),
(7500, 1250) 29. (-2, -4), (-1, -1),
(0, 0), (1, -1), (2, -4); U shape
31. (-2, 7), (-1, 4), (0, 3), (1, 4),
(2, 7); U shape 33. triangle
35. rectangle 37a. f = yards;
c = total cost; c = 2.90f b. f is input;
c is output.
S80
f
c
1
2
3
4
5
6
7
8
2.90
5.80
8.70
11.60
14.50
17.40
20.30
23.20
d. 7 yards 39. y = __12 x + (-3);
(-4,-5), (-2, -4), (0, -3), (2, -2),
(4, -1); line 41a. y = 50 + 1.5x
b. (100, 200); (150, 275); (200, 350);
(250, 425); (300, 500) 43. line
45. line 51. G 53. H 57. (-4, 4)
59. The points make a horizontal
line at y = 6. 61. (-4, 5); 42 square
units 63. cylinder 65. pentagon
67. irrational 69. rational,
terminating decimal, integer
71. x 2 + 3x
Study Guide: Review
Check It Out!
1a.
1b.
1c.
c.
Selected Answers
1. constant 2. whole numbers
3. coefficient 4. origin 5. 1.99g
6. t + 3 7. 5 8. 5 9. 6 10. 150 ÷ m;
30; 25; 15 11. -14 12. -4.6
13. 4 __12 14. -1 15. -24 16. 14.3 17. 5
18. 2231 ft 19. 90 20. 0 21. -15.2
22. -8 23. 0 24. undefined 25. 9
15
26. - __23 27. __
28. 3,650,000 steps
7
29. 64 30. -27 31. 81 32. -25
8
16
33. __
34. __
35. 2 4 36. (-10)3
27
25
2
37. (-8) 38. 12 1 39. 729 in3 40. 6
1
41. 14 42. -7 43. -12 44. __56 45. __
13
46. rational number, terminating
decimal, integer, whole number,
natural number 47. rational
number, terminating decimal,
integer, whole number 48. rational
number, terminating decimal,
integer 49. rational number,
terminating decimal 50. irrational
number 51. rational number,
repeating decimal 52. 3.6 ft 53. 23
54. 8 55. 6 56. __12 57. -18 58. 0
59. 62 60. 10 61. 8 62. 10
12
63. 8 + 7(-2) 64. ____
65. 4 √
20 - x
8+3
66. 168 ft 67. 40 68. 270
69. 13(100) + 13(3) = 1339
70. 18(100) - 18(1) = 1782 71. 4x
72. 7y 2 73. 4x + 24 74. 2x 2 + 2
75. -4y + 3y 2 76. 8y - a
77. $8.84
78–81.
B
y
C
A
x
D
82. I 83. IV 84. I 85. II 86. III
1
87. IV 88. y = p + __
p; $2.10; $15.75;
20
(
)
$31.50; $42.00 89. (-4, 4), -1, __14 ,
(0, 0), 1, __14 , (4, 4); U shape
( )
Chapter 2
2-1
Check It Out! 1a. 8.8 1b. 0 1c. 25
2a. __12 2b. -10 2c. 8 3a. 9.3 3b. 2
3c. 44 4. 35 years old
Exercises 3. 21 5. 16.3 7. __12 9. 0
17
11. 2.3 13. 1.2 15. 32 17. 3.7 19. __
6
4
__
21. 9 23. 17 25. 7 27. 10.5 29. 9
31. 0 33. -17 35. -3100 37. -0.5
39. 0.05 41. 15 43. 1545 45. 30
47. __13 49. a + 500 = 4732; $4232
51. x - 10 = 12; x = 22 53. x + 8 =
16; x = 8 55. 5 + x = 6; x = 1
57. x - 4 = 9; x = 13 59. m + 560 =
1680; $1120 61. 63 + x = 90;
x = 27 63. x + 15 = 90; x = 75
12
65. h - 47 = 28; 75 69. J 71. - __
5
13
__
73. - 12 75. 10 77. 90 79. 9 81. 72
83. 6 ft 85. -80 87. -3
2-2
Check It Out! 1a. 50 1b. -39
1c. 56 2a. 4 2b. -20 2c. 5 3a. - __54
3b. 1 3c. 612 4. 15,000 ft
Exercises 1. 32 3. 14 5. 19 7. 7
9. 5 11. 2.5 13. 14 15. -9 17. __18
19. 16c = 192; $12 21. 24 23. -36
25. -150 27. 55 29. -3 31. 1
33. 13 35. 0.3 37. 2 39. -16 41. -3.5
7
43. -2 45. __
s = 392; $560
10
49. 4s = 84; 21 in. 51. 4s = 16.4;
4.1 cm 53. -3x = 12; x = -4
55. __3x = -8; x = -24 57. 6.25h = 50;
8 h 59. 0.05m = 13.80; 276 min
61. -2 63. 0; 8y = 0; 0 65a. number
of data values c. 185,300 acres
3
67. 7 69. 605 71. __
73. 5.7
16
2
75. __3 g = 2; 3 g 77. D 79. B
81a. 6c = 4.80 b. c = $0.80 83. 2
85. 9 87. 2 89. -20 91. -132
93. Multiply both sides by a. 95. 12
97. 25 99. 6 years old 101. 6 103. 16
2-3
(
35. C 37. D 39. a = __52 c + __34 b
(
)
)
3
3
47. 0.006; ___
49. 0.5 is
45. 0.06; __
50
500
v -u
41. d = 500 t - __12 43. s = ______
2a
2
2
45. 120 s 47. 12 49. -6 51. 20 53. 12
2-6
Check It Out! 1a. 1 1b. 6 1c. 0
55
2a. __
2b. __12 2c. 15 3a. - __56 3b. 5
4
3c. 8 4. $60 5. -42
Exercises 1. 2 3. -18 5. 2 7. 66
9. __54 11. -12 13. 16 15. -3.2 17. 4
19. 15 passes 21. 4 23. -4 25. 4
27. 5 29. -9 31. __14 33. 1 35. 3
28
37. __
39. 3 41. 8 43. 7 45. - __12
5
47. x = 40 49. x = 35
51. 8 - 3n = 2; n = 2
53a. 1963 - 5s = 1863; s = 20 53b. 3
55. 8 57. 4.5 59. -10 61. 10
63. 5k - 70 = 60; 26 in. 65. Stan: 36;
Mark: 37; Wayne: 38 67a. 45,000;
112,500; 225,000; 337,500; 225n
67b. c = 225n 71. H 73. 27 75. 6 __15
77. 14.5 79. -6 81. irrational
83. repeating decimal, rational
85. 8(60) + 8(1) = 488 87. 11(20)
+ 11(8) = 308 89. 13 91. -18
2-4
Check It Out! 1a. -2 1b. 2
2a. 4 2b. -2 3a. no solution
3b. all real numbers 4. 10 years old
Exercises 1. contradiction 3. 1
5. 40 7. - __23 9. 3 11. no solution
13. all real numbers 15. 6 17. 6
19. 2.85 21. 10 23. 6 25. 14 27. __34
29. -4 31. no solution 33a. 15 weeks
33b. 180 lb 35. x - 30 = 14 - 3x;
x = 11 37. -4 39. 7 41. -3 43. 2
45. 1 47. - __75 49. 4 51. no solution
53. 9 59. F 61. H 63. 2 65. no
solution 67. -20 69. 6, 7, 8 71. $1.68
73. 3y cm 75. -63 77. 4 79. 2
81. -125 83. 15 85. 3
2-5
Check It Out! 1. about 1.46 h
5-b
m
2. i = f + gt 3a. t = ____
3b. V = __
2
D
V
Exercises 3. w = __
5. m = 4n + 8
h
10
7. a = ____
9. I = A - P
b+c
k+5
x-2
13. ____
11. x = ____
z =y
y
y-b
15. x = 5(a + g) 17. x = ____
m
PV
21. T = M + R
19. T = ___
nR
c - 2a
25. r = 7 - ax
23. b = _____
2
5 - 4y
t-g
31. a = ______
27. x = _____
3
-0.0035
Check It Out! 1. 12 2. $7.50/h
3. 20.5 ft/s 4a. -20 4b. 5.75
5. 6 in.
Exercises 1. The ratios are
equivalent. 3. 682 trillion 5. 18,749
lb/cow 7. 0.075 page/min
9. 18 mi/gal 11. __35 13. 39 15. 6.5
h
; 2.94 m 21. 72
17. 23 19. __35 = ___
4.9
23. $403.90/oz 25. 2498.4 km/h
27. 10 29. -1 31. 13 33. 1.2 35. __19
37. 45 39. $84 43. 1.625 45. 3
11
47. - __27 49. __
51. 3 53. 24
3
55. -120 59. A 61. D 63. 40°; 50°
65. 0.0006722 people/m2 67. -27
1
69. - __
71. 10 2 73. -5 75. 8
32
nRT
____
77. V = P
2-7
Check It Out! 1. 2.8 in.
150
45
5.5
3.5
___
___
___
2a. ___
x = 195 ; 650 cm 2b. x = 28 ;
44 ft 3. The ratio of the perimeters
is equal to the ratio of the
corresponding sides.
Exercises 3. 10 ft 7. 7 in. 11. 480 ft2
13. 4 15. 2.8 ft 17. 4 cm
1.5
4.5
2
___
21. ___
x = 36 ; 12 m 23. k 25. G
27. w = 4; x = 7.5; y = 8
29. 16.6 cm 31. -12 33. -46
35. (-2, 4); (-1, 1); (0, 0); (1, 1);
(2, 4) 37. (-2, -7); (-1, -4); (0, -1);
(1, 2); (2, 5) 39. 32 41. 3.5
2-8
Check It Out! 1a. 12 1b. 16.8
1c. 1.44 2a. 20% 2b. 300% 3a. 75
3b. 320 4. 10 karats
Exercises 3. 21 5. 5.6 7. 80%
9. 12.5% 11. 175 13. 36 15. 48
17. 2.5 19. 25% 21. 50% 23. 40
25. 511.1 27. 100 mg 29. 2% 31. 8%
33. 64% 35. 85% 37. 85% 39. 0.52;
13
90
28
__
41. 90.0; ___
43. 1.12; __
25
100
25
greater than __12 % because __12 % = 0.005.
1
51. 0.001, 1%, __
, 11%, 1.1 53. 0.49,
10
5 __
4
__
,
,
82%,
0.94
55a.
40%
9 5
b. action c. 3% d. 36.9%
57. box 1: 200; 100; 50
box 2: 12; 24; 148; 96
box 3: 25; 50; 100; 200
x
40
59a. __
= ___
; $36 b. $54 61. F
90
100
63. G 65. 17.2% 67. 88.5 71. 120
73. 160 75. 6 in. 77. 3
2-9
Check It Out! 1. $462.80 2a. $270
2b. $7650 3a. about $3.30
3b. about $5.60
Exercises 3. $41,775 5. 4 __12 yr
7. about $6.45 9. $462.50
11. $266.75 13. 5 yr 15. about $30
17. $50,400 19. 2 yr 21. $2.89 25. A
27. D 29. 900 31. $47.17 33. $93
35. x - 2 37. > 39. > 41. 24
43. 22.2%
2-10
Check It Out! 1a. 45% decrease
1b. 20% increase 1c. 43.75% increase
2a. 90 2b. 6 3a. $88 3b. 20%
4a. $15.30 4b. 130%
Exercises 3. 20% decrease
5. 12.5% increase 7. 20% decrease
9. 61.8 11. 8 13. 70% 15. 90%
17. 25% decrease 19. 400% increase
21. 30% increase 23. 15% decrease
25. 20% increase 27. 8 __13 % decrease
29. 252 31. 7.6 33. 15% 35. 650%
37. 50% 41. 18 43. 200% increase
45. 20 47. 60 49. 25% decrease
60
18
51a. 60% b. ___
= __
x ; x = $30
100
53. H 55. G 57. 200 59. 625
61. 64 fl oz 63. $9.43 65. 80°; 170°
67. 60°; 150° 69. -20 71. 57 73. 36
75. -100 77. about $4.20
Extension Answers
Check It Out! 1a. -7, 7 1b. -6,
10 2a. no solution 2b. 4
Exercises 1. -6, 6 3. 0 5. -2, 2
7. -11, 5 9. -9, 13 11. -57, 57
13. -3, 3 15. -16, 16 17. 0, 4
19. -5, 5 21. -5, 3 23. -3
25. 8, -2 27. 6.54 mm; 6.46 mm
29. ⎪x - 5⎥ = 0.001; 4.999 mm,
5.001 mm 31. 18.8, 65.28
Selected Answers
S81
33. -9.5, 3.75 35. 0 37. no solution
39. no solution 41. -2.7, 10.3
43. ⎪x - 2⎥ = 2.5; -0.5°F; 4.5°F
45. ⎪x - 168⎥ = 3; 165 lb, 171 lb
Study Guide: Review
1. literal equation 2. ratio 3. 36
4. -2 5. -21 6. 18 7. __98 8. __73
10
9. 27 + s = 108; 81 10. 7 11. - __
3
12. -90 13. 13 14. 0 15. -2
16. 17.5 17. -5 18. 40 19. -3
20. - __12 21. 15 22. 18 23. 1
24. 41; 123°; 57° 25. -2 26. -2 27. 1
28. - __23 29. no solution 30. all real
360
numbers 31. 9 32. n = ___
c
225 - y
2S
______
33. a = __
n - 34. x = 0.25
1
37. 3 __1 c
35. 3.7 gal 36. __
16
3
38. $1.83/golf ball 39. $0.18/oz.
40. 1080 m/h 41. 0.85 mi/min
42. 1.6 43. 54 44. 5 45. -3
46. 3.85 in. 47. 2.5 cm 48. 16 ft
49. The ratio of the areas is the
square of the ratio of the radii.
50. 5.29 51. 3105 52. 66.7%
53. 400% 54. 133.3 55. 240 56. 80%
57. $48,500 58. $9000 59. about
$5.60 60. 37% increase 61. 33%
decrease 62. 91 63. 127.5 64. $3.75;
$6.25 65. 37.5%
Chapter 3
3-1
Check It Out! 1. all real numbers
greater than 4
2a.
Ê??
Ê??
2b.
2c.
3. x < 2.5 4. d = amount employee
can earn per hour; d ≥ 8.25
Exercises 1. A solution of an
inequality makes the inequality
true when substituted for the
variable. 3. all real numbers greater
than -3 5. all real numbers greater
than or equal to 3 11. b > -8 __12
13. d < -7 15. f ≤ 14 17. r < 140
19. all real numbers less than 2
21. all real numbers less than or
S82
Selected Answers
equal to 12 27. v < -11 29. x > -3.3
31. z ≥ 9 33. y = years of experience;
y ≥ 5 35. h is less than -5. 37. r is
greater than or equal to -2.
39. p ≤ 17 41. f > 0 43. p = profits;
p < 10,000 45. e = elevation;
e ≤ 5000 51. D 53. C 59. D 61. C
65. < 71. 10 73. 7 75. 3x + 3
77. g = 2b; g = 2(8) = 16
79. b = 9 81. no solutions
3-2
2a. x ≥ -10
2b. h > -17
3. 10g ≤ 128; g ≤ 12.8; 0, 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, or 12 servings
Exercises 1. b > 9 3. d > 18
Check It Out! 1a. s ≤ 9
Ê??
1b. t < 5 __12
Ê??
1c. q < 11
2. 11 + m ≥ 15; m ≥ 4; Sarah must
get at least 4 mg more iron to reach
the RDA. 3. 250 + p > 282; p > 32;
Josh needs to bench press more
than 32 additional pounds to break
the school record.
Exercises 1. p > 6 3. x ≤ -15
5. 102 + t ≤ 104; t ≤ 2 where t is
nonnegative 7. a ≥ 5 9. x < 15
11. 1400 + 243 + w ≤ 2000;
w ≤ 357 where w is nonnegative
13. x - 10 > 32; x > 42
15. r - 13 ≤ 15; r ≤ 28 17. q > 51
19. p ≤ 0.8 21. c > -202 23. x ≥ 0
25. 21 + d ≤ 30; d ≤ 9 where d is
nonnegative 27. x < 3; B
29. x ≤ 3; D 31. 936 + 4254 + p ≤
45,611; 5190 + p ≤ 45,611; p ≤ 40,421
where p is nonnegative 35. a. 411 +
411 = 882 miles
b. 822 + m ≤ 1000 c. m ≤ 178, but
m cannot be negative. 37. F 39. J
1
41. r ≤ 5 __
43. sometimes
10
45. always 47. y = 3 - __23 x
c
49. a = ____
51. k = 2s - 11
2+b
53. x = 10 55. x ≥ -1
3-3
Check It Out! 1a. k > 6
1c. g > 36
1b. q ≤ -10
5. m ≤ 1.1 7. s > -2 9. x > 5
11. n > -0.4 13. d > -3 15. t > -72
17. 80n ≤ 550; n ≤ 6.875; 0, 1, 2, 3,
4, 5, or 6 nights 19. j ≤ 12 21. d < 7
1
23. h ≤ __87 25. c ≤ -12 27. b ≥ __
10
3
__
29. b ≤ -16 31. r < - 2 33. y < 2
35. t > 4 37. z < -11 39. k ≤ -7
41. p ≥ -12 43. x > -3 45. x < 20
47. p ≤ -6 49. b < 2 51. 7x ≥ 21;
x ≥ 3 53. - __45 b ≤ -16; b ≥ 20 57. C
-14
4
59. A 67. B 71. g ≤ ____
73. m > __
5
15
3
75. x = 5 79. 2 81. $1.89/gal
83. 25 words/min 85. t < 1
3-4
Check It Out! 1a. x ≤ -6
1b. x < -11
1c. n ≤ -10
2a. m > 10
2b. x > -4
2c. x > 2 __13
Ê??
95 + x
3. _____
≥ 90; 95 + x ≥ 180; x ≥ 85;
2
Jim’s score must be at least 85.
Exercises 1. m > 6 3. x ≤ -2
5. x > -16 7. x ≥ -9 9. x > - __12
11. x ≤ 19 13. x > 1
15. 300 + 0.1x > 1200; sales of more
than $9000 17. x ≤ 1 19. w < -2
21. x < -6 23. f < -4.5 25. w > 0
27. v > __23 29. x > -5 31. x < -2
33. a ≥ 11 35. x > 3
37. 29.99 < 19.99 + 0.35x;
x > 28.57; starting at 29 min 39. x ≤ 2
41. x < 4 43. x < -6 45. r < 8
47. x < 7 49. p ≥ 18 51. __12 x + 9 < 33;
x < 48 53. 4(x + 12) ≤ 16; x ≤ -8
55. B 57. A 59. 225 + 400 < 275 +
15m; 23 __13 < m; 24 months or more
61a.
59. x can never be greater than
itself plus 1. 61. D 63. A
67. x < -3 69. w ≥ -1 __67
71. The number in the square
should be greater than the number
w
in the circle. 73. __25 = __
; w = 26 in.
65
75. y = years; y ≥ 14
1b. -1 < x < 1
2a. x ≤ -2 OR x ≥ 2
2b. x < -6 OR x > 6
3-6
Number
Process
Cost
1
350 + 3
353
2
350 + 3(2)
356
3
350 + 3(3)
359
10
350 + 3(10)
380
n
350 + 3n
350 + 3n
b. c = 350 + 3n c. 350 + 3n ≤ 500;
n ≤ 50; 50 CDs or fewer 65. G 67. 59
69. x > 5 71. x > 0 73. x ≥ 0
75. -3x > 0 77. 7 79. __23 81. -1
83. 25 + 2m = 10 + 2.5m; m = 30
85. a ≥ 6
Check It Out! 1. 1.0 < c < 3.0
1b. t < -1
2. more than 160 flyers
3a. r ≤ 2
3b. x < 3
4a. no solutions 4b. all real numbers
Exercises 1. x < 3 3. x < 2
5. c < -2 7. 100 + 4p < 7p;
p > 33.33; they’ll have to sell at
least 34 pizzas. 9. p < -17
11. x > 3 13. t < 6.8 15. no solutions
17. all real numbers 19. no solutions
21. y > -2 23. b ≥ -7 25. m > 5
27. x ≥ 2 29. w ≥ 6 31. r ≥ -4
33. no solutions 35. all real numbers
37. all real numbers 39. t < -7
41. x > 3 43. x < 2 45. x > -2
47. x ≤ -6 49. s > 26.67; 27 s
51a. 400 + 4.50n
b. 12n c. 400 + 4.50n < 12n;
n > 53 __13 ; 54 CDs or more
53. 5x - 10 < 6x - 8; x > -2
55. __34 x ≥ x - 5; x ≤ 20
2a. 1 < x < 5
2b. -3 ≤ n < 2
3a. r < 10 OR r > 14
3b. x ≥ 3 OR x < -1
Exercises 1. intersection
3. -5 < x < 5 5. 0 < x < 3
7. x < -8 OR x > 4 9. n < 1 OR n > 4
11. -5 ≤ a ≤ -3 13. c < 1 OR c ≥ 9
15. 16 ≤ k ≤ 50 17. 3 ≤ n ≤ 6
19. 2 < x < 6 21. x < 0 OR x > 3
23. x < -3 OR x > 2
25. q < 0 OR q ≥ 2 27. -2 < s < 1
29a. 225 + 80n; they will spend
between $200 and $550.
b. -0.3125 ≤ n ≤ 4.0625; n cannot
be a negative number
c. 4.0625 h; they need an additional
$155 to use the studio for 6 h.
31. 1 ≤ x ≤ 2 33. -10 ≤ x ≤ 10
35. t < 0 OR t > 100 37. -2 < x < 5
39. a < 0 OR a > 1 41. n < 2 OR n > 5
43. 7 ≤ m ≤ 60 47. D 49. B
51. 0.5 < c < 3 53. s ≤ 6 OR s ≥ 9
55. -1 ≤ x ≤ 3 57. 4x - 5 59. 3a + 3
61. (-2, 3), (-1, 0), (0, -1),
(1, 0), (2, 3); U-shaped 63. m < 2
65. x ≤ -2
Extension Answers
Check It Out! 1a. -3 < x < 3
Exercises 1. -3 ≤ x ≤ 3
3. -15 < x < 13 5. -2 < x < 2
7. ⎪x⎥ ≤ 15; -15 ≤ x ≤ 15 9. ⎪x - 2⎥
< 3; -1 < x < 5 11a. -6 < x < 16
b. x ≤ 1 OR x ≥ 9 c. -3 ≤ x ≤ 13
13. no 15. yes 17. ⎪b⎥ > 3 19. ⎪d⎥ < 7
Study Guide: Review
4b. x ≤ -13 or x ≥ 2
4a. -9 < y < -2
Check It Out! 1a. x ≤ -2
2c. x ≤ -6 OR x ≥ 1
3-5
1. inequality 2. union 3. compound
inequality 4. intersection
5. solution of an inequality
6.
7.
8.
9.
10.
11.
12. a < 2 13. k ≥ -3.5
14. q < -10 15. t = temperature;
t ≥ 72 16. s = students; s ≤ 12
where s is a natural number
17. m = minutes; m < 30 where m
is nonnegative 18. t < 7 19. k ≤ 2
20. m > -5 21. x ≥ 4.5 22. w < 9.5
23. a < 5 24. h < 1 25. v < -2
26. 4.5 + m ≥ 10; m ≥ 5.5; Tammy
must run 5.5 mi or more. 27. 32 +
d ≤ 50; d ≤ 18; Rob can spend $18
or less. 28. a ≤ 5 29. t > -3
30. p > 8 31. x ≤ -25 32. n > 6
33. g < -12 34. k > -7 35. r < -9
36. h < -3 37. g < 2.5 38. 0, 1, 2, 3,
4, 5, 6, 7 39. 0.75n ≥ 250;
n ≥ 333 __13 ; they must sell at least
334 lanyards. 40. x < 5 41. t ≥ 6
42. m > -11 43. r < 6 44. p > -4
45. g > -7 46. x < -1 47. h > -3
Selected Answers
S83
48. x > 1 __12 49. b ≤ 10 50. y > 3 __12
51. n > -15 52. 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12, or 13 53. 26 mo
total 54. less than $300,000
55. m < -1 56. y ≥ -2 57. c < -3
58. q ≤ -4 59. x > 2 60. t < 3
61. no solutions 62. all real numbers
63. p > - __12 64. all real numbers
65. k > 2 66. no solutions
67. 210 + 16m > 175 + 20m;
8.75 > m 68. -10 < t < 4
69. -6 < k ≤ 7 70. r > 7 OR r < -2
71. no solutions 72. -2 < p ≤ 5
73. all real numbers 74. 68 ≤ t ≤ 84
75. 102 ≤ n ≤ 183.6
Chapter 4
4-1
Check It Out! 1. graph C
2a. discrete;
7ORDSPERMINUTE
+EYBOARDING
4-2
4-3
Check It Out! 1. x
y
1
3
2
4
3
5
x
x
y
1
1
5.
x
y
1
-7
7
2
-3
3
-1
1
5
-5
7ATERLEVEL
7ATER4ANK
4IME
Exercises 1. continuous 3. graph
B 5. graph C 11. graph A
13. continuous 19. The point of
intersection represents the time
of day when you will be the same
distance from the base of the
mountain on both the hike up and
the hike down. 23. C 27. Container
C 29. -8 31. __19 33. (-2, 5), (-1, 3),
(0, 1), (1, -1), (2, -3); the points
form a line. 35. (-2, 6), (-1, 3),
(0, 2), (1, 3), (2, 6); the points form
a U-shaped figure.
37. n - 5 = -2; 3
S84
Selected Answers
Exercises
7EEKS
3. Possible answer: When the
number of students reaches a
certain point, the number of pizzas
bought increases.
2a. D: {6, 5, 2, 1}; R: {-4, -1, 0}
2b. D: {1, 4, 8}; R: {1, 4}
3a. D: {-6, -4, 1, 8}; R: {1, 2, 9};
function; each domain value is
paired with exactly one range
value. 3b. D: {2, 3, 4}; R: {-5, -4,
-3}; not a function; the domain
value 2 is paired with both -5
and -4.
3.
2b. continuous;
y
Check It Out! 1. y = 3x
7. D: {-5, 0, 2, 5}; R: {-20, -8, 0,
7} 9. D: {2, 3, 5, 6, 8}; R: {4, 9, 25,
36, 81} 11. D: {1}; R: {-2, 0, 3, 8};
not a function 13. D: {-2, -1, 0, 1,
2}; R: {1}; function
15. x
y
-2 -4
-1 -1
0
0
1
-1
2
-4
17. D: {3}; R: 1 ≤ y ≤ 5 19. D: -2 ≤
x ≤ 2; R: 0 ≤ y ≤ 2; not a function
21. yes 23. yes 25. yes 27. no
29a. D:0 ≤ t ≤ 5; R: 0 ≤ v ≤ 750
b. yes c. (2, 300); (3.5, 525) 33. G
35a. {(-3, 5), (-1, 7), (0, 9), (1, 11),
(3, 13)} b. D: {-3, -1, 0, 1, 3};
R: {5, 7, 9, 11, 13} c. yes 37. all real
x
numbers 39. __34 = __
; 27 cm
36
41. x + 45 ≥ 64; x ≥ 19
2a. independent variable: time;
dependent variable: cost
2b. independent variable: pounds;
dependent variable: cost
3a. independent variable: pounds;
dependent variable: cost; f (x) =
1.69x 3b. independent variable:
people; dependent variable: cost;
f (x) = 6 + 29.99x 4a. h(1) = 1;
h(-3) = -7 4b. g(-24) = -5;
g(400) = 101 5. f (x) = 500x;
D: {0, 1, 2, 3}; R: {0, 500, 1000, 1500}
Exercises 1. dependent
3. y = x - 2 5. independent
variable: size of bottle; dependent
variable: cost of water
7. independent variable: hours;
dependent variable: cost;
f (h) = 75h 9. f (0) = 2; f (1) = 9
11. h(27) = -1; h(-15) = -15
13. y = -2x 15. independent
variable: size of lawn; dependent
variable: cost 17. independent
variable: days late; dependent
variable: total cost; f(x) = 3.99 +
0.99x 19. independent variable:
gallons of gas; dependent variable:
miles; f(x) = 28x 21. g(1) = 7;
g(2) = 10 23. f(n) = 2n + 5;
D: {1, 2, 3, 4}; R: {$7, $9, $11, $13}
25.
z
1
2
3
4
-3 -1
g(z)
1
3
27. f (-6.89) ≈ -16; f (1.01) ≈ 8;
f (4.67) ≈ 20 33. D 35. 3.5
37. 44.1 m 39. y = -3 41. x = 2
43. D: x ≥ 0; R: all real numbers;
not a function
4-4
Check It Out! 1a.
y
x
1b.
7.
y
y
29.
y
x
x
9.
y
x
x
y
x
y
x
31.
2a.
13.
2b.
y
y
x
x
35.
3. x = 3 4. Possible answer: about
32.5 mi
15.
y
x
y
33.
11. y = -1
y
x
!VERAGE3PEEDOF,AVA&LOW
$ISTANCEMI
x
17.
37. x = 1 39. y = -8 41. yes;
yes 43. no; yes 45. no; yes; yes
47. yes; no; yes 55a. v = 10,000 1500h b. 8500 gal
c.
y
4IMEH
Time
(h)
Volume
(gal)
0
10,000
1
8,500
2
7,000
3
5,500
4
4,000
x
Exercises
1.
y
19.
x
y
59. J 61. J 63. y = 4x + 64
65. 2 3 67. p < -4 69. b ≥ 20
71. h(-6) = -3; h(9) = 7
x
21.
3.
y
4-5
y
Check It Out!
1.
x
5.
23.
0OINTSSCORED
y
y
x
x
25. y = 5
&OOTBALL4EAM3CORES
'AME
2. positive correlation 3a. No
correlation; the temperature in
Selected Answers
S85
Houston has nothing to do with the
number of cars sold in Boston.
3b. Positive correlation; as the
number of family members
increases, more food is needed, so
the grocery bill increases too.
3c. Negative correlation; as the
number of times you sharpen
your pencil increases, the length
of the pencil decreases. 4. Graph A;
it cannot be graph B because
graph B shows negative minutes;
it cannot be graph C because
graph C shows the temperature
of the pie increasing, a positive
correlation. 5. about 75 rolls
Exercises 3. no 5. positive
correlation 7. negative correlation
9. positive correlation 11. Graph A
15. positive correlation 17. positive
correlation 19. Graph A 23. Positive
correlation; as the number of left
shoes sold increases, the number
of right shoes sold also increases,
because people need shoes for
both feet. 25. B
1d. arithmetic; common difference:
-3 2a. -343 2b. 19.6 3. 750 lb
Exercises 1. common difference
3. arithmetic; common difference:
-0.7; -0.7, -1.4, -2.1 5. not
arithmetic 7. -53 9. not arithmetic
11. arithmetic; common difference:
-9; -58, -67, -76 13. 5.9
15. 9500 mi 17. __14 19. -2.2
21. 0.07 23. - __38 , - __12 , - __58 , - __34
25. -0.2, -0.7, -1.2, -1.7 27. -0.3,
-0.1, 0.1, 0.3 29. 22 31. 122 33a. It
could be arithmetic because you
pay $2 per lap, so the common
difference could be 2. b. $9, $11,
$13, $15; a n = 2n + 7 c. $37 d. no
20
35. -104.5 37. __
3
39a. a n = 6 + 3(n - 1)
b. 48 c. $7800 d. a n = 7 + 3(n - 1);
$8200
41a.
Time
Interval
Mile
Marker
1
520
2
509
3
498
4
487
5
476
6
465
*UANS4RIP
$ISTANCEMI
27a.
4IMEMIN
b. positive correlation 29. C
35. 5(n + 2) = 2n - 8, n = -6
37. no solution
39.
y
x
y
x
10.
arithmetic 1c. not arithmetic
S86
Selected Answers
2
y
0
1
1
x
-2 -1
2
3
y
-1
3
4
1
y
x
1. domain 2. negative
correlation 3. term
4.
28.
4IME
5.
y
x
6.
29.
y
(EIGHT
common difference: __12 1b. not
0
27.
4IME
Check It Out! 1a. arithmetic;
-1
Study Guide: Review
4-6
x
11. D: {-4, -2, 0, 2}; R: { -1, 1, 3, 5}
12. D: {-2, -1, 0, 1, 2}; R: {-1, 0}
13. D: {0, 1, 4}; R: {-2, -1, 0, 1, 2}
14. D: -4 ≤ x ≤ 3; R: -3 ≤ y ≤ 5
15. D: {-5, -3, -1, 1}; R: {-3, -2,
-1, 0}; function 16. D: {-4, -2,
0, 2}; R: {-2, 1}; function
17. D: {1, 2, 3 ,4}; R: {-1, 0, 1, 2, 3};
not a function 18. {(1, 5.00), (2, 6.50),
(3, 8.00), (4, 9.50), (5, 11.00)};
yes 19. yes 20. The value of y is 7
less than x; y = x - 7. 21. The
value of y is 9 times x; y = 9x.
22. independent variable: number
of cakes; dependent variable: cost;
f (c) = 6c 23. independent variable:
number of CDs Raul will buy;
dependent variable: number of
CDs Tim will buy; g(n) = 2n
24. f(5) = 14 25. g(-3) = -11
26. h(-4) = 6; h(5) = -1
(EIGHTOFBALL
41.
9.
$ISTANCE
b. a n = 520 + (n - 1)(-11)
c. number of miles per interval
d. 421 43. F 45. 20th and 21st
terms 47a. session 16; yes
b. Thursday 49. x = 16 51. t < -2
OR t > 2 53. negative correlation
7. Possible answer: A family buys a
fish tank and some fish. After two
weeks, they buy some more fish.
After two more weeks, they buy
more fish. 8. Possible answer: A
monkey swings from a high branch
to a lower branch. He climbs along
the branch. Then he jumps to a
higher branch and takes a nap.
x
4IME
30.
y
x
x
3a.
y
3b. yes
y
x
x
y
32.
3b.
3c. no
4.
2ENTALPAYMENT
33. Possible answer: about $43
34. negative correlation
35. Possible answer: 33 36. appears
to be arithmetic; -6; -4, -10, -16
37. not arithmetic
38. not arithmetic 39. appears
to be arithmetic; 2.5; 2, 4.5, 7
40. 105 41. -62 42. 20 43. $420
44. -15.5°C
Chapter 5
5-1
Check It Out! 1a. yes; each
domain value is paired with exactly
one range value; yes 1b. yes;
each domain value is paired with
exactly one range value; yes 1c. no;
each domain value is not paired
with exactly one range value
2. yes; a constant change of +2
in x corresponds to a constant
change of -1 in y.
3a. yes
y
x
Exercises 1. y-intercept
-ANICURES
D: {0, 1, 2, 3, …}
R: {$10, $13, $16, $19, …}
Exercises 1. No; it is not in the
form Ax + By = C. 3. Yes; each
domain value is paired with exactly
one range value; yes. 5. yes 7. yes
9. yes 11. no 15. Yes; each domain
value is paired with exactly one
range value; no. 17. Yes; each
domain value is paired with exactly
one range value; no. 19. yes
23. no 27. yes; yes 29. yes; yes
31. yes; -4x + y = 2; A = -4; B = 1;
C = 2 33. no 35. yes; x = 7; A = 1;
B = 0; C = 7 37. yes; 3x - y = 1;
A = 3; B = -1; C = 1 39. yes; 5x 2y = -3; A = 5, B = -2, C = -3
41. no 55. no 57. C 63. not
linear 65. -1 67. __19 69. 2 71. 9
3. x-intercept: 2; y-intercept: -4
5. x-intercept: 2; y-intercept: -1
7. x-intercept: 2; y-intercept: 8
13. x-intercept: -1; y-intercept: 3
15. x-intercept: -4; y-intercept: 2
17. x-intercept: -4; y-intercept:
2 19. x-intercept: 2; y-intercept:
8 21. x-intercept: __18 ; y-intercept: -1
35. A 37. B 41. F 47. x-intercept:
950; y-intercept: -55
5-3
Check It Out! 1. day 1 to day 6:
-53; day 6 to day 16: -7.5; day 16
to day 22: 0; day 22 to day 30:
-4.375; from day 1 to day 6
"ANK"ALANCE
2.
0ENS
x-intercept: 30; y-intercept: 20
2b. x-intercept: number of pens
that can be purchased if no
notebooks are purchased;
y-intercept: the number of
notebooks that can be purchased
if no pens are purchased.
DAY
DAY
DAY
Check It Out! 1a. x-intercept: -2;
y-intercept: 3 1b. x-intercept: -10;
y-intercept: 6 1c. x-intercept: 4; yintercept: 8
2a.
3CHOOL3TORE0URCHASES
DAY
5-2
.OTEBOOKS
x
y
x
2ENTAL0AYMENT
"ALANCE
31.
$AY
3. - __25 4a. undefined 4b. 0
5a. undefined 5b. positive
Exercises 1. constant 5. - __34
7. undefined 9. undefined
11. positive 15. 1 17. 0
17
19. positive 23. __
29. C 31. G
18
35. -2 37. D: {3}; R: {4, 2, 0, -2};
no 39. x-intercept: 3; y-intercept: 6
41. x-intercept: _14_; y-intercept: __12
5-4
Check It Out! 1a. m = 0 1b. m = 3
1c. m = 2 2a. m = __12 2b. m = -3
2c. m = 2 2d. - __32 3. m = __12 ; the
height of the plant is increasing at a
rate of 1 cm every 2 days.
4. m = - __23
Selected Answers
S87
1
Exercises 1. 1 3. - __12 5. 10 7. ___
540
9.
- __59
11. -4 13. undefined
9
13
19. - __
15. - __34 17. - ____
5
5000
21. Student A is correct.
23a. Car 1; 20 mi/h b. The speed
and the slope are both equal to the
distance divided by time. c. 20 mi/h
25a. y = 220 - x 27. G 29. - __ab
31. __32 - y 33. x = __12 35. x = -3
37. x = 0 39. p = 5 41. n = -11
43. a = 2 45. yes
29. k = - __29 x
3c. y = -4
y
y
x
x
The value of k is - __2 , and the graph
9
shows that the slope of the line is
- __29 .
33. y = -6x
4a. y = 18x + 200 4b. slope: 18;
cost per person; y-intercept: 200;
fee 4c. $3800
Exercises
1.
y
y
5-5
0ERIMETEROFA3QUARE
Check It Out! 1a. no 1b. yes; - __34
4. y = 4x
x
1c. yes; -3 2a. No; possible
y
answer: the value of __x is not the
same for each ordered pair. 2b. Yes;
y
possible answer: the value of __x is
the same for each ordered pair.
2c. No; possible answer: the value
y
of __x is not the same for each
ordered pair. 3. 90
x
5. y = 8x + 2 7. y = -3
9. y = __25 x - 6
The value of k is -6, and the graph
shows that the slope of the line is
-6. 41. C 43. B 47. p = 7 - 4q
x
y
4 - 2y
49. x = _____
51. y = -2x 53. -4
y
1
__
55.
2
0ERIMETER
5-6
Check It Out!
1a.
13.
y
x
Exercises 1. direct variation
3. yes; -4 5. no 7. 18 11. yes; __14
13. yes 15. -16 19. no 21. y = -3x
x
y
1b.
x
17. y = 5x - 9 19. y = - __12 x + 7
21. y = - __12 x + 3
y
x
The value of k is -3, and the graph
shows that the slope of the line is
-3.
25. y = 2x
25. y = __72
y
y
x
x
3b. y = -3x + 5
x
y
The value of k is 2, and the graph
shows that the slope of the line is 2.
Selected Answers
x
x
2. y = 8x - 25
3a. y = __23 x
y
S88
y
3IDELENGTH
y
29. y = -2x + 8
y
x
31. Student B is correct. 33. possible
35. impossible 37. A 41. B 43. B
45. y = __13 x - 3 47. -6 51. n ≤ 8
53. t < -3 55. no
5-7
Check It Out!
1.
y
x
(
)
2a. y - 1 = 2 x - __12 2b. y + 4 =
0(x - 3) 3. y = __13 x + 2 4a. y =
6x - 8 4b. y = __23 x - 1 5. y = 2.25x +
6; $53.25
Exercises 5. y - 5 = -4(x - 1)
7. y = - __13 x + 7 9. y = __13 x
11. y = 3x - 13 13. y = -x
15. y = - __13 x + __43 17. y = -x + 15
19. y = __15 x + 3; 9 ft 23. y - 5 =
2
__
(x + 1) 25. y - 8 = 8(x - 1)
9
27. y - 7 = 3(x - 4) 29. y = - __27 x + 1
31. y = - __14 x 33. y = -5x + 13
35. y = __17 x + 7 37. y = -5x - 3
1
39. y = 2x + 11 41. y = - ___
x + 212;
500
200°F 43. y = 6; x = 6 49. D
51. slope: __52 ; y-intercept: 2
product of their slopes is -1. Since
PQR contains a right angle, PQR is
a right triangle. 5a. y = __45 x + 3
5b. y = - __15 x + 2
translation 2 units up 5. The graph
will be rotated about (0, 175) and
become less steep; the graph will
be translated 5 units up.
3
Exercises 1. parallel 3. y = __
x-1
4
3
2
__
__
and y - 3 = 4 (x - 5) 5. y = 3 x - 4
3.
and y = - __32 x + 2; y = -1 and x = 3
9. x = 7 and x = -9; y = - __56 x + 8
and y = - __56 x - 4 11. y = -3x + 2
and 3x + y = 27; y = __12 x - 1 and
-x + 2y = 17 13. y = 6x and y = - __16 x;
y = __1 x and y = -6x 15. x - 6y = 15
6
and y = -6x - 8; y = 3x - 2 and
3y = -x - 11 17. y = - __67 x 19. neither
21. parallel 23. y = __12 x - 5
25. y = 2x + 5 27. y = 3x + 13
29. y = -x + 5 31. y = 4x - 23
33. y = - __34 x 35. y = -x + 1
31
2
11
37. y = __
x - __
39. y = - __15 x - __
5
5
5
1
1
1
__
__
__
41. y = - 2 x - 2 43. y = 2 x + 6
45. y = x - 3 47. y = -4 51a. y = 50x
b. y = 50x + 30 53. H 57. - __15
59. 94 + t > 112; t > 18 63. y = __23 x - 5
65. y = - __12 x - __12 67. y = 3
y = 2x + 1 1b. y = 3x and y - 1 =
−−
3(x + 2) 2. slope of AB = 0; slope
−− __5
−−
of BC = 3 ; slope of CD = 0; slope
−−
−−
−−−
of AD = __53 ; AB is parallel to CD
because they have the same slope.
−−
−−
AD is parallel to BC because
they have the same slope. Since
opposite sides are parallel, ABCD is
a parallelogram. 3. y = -4 and x = 3;
y - 6 = 5(x + 4) and y = - __15 x + 2
−−
−−
4. slope of PQ = 2; slope of QR = -1;
−−
−−
slope of PR = - __12 ; PQ is
−−
perpendicular to PR because the
y
fx
x
gx
translation 4 units down
7.
y
fx
gx
x
rotation about (0, 0) (less steep)
9.
y
gx
fx
x
5-9
1.
Check It Out!
y
fx
rotation about (0, -2) (steeper)
y
13.
x
x
gx
translation 6 units down
2.
y
gx
fx
g(x) = - __13 x - 6
x
53. y = __23 x 59. y = 3x - 5
5-8
Check It Out! 1a. y = 2x + 2 and
Exercises 1. translation
17.
rotation about (0, -1) (less steep)
y
3.
gx y
fx
x
fx
x
g(x) =
- __23 x
4.
rotation about (0, 0) (steeper) and
translation 1 unit up
gx
+2
23.
y
y fx
gx
x
x
fx
gx
reflection across y-axis and
rotation about (0, 2) (less steep)
Selected Answers
S89
y
f x
gx
x
rotation about (0, 0) (steeper) and
translation 5 units down
31. rotation about (0, 0) (steeper)
y
f x
x
g x
They have different slopes and the
same y-intercept.
37.
y
Extension Answers
41. y = __13 x + 5 42. y = 4x - 9
y
y
axis of symmetry: x = 0; vertex:
(0, 0); x-intercept: 0; y-intercept: 0;
D: all real numbers; R: y ≥ 0
Exercises 5. D: all real numbers
R: y ≥ 0 7. D: all real numbers
R: y ≥ 7 9. never 11. never
Study Guide: Review
1. translation; rotation; reflection
2. y-intercept 3. slope; y-intercept
4. No; a constant change of +2 in
x corresponds to different changes
Selected Answers
45. y - 3 = 2(x - 1) 46. y - 4 = -5
(x + 6) 47. y = 2x + 2
48. y = -x + 3 49. y = 2x + 8
50. y = 2
51. y = - __13 x and y = - __13 x - 6
52. y - 2 = -4 (x - 1) and
y = -4x - 2 53. y - 1 = -5(x - 6)
and y = __15 x + 2 54. y - 2 = 3(x + 1)
and y = - __13 x 56. y = 2x - 3
57.
y
gx
4IMES
20. 5 21. - __43 22. -3 23. - __12
24. 3 25. 7 26. 4 27. -5 28. -1
29. 1 30. 2 31. undefined 32. 0
33. yes; -6 34. yes; 1 35. no
36. yes; -__12 37. -12
38.
-ALEKAS"ABYSITTING%ARNINGS
-ONEYEARNED
FT
S
x
FT
S
x
FT
S
y
44.
FT
S
x
x
#UPCAKESSOLD
y
40.
Check It Out!
S90
x
D: Whole numbers;
R: positive multiples of 0.5
13. x-intercept: 2; y-intercept: -4
14. x-intercept: 5; y-intercept: 6
15. x-intercept: 3; y-intercept: -9
16. x-intercept: -__12 ; y-intercept: 1
17. x-intercept: -18; y-intercept: 3
18. x-intercept: __13 ; y-intercept: -__14
19.
2ATE
$ISTANCEFT
(steeper) 43. rotation about (0, 0)
(steeper) 45a. $300 b. 20%
c. Commission changes to 25%.
Base pay changes to $400. 49. D
53. 15x 55. positive 57. negative
59. y = - __35 x and y + 1 = - __35 (x - 2)
61. x = 4 and y = -3; 2y + x = 6 and
y = 2x + 3
y
g(x) = __16 x - 4 39. translation 9
units down 41. rotation about (0, 0)
43.
1.
39.
x
in y. 5. Yes; a constant change
of +1 in x corresponds to a
constant change of +2 in y.
6. Yes; a constant change of +1 in x
corresponds to a constant change
of -2 in y. 7. No; a constant
change of -1 in y corresponds to
different changes in x.
8. 5x + y = 1; A = 5; B = 1; C = 1
9. x + 6y = -2; A = 1; B = 6; C =
-2 10. 7x - 4y = 0; A = 7; B = -4;
C=0
11. y = 9; A = 0; B = 1; C = 9
12.
#UPCAKE3ALES
!MOUNTEARNED
27.
x
fx
translation 4 units up
58.
y
fx
gx
x
59.
y
x
gx
fx
4IMEH
rotation about (0, 0) (less steep)
60.
fx
x
rotation about (0, 0) (less steep)
y fx
gx
x
reflection across y-axis, rotation
about (0, 0)
62.
y
gx
f x
x
reflection across y-axis; rotation
about (0, -2)
63. translation 2 units up; rotation
about (0, 3) (steeper)
Chapter 6
1b. (0, 2) 1c. (3, -10) 2. (-1, 6)
3. 10 months; $860; the first option;
the first option is cheaper for the
first 9 months; the second option is
cheaper after 10 months.
Exercises 1. (9, 35) 3. (3, 8)
5. (-3, -9) 7a. 3 months; $136
b. Green Lawn 9. (-4, 2)
11. (-1, 2) 13. (1, 5)
15. (3, -2) 17. 6 months; $360; the
second option 19. (2, -2)
21. (8, 6) 23. (-9, -14.8)
25. 12 nickels; 8 dimes
⎧x + y = 1000
27. ⎨
; $200 at 5%;
⎩ 0.05x + 0.06y = 58 $800 at 6%
29. m∠x = 60°; m∠y = 30°
35. Possible estimate: (1.75, -2.5);
(1.8, -2.4) 37. F 39. r = 5; s = -2;
t = 4 41. a = 9; b = 5; c = 0
45. x-intercept: 2; y-intercept: -6
47. x-intercept: 8; y-intercept: 10
49. yes
6-3
6-1
Check It Out! 1a. yes 1b. no
2a. (-2, 3) 2b. (3, -2) 3. 5 movies;
$25
Exercises 1. an ordered pair that
satisfies both equations 3. yes
5. (2, 1) 7. (-4, 7) 9. no 11. yes
13. (3, 3) 15. (3, -1)
⎧y = 2x
17a. ⎨
⎩ y = 16 + 0.50x
#ARNATION3ALES
b.
#OST
6-4
6-2
Check It Out! 1a. (-2, 1)
gx
61.
the number is 14.
41. y = 3x 43. yes; __12 45. no 47. (4, 9)
less than 5 39. numbers greater
than 6 41. c ≤ -9
y
&LORISTSPRICE
3CHOOLBANDSPRICE
#ARNATIONS
It represents how many carnations
need to be sold to break even.
c. No, because the solution is not
a whole number of carnations; 11
carnations. 19. (-2.4, -9.3)
21. (0.3, -0.3) 23. 45 white; 120
pink 25. 8 yr 29. C 31. month 11;
400 33. 42 35. 2.2 37. numbers
Check It Out! 1. (-2, 4) 2. (4, 1)
3a. (2, 0) 3b. (3, 4) 4. 9 lilies;
4 tulips
Exercises 1. (-4, 1) 3. (-2, -4)
5. (-6, 30) 7. (3, 2) 9. (4, -3)
11. (-1, -2) 13. (1, 5) 15. 6, - __12
17. (-1, 2) 19. (-1, 2)
(
)
⎧ - w = 2
; length: 11 units;
21. ⎨
⎩ 2 + 2w = 40 width: 9 units
25. (3, 3)
(
)
46 __
27. __
,8
7 7
(
15 __
29. __
,9
7 7
Check It Out! 1. no solution
2. infinitely many solutions
3a. consistent, dependent;
infinitely many solutions
3b. consistent, independent; one
solution 3c. inconsistent; no
solution 4. Yes; the graphs of the
two equations have different slopes
so they intersect.
Exercises 1. consistent 3. no
solutions 5. infinitely many
solutions 7. infinitely many
solutions 9. inconsistent; no
solutions 11. Yes; the graphs of the
two equations have different slopes
so they intersect. 13. no solutions
15. no solutions
17. infinitely many solutions
19. infinitely many solutions
21. consistent, independent; one
solution 23. Yes; the graphs of
the two equations have different
slopes, so they intersect. 27. They
will always have the same amount;
both started with 2 and add 4 every
year. 29. The graph will be
2 parallel lines. 31. A 33. D
35. p = q; p ≠ q 37. 11 km 39. not
arithmetic 41. d = -1 __12 ; -6,
-7 __12 , -9 43. (-2, -4)
6-5
Check It Out! 1a. no 1b. yes
2a.
x
31a. ⎨
c. Buying the first package will save
$8; buying the second package will
save $7. 33. A 35a. s = number
of student tickets; n = number of
nonstudent tickets;
⎧s + n = 358
⎨
⎩ 1.50s + 3.25n = 752.25
b. s = 235; n = 123; 235 student
tickets, 123 nonstudent tickets
37. x = 4; y = -1; z = 10
⎧x + y = 5
39. ⎨
; x = 1; y = 4;
⎩ 3(10x + y) = 42
y
)
⎧3A + 2B = 16
b. A = 4; B = 2
⎩ 2A + 3B = 14
2b.
y
x
2c.
y
x
3a. 2.5b + 2g ≤ 6
Selected Answers
S91
3b.
/LIVE#OMBINATIONS
23.
(4, 4); not solutions: (-3, 1),
(-1, -4)
y
x
'REENOLIVES
2b.
y
x
25.
x
Possible answer: solutions: (0, 0),
(3, -2); not solutions: (4, 4), (1, -6)
y
3a.
29.
y
3b.
x
x
y
y
31.
x
y
7.
x
y
x
Exercises 3. yes
5.
y
"LACKOLIVES
3c. Possible answer: (1 lb black, 1 lb
green), (0.5 lb black, 2 lb green)
4a. y < -x 4b. y ≥ -2x - 3
3c.
y
33.
x
y
4.
35.
y
x
37. 7a + 4s ≥ 280 41. A 43. B 45. C
47.
y
x
0EPPERJACKCHEESELB
Possible answer: (3 lb pepper jack,
2 lb cheddar), (2.5 lb pepper jack,
4 lb cheddar)
5.
x
19a. 3b + 2d ≤ 30
&OOD#OMBINATIONS
(OTDOGSLB
Exercises 1. all 3. yes
y
49. y ≥ __12 x + 3 51. yes 53. yes
55. y = __3 x + __7 57. y = 3x + 1
4
x
4
59. y = __12 x + __12 61. (-2, 15) 63. (2, 5)
65. (12, 3)
6-6
Check It Out! 1a. yes 1b. no
2a.
Possible answer: solutions: (3, 3),
(4, 3); not solutions: (0, 0), (2, 1)
7.
y
y
x
x
(AMBURGERMEATLB
c. Possible answer: (3 lb hamburger,
2 lb hot dogs), (5 lb hamburger, 6 lb
hot dogs) 21. y ≤ - __15 x + 3
S92
/RANGEJUICEC
y
c. Possible answer: (2 c orange,
2 c pineapple), (4 c orange, 10 c
pineapple) 11. y ≥ x + 5 13. yes
15.
#HEESE#OMBINATIONS
#HEDDARCHEESELB
0INEAPPLEJUICEC
b.
x
9a. r + p ≤ 16
b.
0UNCH#OMBINATIONS
Selected Answers
Possible answer: solutions: (3, 3),
Possible answer: solutions: (0.5, 3),
(1, 3); not solutions: (0, 0), (-1, 2)
9.
27.
y
y
x
x
11.
29.
y
x
13.
,INDAS7ORK(OURS
(OURSBABYSITTING
y
(OURSATPHARMACY
x
Possible answer: (0, 9), (8.5, 10)
31.
15.
y
x
3ALES'OALS
#UPCAKES
x
Possible answer: (6 lemonade,
13 cupcakes), (10 lemonade, 10
cupcakes) 17. yes
y
x
Possible answer: solutions: (-2, 0),
(-3, 1); not solutions: (0, 0), (1, 4)
49.
Possible answer: solutions: (-1, 3),
(0, 5); not solutions: (0, 0), (1, 4)
y
x
25.
x
x
49.
y
x
51. 25 cm 2 53. 12.5 cm 2 55. no
57. yes
x
1. independent system 2. system
of linear equations 3. solution of a
system of linear inequalities
4. inconsistent system
5. independent system 6. no
) 15. (-1, 6) 16. (4, -5)
17. (-5, 2) 18. (6, 6) 19. 10 h;
$1350; Motor Works 20. (-1, 3)
21. (5, -3) 22. (11, 1) 23. (0, 3)
50.
y
Study Guide: Review
14. __12 , -2
y
y
(
y
48.
x
51.
y
7. yes 8. yes 9. no 10. (-1, -1)
11. (3, 4) 12. 8 h; $10 13. (-9, -6)
x
⎧y > x + 1
35. ⎨
⎩y<x+3
⎧y < 2
37. ⎨
⎩ x ≥ -2
23.
x
y
y
47.
39. Student B 45. G
47. about 12 square units
33.
,EMONADEC
19.
y
x
21.
24. (-2, 8) 25. (3, -5) 26. (4, -6)
27. (2, 2) 28. no solution
29. infinitely many solutions
30. (-2, -4) 31. infinitely many
solutions 32. infinitely many
solutions 33. (-1, -3) 34. no 35.
consistent, independent; one
solution 36. inconsistent; no
solution 37. consistent, dependent;
infinitely many solutions
38. inconsistent; no solution
39. consistent, independent;
one solution 40. consistent,
dependent; infinitely many
solutions 41. inconsistent; no
solution 42. no 43. yes 44. yes
45. no
46.
y
x
52. x = slices of pizza; y = bottles of
soda; 2x + 1y ≥ 450
Selected Answers
S93
"OTTLESOFLEMONADE
&UNDRAISING.EEDS
y
1
1
Check It Out! 1. ___
m 2a. _____
125
10,000
1
1
1
1
2c. - __
2d. - __
3a. __
2b. __
16
32
32
64
3LICESOFPIZZA
Possible answer: (200, 50),
(150, 150) 53. no 54. yes
55.
m
1
1
1
9. 1 11. __
13. ___
7. - ___
512
16
256
1
1
__
__
23. __
q 25. 1 27. 81 29. - 36 31. 1
x
Possible answer: solutions: (0, 0),
(-5, 0); not solutions: (8, 0), (3, -3)
y
x
Possible answer: solutions: (-6, 2),
(-8, 1); not solutions: (0, 0), (4, 1)
y
Possible answer: solutions: (8, -8),
(9, 0); not solutions: (0, 0), (0, -4)
59.
y
x
51. s t
2
x3
60.
y
7
h3
1
53. 1 55. __
57. _____
2
2
q
6m k
2
w
5
3
__
69. ___
y 71. - 6 73. 2a b 75.
b
1
_____
3x 8y 12
79. never 81. sometimes
83. sometimes 87. 81 89. 1 91. -3
93. -1 95. D 97. A 103. -2
105. 4 107. 28 111. y = __13 x + 5
113. y = -4x + 9
x
1c. 10,000,000,000 2a. 10 8 2b. 10 -4
2c. 10 -1 3a. 85,340,000 3b. 0.00163
4a. 1.43 × 10 5 km 4b. 13,000 m/s
5. 2 × 10 -12, 4 × 10 -3, 5.2 × 10 -3,
3 × 10 14, 4.5 × 10 14, 4.5 × 10 30
Exercises 3. 0.00001 5. 100,000,000
7. 10 -6 9. 650,300,000 11. 0.092
13. 5.85 × 10 -3, 2.5 × 10 -1,
8.5 × 10 -1, 3.6 × 10 8, 8.5 × 10 8
15. 0.000000001
17. 100,000,000,000,000 19. 10 6
21. 92,000 23. 0.00042
25. 10,000,000,000,000 27. 1.23 ×
10 -3, 1.32 × 10 -3, 3.12 × 10 -3,
2.13 × 10 -1, 2.13 × 10 1, 3.12 × 10 2
29. 2.7 × 10 7 31. 2.35 × 10 5
33. 6 × 10 -7 35. 4.12 × 10 -2
37. yes 39. no; 2.5 × 10 2 41. yes
43. yes 47. 10 -3 51. F 55. Let
m = number of minutes; m ≥ 45.
3
1
59. (-2, 1) 61. __
63. ___
16
125
Check It Out! 1a. 7 12 1b. 3 × 5 10
m
1
1c. ___
1d. __
2. 6.696 × 10 8 mi
4
7
x
3a. 3 20 3b. 1 3c. a 18 4a. 64p 3
1
4b. 25t 4 4c. __
4
y
Exercises 1. 2 5 3. n 8 5. 7.5 × 10 8
S94
Selected Answers
3
n
1
Check It Out! 1a. ___
1b. __
1c. m 5
m5
y3
3
2. 1.1 × 10 -2 3. $12,800
n 31d. __
16
5 20
6
3
3
64
a b
a
9
2
, or __
4b. _____
4c. __
5a. __
,
4a. __
4
10 15
3
3
81
or
3
729
___
64
8 12
c d
b
4
b c
t
5b. ____
5c. __
4
4
16a
s
Exercises 1. 25 3. 3 5. 7 × 10 2 7. 1
2
Check It Out! 1a. 0.01 1b. 100,000
n
)
7-4
a b
5
(
16
2b
4
1
9. __
11. ____
13. __
15. ___
17. 27
6 4
2
25
9
7-2
7-3
b
x
29. 27x 3 31. p 28q 14 33. -256x 12
35. 6 37. 3 39. 8 41. 2x 3 43. 2m 10n 6
45. 108x 13 47. 125x 6 49. 3a 6
a7
51. 10 3, or 1000 57. __
59. 15m 12n 9
b5
2 7
7
61. 9s t 63. t 67. yes 69. 17k 2
71. 6x 4 73. 15a 2b 3 75a. 6 × 10 -7 m
b. 3 × 10 8 m/s c. Associative
and Commutative Properties of
2
2
1
Multiplication 77. (6ab) 79. _____
2kmn
81. H 83. F 85. 3 2x 87. x + 1
2
89. x 3y + 3z 91. x x 93. x = 4
95. x = 4 97. 1.728 × 10 -6 99. 15
101. no 103. 7,800,000 105. 98.3
3
a
1
61. - __16 63. 3 65. 3 67. __
59. __
2
16
y
y
f
1
1
39. 1 41. ___
33. - __13 35. 4 37. ___
256
144
10
3
2
g
b
5
1
45. __
47. - __
49. ____
43. __
k4
Possible answer: solutions: (-6, 6),
(-10, 0); not solutions: (0, 0), (4, -4)
k
p7
5 12
g6
56.
7r
1
1
Exercises 1. ________
m 3. 1 5. __
10,000,000
27
3
1
17. __
19. x 10d 3 21. __4
15. - __
4
32
2
1
4b. ___
4c. g 4h 6
3b. 2 4a. ___
3
3
y
x
58.
3
13. 36k 2 15. -8x 15 17. b 10 19. 6 8
x
a 12
1
21. __
23. 2 9, or 512 25. __
27. ___
5
3
2
7-1
57.
1
1
, or __
11. x 7 y 13
mi 7. y 32 9. __
4
81
Chapter 7
3a
19. x 5 21. 5 × 10 -7 23. 7 × 10 -3
12
y3
a
29. __6
25. 2 × 10 27 kg 27. ___
6
b
31.
39.
x
y 25
196
3x 5
2
___
___
___
33.
35.
2
d
37.
4
x 10
9x 2
c4
25
1
__
__
___
41.
43.
45.
-1
100
a4
p2
47. 2000: 3 × 10; 1995: 2.84 × 10;
1990: 2.65 × 10 1 51. 3 53. 3; 4
55. B 57. A 59. 3 61. m; (-n);
m; -n; Definition of negative
exponent; an 63. 1 65. 12 67 x = - __12
69. 1 71. -125x 12
7-5
Check It Out! 1a. 3 1b. 1 1c. 3
2a. 1 2b. 5 3a. x 5 + 9x 3 - 4x 2 +
16; 1 3b. -3y 8 + 18y 5 + 14y; -3
4a. cubic polynomial 4b. constant
monomial 4c. 8th degree trinomial
5. 1606 ft
Exercises 1. d 3. a 5. 3 7. 0 9. 8
11. 3 13. 4 15. -8a 9 + 9a 8; -8
17. 3x 2 + 2x - 1; 3 19. 5c 4 + 5c 3 +
3c 2 - 4; 5 21. linear binomial
23. quartic polynomial 25. quartic
trinomial 27. 4 29. 6 31. 7 33. 1
35. 4 37. 2 39. 3 41. 4.9t 3 - 4t 2 +
t + 2.5; 4.9 43. x 10 + x 7 - x 5 +
x 3 - x; 1 45. 5x 3 + 3x 2 + 5x - 4; 5
47. -d 3 + 3d 2 + 4d + 5; -1
49. -x 5 - x 3 + 4x 2 + 1; -1
51. linear monomial 53. quadratic
trinomial 55. quartic trinomial
57. quadratic monomial 59. always
61. never 63a. 58.5 in3 b. 66 in3
c. 0 d. yes 65. -48; 0; 3270 75. A is
incorrect 77. J 79a. 58 cm; 65 cm
b. 50.310 cm 81. 90 - m
83. inconsistent; no solutions
85. consistent and independent;
p8
x2
one solution 87. __
89. __
5
16
y
7-6
Check It Out! 1a. 5s 2 + s
1b. 20z 4 - 6 1c. x 8 + 6y 8 1d. b 3c 2
2. 12a 3 + 15a 2 - 16a 3. -2x 2 - x
4. -0.05x 2 + 46x - 3200
Exercises 1. -3a 2 + 9a 3. 0.26r 4 +
0.32r 3 5. 3b 3c 7. 23n 3 + 3n + 15
9. 9x 2 - x - 6 11. 4c 4 + 8c + 6
13. -3r + 11 15. 8a 2 + 5a + 9
17. 12n 2 + 6n - 3m 19. d 5 + 1
21. 5x 23. 2x 3 - 5 25. 10t 2 + t
27. x 5 + x 4 29. -2t 3 + 8t 2
31. -6m 3 + 2m 2 + 5m + 3
33. 4w 2 + 6w + 4 35. t - 5
37. 2n -2 39. 6x 2 - x - 1
41. -u 3 + 3u 2 + 3u + 6 43. x = __32 ,
or 1.5 45. B is incorrect 47. 3x + 6
49. 6x + 14 51. 2x 2 + x - 5 55. G
57. 3x 2 - 2 69. b 11 71. 9z 12
7-7
Check It Out! 1a. 18x 5 1b. 10r 2t 4
1c. 4x 5y 5z 7 2a. 8x 2 + 2x + 6
2b. 15a 3b + 3ab 2 2c. 5r 3s 2 - 15r 2s 3
3a. a 2 - a - 12 3b. x 2 - 6x + 9
3c. 2a 2 + 7ab 2 - 4b 4 4a. x 3 - x 2 6x + 18 4b. 3x 3 - 4x 2 + 11x + 10
5a. x 2 - 4x 5b. 12 m 2
Exercises 1. 14x 6 3. 3r 5s 5t 5
5. 21x 7y 3 7. 4x 2 + 8x + 4
9. 6a5b 2 + 2a 4b 3
11. 10x 3y 4 - 5x 2y 2 13. x 2 - x- 2
15. x 2 - 4x + 4 17. 4a 4 - 2ab
- 12a 3b 2 + 6b 3 19. x 3 + 3x 2 - 7x
+ 15 21. -6x 4 + 12x 3 + 4x 2 - 18x
+ 20 23. x 3 - 4x 2 - 4x - 5
25a. 2x 2 - 3x b. 20 in2 27. -12r 5s 5
29. 10a 4 31. -6a 5b 6 33. -12a 7b 7c 8
35. 9s 2 + 54s 37. 27x 3 - 12x 2
39. 10s 3t 3 - 15s 2t 5 41. -10x 3 +
15x 2 + 5x 43. -14x 6y 3 + 7x 5y 4
45. x 2 + 8x + 16 47. 5x 2 + 13x - 6
49. 10x 2 - x - 2 51. 7x 2 - 52x - 32
53. x 3 - x 2 - x + 10
3
55. -10x 4 + 2x + 20x 2 - 19x +
3 57. 8x 5 - 12x 3 - 2x 4 + 17x 2 21 59. x 3 - 3x - 2
61. -x 3 + 3x 2 - 3x + 1 63. 16x 2 48x + 36 65a. 3; 2; 10x 5 + 5x 3; 5
b. 2; 2; x 4 - x 3 + 2x 2 - 2x; 4 c. 1; 3;
x 4 - 5x 3 + 6x 2 + x - 3; 4 d. m + n
67. 12x 2 + 12x + 3 69a. 2x 2
b. 800 m 2 71. 2x 2 - 7x - 30
73. 8x 2 - 16xy + 6y 2 75. 6x 2 9x - 6 77. x 3 + 3x 2 79. 2x 3 7x 2 - 10x + 24 81. 8p 3 - 36p 2q +
54pq 2 - 27q 3 87. C 89. D
91. -x 2 - 6 93. a. x 2 - 1 b. 8x +
16 95. x 3 + 3x 2 + 2x 97. a = 2
103. quadratic monomial
7-8
Check It Out! 1a. x 2 + 12x + 36
1b. 25a2 + 10ab + b2 1c. 1 + 2c 3 + c6
2a. x 2 - 14x + 49 2b. 9b 2 - 12bc +
4c 2 2c. a 4 - 8a 2 + 16 3a. x 2 - 64
3b. 9 - 4y 4 3c. 81 - r 2 4. 25
Exercises 3. 4 + 4x + x 2 5. 4x 2 +
24x + 36 7. 4a 2 + 28ab + 49b 2
9. x 2 - 4x + 4 11. 64 - 16x + x 2
13. 49a 2 - 28ab + 4b 2 15. x 2 - 36
17. 4x 4 - 9 19. 4x 2 - 25y 2
21. x 2 + 6x + 9 23. x 4 + 2x 2y 2 + y 4
25. 4 + 12x + 9x 2 27. s 4 - 14s 2 + 49
29. a 2 - 16a + 64 31. 9x 2 - 24x +
16 33. a 2 - 100 35. 49x 2 - 9
37. 25a 4 - 81 39. π x 2 + 8π x + 16π
41. x 2 + 2xy + y 2 43. x 4 - 16
45. x 4 - 8x 2 + 16 47. 1 + 2x + x 2
49. x 6 - 2a 3x 3 + a 6 51. 36a 2 25b 2 53. 4; 4 55. 25; 25 57. 9; 9
59. -5; -5 61. 840 65. 1, 4, 9, 16,
25, 36, 49, 64, 81, 100 67. B
69. D 71. x 3 + 4x 2 - 16x - 64
73. b = ± 2 √c 75. 13 cm
31. 2 3 · 3 4 32. b 10 33. r 5 34. x 12
1
1
1
35. 1 36. __
, or __18 37. __
, or ___
4
3
625
5
2
1
39. g 12h 8 40. x 4y 2
38. ____
6
16b
41. -x 4y 2 42. x 6y 15 43. j 6k 9
44. __15 45. m 8n 30 46. 8 × 10 11
47. 9 × 10 7 48. 1 × 10 10 49. 2.8 ×
10 15 50. 6 × 10 1 51. 1.8 × 10 -8
52. 3.55 × 10 7 53. 64 54. 4 55. m 5
7
56. 1 57. __
58. 6b 59. t 3v 4
32
60. 16 61. 5 × 10 1 62. 2.5 × 10 7
63. 2 × 10 4 64. 2.25 × 10 7 65. 0
66 4 67. 6 68. 7 69. 2 70. 1
71. 3n 2 + 2n - 4; 3 72. -a 6 - a 4 +
3a 3 + 2a; -1 73. -5t 2 - t + 1; -5
74. 6v 4 + 12v + 3; 6 75. -2x 2 + x +
5; -2 76. -2w 6 - w 3 + w 2 - w; -2
77. linear binomial 78. quintic
monomial 79. quadratic trinomial
80. cubic polynomial 81. quartic
trinomial 82. constant monomial
83. quintic trinomial 84. 7th-degree
polynomial 85. -4t + 3
86. -6x 6 - x 5 87. 3h 3 - 3h 2 + 5
88. 2m 2 - 5m - 1 89. p 2 + 5p + 8
2
90. -7z 2 - z + 10 91. 3g + 2g + 4
92. -x 2 + 4x + 8 93. 8r 2
94. 6a 6b 95. 18x 3y 2 96. 3s 6t14
97. 2x 2 - 8x + 12 98. -3a 2b 2 +
6a 3b 2 - 15a 2b 99. a 2 - 3a - 18
100. b 2 - 6b - 27 101. x 2 12x + 20 102. t 2 - 1 103. 8q 2 +
34q + 30 104. 20g 2 - 37g + 8
105. p 2 - 8p + 16 106. x 2 + 24x +
144 107. m 2 + 12m + 36 108. 9c 2
+ 42c + 49 109. 4r 2 - 4r + 1
110. 9a 2 - 6ab + b 2 111. 4n 2 20n + 25 112. h 2 - 26h + 169
113. x 2 - 1 114. z 2 - 225
115. c 4 - d 2 116. 9k 4 - 49
Chapter 8
Study Guide: Review
1. cubic 2. standard form of a
polynomial 3. monomial
4. trinomial 5. scientific notation
1
1
1
6. __
in. 7. 1 8. 1 9. ___
10. _____
,
32
125
10,000
27
1
1
12. ___
13. __
or 0.0001 11. __
4
16
256
1
1
15. b 16. - ____
17. 2b 6c 4
14. ___
2
2 4
18.
m
3a 2
___
4c 2
2x y
3
s
19. ___
20. 10,000,000
2
qr
21. 0.00001 22. 10 2 23. 10 -11
24. 325,000 25. 1800 26. 0.17
27. 0.000299 28. 5.8 × 10 -7,
6.3 × 10 -3, 2.2 × 10 2, 1.2 × 10 4
29. $38,500,000,000 30. 5 9
8-1
Check It Out! 1a. 2 3 · 5 1b. 3 · 11
1c. 7 2 1d. 19 2a. 4 2b. 5 3a. 9g 2
3b. 1 3c. 1 4. 7
Exercises 3. 3 2 · 2 2 5. 3 3 · 2 7. 7
(prime) 9. 3 · 5 2 11. 7 13. x 2
15. 1 17. 2 · 3 2 19. 2 2 · 3
21. 17 23. 7 2 25. 9 27. 10 29. 9s
31. 5 33. 4x 2 35. 2n 39. 15
rows 41. 8 and 20; 4 43. 63 and
105; 21 45. 54 and 72; 18 47. 36; 2;
9; 3 49. 105; 5; 7 51. 2; 2; 27; 3
Selected Answers
S95
53. 24; 2; 6; 3 55. 2; 2; 10, 5 57. D
61. 9y 63. 2p 2r 65. 4a 2b 3 69. 24
71. 25% 73. no 75. 3x 2 + 14x - 3
8-2
Check It Out! 1a. b(5 + 9b 2)
1b. cannot be factored
1c. -y 2(18y + 7)
1d. 2x 2(4x 2 + 2x - 1)
2. 2x cm; (x + 2) cm
3a. (4s - 5)(s + 6) 3b. (7x + 1)(2x + 3)
3c. cannot be factored 3d. (5x - 2)2
4a. (2b 2 + 3)(3b + 4)
4b. (4r + 1)(r 2 + 6)
5a. (5x 2 - 4)(3 - 2x)
5b. (8 - x)(y - 1)
Exercises 1. 5a(3 - a) 3. 7(-5x + 6)
5. 2h(6h 3 + 4h - 3) 7. m(9m + 1)
9. 3(12f + 6f 2 + 1) 11. 16t(-t + 20)
13. (2b + 5)(b + 3)
15. (x 2 + 2)(x + 4)
17. (2b 2 + 5)(2b - 3)
19. (7r 2 + 6)(r - 5)
21. 2(r - 2)(r - 3)
23. (7q - 2)(2q - 3)
25. (2m 2 - 3)(m - 3) 27. 9y(y + 5)
29. x 2(-14x 2 + 5)
31. -d 2(4d 2 - d + 3)
33. 7c(3c + 2) 35. -5g 2(g + 3)
37. cannot be factored
39. (6y + 1)(y - 7)
41. (-3 + 4b)(b + 2)
43. (2a 2 + 3)(a - 4)
45. (6x 2 + 1)(x + 3)
47. (n 2 + 5)(n - 2)
49. (2m 2 - 3)(m - 1)
51. (2f 2 - 5)(3f - 4)
53. (b 2 - 2)(b + 4) 55. 3v
57. 2k 59. 2; binomial; x(x + 5)
61. 3; trinomial; a 2(a 2 + a + 1)
63a. 100x 3; 200x 2; 400x
b. 100x 3 + 200x 2 + 400x + 800
c. 100(x 2 + 4)(x + 2); $1603.12
67. The sum of opposite binomials
is 0. 69a. Commutative Property
of Addition b. Associative Property
of Addition c. Distributive
Property d. Distributive Property
71. D 73. C 75. -9ab(8ab + 5)
77. (a + c)(b + d)
79. (x 2 + 3)(x - 4) 83. 2 2 · 13
85. 2 3 · 3
8-3
Check It Out! 1a. (x + 4)(x + 6)
1b. (x + 4)(x + 3) 2a. (x + 6)(x + 2)
S96
Selected Answers
2b. (x - 6)(x + 1) 2c. (x + 6)(x + 7)
2d. (x - 8)(x - 5) 3a. (x + 5)(x - 3)
3b. (x - 4)(x - 2) 3c. (x - 10)(x + 2)
4.
n
n 2 - 7n + 10
0
0 2 - 7 (0) + 10 = 10
1
1 2 - 7(1) + 10 = 4
2
2 2 - 7(2) + 10 = 0
3
3 2 - 7(3) + 10 = -2
4
4 2 - 7(4) + 10 = -2
n
(n - 5)(n - 2)
(0 - 5)(0 - 2) = 10
(1 - 5)(1 - 2) = 4
(2 - 5)(2 - 2) = 0
0
1
2
3
4
(3 - 5)(3 - 2) = -2
(4 - 5)(4 - 2) = -2
Exercises 1. (x + 4)(x + 9)
3. (x + 4)(x + 10) 5. (x + 2)(x + 8)
7. (x - 1)(x - 6) 9. (x - 3)(x - 8)
11. (x + 9)(x - 3) 13. (x - 2)(x + 1)
15. (x - 9)(x + 5) 17. (x + 3)(x + 10)
19. (x + 4)(x + 12)
21. (x + 2)(x + 14) 23. (x - 1)(x - 5)
25. (x - 4)(x - 8) 27. (x + 7)(x - 3)
29. (x - 13)(x + 1) 31. (x - 7)(x + 5)
33. C 35. D 37. They are inverse
operations. 39. (x - 2)(x - 9)
41. (x + 1)(x + 9) 43. (x + 6)(x + 7)
45. (x + 2)(x + 9) 47. (x - 3)(x + 8)
49. (x - 5)(x + 9) 51. approximately
1.5 55. x 2 + 6x + 8; (x + 4)(x + 2)
57. Positive; - , - ; Both negative
59. Negative; + , - ; Positive;
negative 61a. d = t 2 b. d = 4t
c. t(t - 4) 63. true 65. false 67. 4
69. 4 71a. (x + 10) ft b. = (x + 14) ft;
w = (x + 6) ft c. A = (x 2 + 20x + 84) ft 2
73. D 75. C 77. (x 2 + 9)(x 2 + 9)
79. (d 2 + 21)(d 2 + 1)
81. (de - 5)(de + 4) 83. 16; 11; 29
85a. (x + 7) ft b. (4x + 26) ft c. $92.00
d. $36.96 e. $128.96 87. x 5 89. t 12
91. (x + 2)(x 2 + 5)
93. (p - 2)(2p 3 + 7)
8-4
Check It Out! 1a. (3x + 1)(2x + 3)
1b. (3x + 4)(x - 2)
2a. (2x + 5)(3x + 1)
2b. (3x - 4)(3x - 1)
2c. (3x + 4)(x + 3)
3a. (3x - 1)(2x + 3)
3b. (4n + 3)(n - 1)
4a. -1(2x + 3)(3x + 4)
4b. -1(3x + 2)(x + 5)
Exercises 1. (2x + 5)(x + 2)
3. (5x - 3)(x + 2) 5. (3x + 4)(x - 6)
7. (x + 2)(5x + 1)
9. (4x - 5)(x - 1)
11. (5x + 4)(x + 1)
13. (2a - 1)(2a + 5)
15. (2x - 3)(x + 2)
17. (10x + 1)(x - 1)
19. (2x + 3)(4 - x)
21. -1(5x + 3)(x - 2)
23. -1(2x - 1)(2x + 5)
25. (3x + 2)(3x + 1)
27. (n + 2)(3n + 2)
29. (4c - 5)(c - 3)
31. (2x + 5)(4x + 1)
33. (5x - 6)(x + 3)
35. (10n - 7)(n - 1)
37. (7x + 1)(x + 2)
39. (3x - 4)(x - 5)
41. (x - 7)(4x - 3)
43. (4y - 1)(3y + 5)
45. (2x - 1)(2x + 3)
47. (3x + 5)(x - 3)
49. -1(2x - 3)(2x + 5)
51. -1(3x - 2)(x + 1)
53. 2x 2 - 5x + 2; (x - 2)(2x - 1)
55. (9n + 8)(n + 1)
57. (2x - 1)(2x - 5)
59. (3x + 8)(x + 2)
61. (3x + 4)(2x - 3)
63. (2x - 3)(2x - 3)
65. (2x + 3)(3x + 2)
69a. -16t 2 + 20t + 6
b. -2(4t + 1)(2t - 3) c. 10 ft 71. D
73. B 77. B 79. A 81. (2x + 1)
(2x + 1) 83. (9x + 1)(9x + 1)
85. (5x + 2)(5x + 2) 87. -7; -5; 5; 7
89. -6; 6 95. (x + 1)(x - 9)
8-5
Check It Out! 1a. (x + 2)2
1b. ( x - 7) 2 1c. no; -6x ≠ 2(3x)(2)
2. 4(3x + 1) m; 40 m
3a. (1 - 2x)(1 + 2x)
3b. (p 4 + 7q 3)(p 4 - 7q 3) 3c. no; 4y 5
is not a perfect square.
Exercises 1. yes; (x - 2)2 3. yes;
(3x - 2)2 5. yes; (x - 3) 2
7. 4(x + 12); 88 yd 9. yes;
(s + 4)(s - 4) 11. yes;
(2x 2 + 3y)(2x 2 - 3y)
13. yes; (x 3 + 3)(x 3 - 3) 15. No; the
last term must be positive. 17. no;
10x ≠ 2(5x)(2) 19. yes; (4x - 5)2
21. yes; (1 + 2x)(1 - 2x) 23. No;
4x and 9y are not perfect squares.
25. yes; (9 - 10x 2)(9 + 10x 2)
27. 49 29. 4y 2
31. (10x + 9y)(10x - 9y); difference
of 2 squares 33. (2r 3 + 5s 3)
(2r 3 - 5s 3); difference of 2 squares
35. (x 7 + 12)(x 7 - 12); difference of
2 squares 39. c = 32 41a. 5z - 4
b. 20z - 16 c. 11; 44; 121
43a. 0; 0; 100; 100; 0 b. 16; 16; 36;
36; -24 c. 25; 25; 25; 25; -25
d. 36; 36; 16; 16; -24 e. 100; 100; 0;
0; 0 45. a - b; a + b 47. C 49. 1
51a. a = 2; b = (v + 2)
b. [2 + (v + 2)][2 - (v + 2)] =
(v + 4)(-v) = -v 2 - 4v 53. a = 3y;
b = y; (3y - 4)(9y 2 + 12y + 16)
55. D: {5, 4, 3, 2}; R: {2, 1, 0, -1}; yes
57. D: {2}; R: {-8, -2, 4, 10}; no
59. 6a 3 + 14a 2 - 10a 61. t 2 - 8t + 16
63. 8
8-6
Check It Out! 1a. yes 1b. no;
4(x + 1) 2 2a. 4x(x + 2) 2
2b. 2y(x - y)(x + y)
3a. (3x + 4)(x + 1)
3b. 2p 3(p + 6)(p - 1)
3c. 3q 4(3q + 4)(q + 2) 3d. 2(x 4 + 9)
Exercises 1. yes 3. yes 5. no;
4(2p 2 + 1)(2p 2 - 1)
7. 3x 3(x + 2)(x - 2) 9. 2p(2q + 1) 2
11. mn(n 2 + m)(n 2 - m)
13. 3x 2(2x - 3)(x + 1)
15. (p 3 + 1)(p 2 + 3)
17. unfactorable 19. no;
2xy(y 2 - 4y + 5)
21. no; 3n 2(n + 5)(n - 5) 23. yes
25. -4x(x - 3)2 27. 5(d - 3)(d - 9)
29. 2x(7x + 5y)(7x - 5y)
31. unfactorable
33. (p 2 + 4)(p + 2)(p - 2)
35. (k 2 + 3)(2k + 3) 37. x 2 + 12x +
36 = (x + 6)2 39. s 2 - 16s + 28 =
(s - 2)(s - 14) 41. b 2 - 49 =
(b + 7)(b - 7) 45. (3x - 1)(x + 7)
47. (3x + y - 3)(3x - y - 7)
53. 8 55. C 57. C 59a. V =
8p⎡⎣π(3p + 1)2⎤⎦ b. r = (3p + 1) cm
c. h = 8 cm; V = 128π cm 3
61. h 2(h 4 + 1)(h 2 + 1)
63. x n + 3(x 2 + x + 1) 65. -2n
23
67. 12.3r 69. __
= __3x ; 34.5 cm
2
71. (2x - 1)(2x + 3)
Study Guide: Review
1. prime factorization 2. greatest
common factor 3. 2 2 · 3 4. 2 2 · 5
5. 2 5 6. prime 7. 2 3 · 5 8. 2 6
9. 2 · 3 · 11 10. 2 · 3 · 19 11. 5
12. 12 13. 1 14. 27 15. 4 16. 3
17. 2x 18. 9b 2 19. 25r 20. 6 boxes;
13 rows 21. 5x(1 - 3x 2)
22. 16(-b + 2) 23. -7(2v + 3)
24. 4(a 2 - 3a - 2)
25. 5g(g 2 - 3)(g 2 + 1)
26. 10(4p 2 - p + 3)
27. (6x + 5) ft by x ft 28. (2x + 9)
(x - 4)
29. (t - 6)(3t + 5)
30. (5 - 3n)(6 - n)
31. (b + 2)(b + 4)
32. (x 2 + 7)(x - 3)
33. (n 2 + 1)(n - 4)
34. (2b + 5)(3b - 4)
35. (2h 2 - 7)(h + 7)
36. (3t + 1)(t + 6)
37. (5m - 1)(2m + 3)
38. (4p - 3)(2p 2 + 1)
39. -1(r - 5)(r - 2)
40. (b 2 - 5)(b - 3)
41. (t + 4)(-t 2 + 6)
42. -1(3h - 1)(h - 4)
2
43. -1(d - 1) 44. (2 - b)(5b - 6)
45. (t + 1)(5 - t)
46. (2b 2 + 5)(4 - b)
47. -1(3r - 1)(r - 1)
48. left rectangle: 2x 2 + 3x; right
rectangle: 8x + 12; combined:
2x 2 + 8x + 3x + 12; (2x + 3)(x + 4)
49. (x + 1)(x + 5) 50. (x + 2)(x + 4)
51. (x + 3)(x + 5) 52. (x - 6)(x - 2)
53. (x + 5) 2 54. (x - 2)(x - 11)
55. (x + 4)(x + 20) 56. (x - 6)(x - 20)
57. (x + 12)(x - 7) 58. (x + 3)(x - 8)
59. (x + 4)(x - 7) 60. (x - 1)(x + 5)
61. (x + 3)(x - 2) 62. (x + 5)(x - 4)
63. (x - 8)(x + 6) 64. (x - 9)(x + 4)
65. (x - 12)(x + 6)
66. (x - 10)(x + 7)
67. (x + 20)(x - 6)
68. (x + 7)(x - 1) 69. (y + 3) m
70. (2x + 1)(x + 5)
71. (3x + 7)(x + 1)
72. (2x - 1)(x - 1)
73. (3x + 2)(x + 2)
74. (5x + 3)(x + 5)
75. (2x - 3)(3x - 5)
76. (4x + 5)(x + 2)
77. (3x + 4)(x + 2)
78. (7x - 2)(x - 5)
2
79. (3x + 2)(3x + 4)
80. (2x + 1)(x - 1)
81. (3x + 1)(x - 4)
82. (2x - 1)(x - 5)
83. (7x + 2)(x - 3)
84. (5x + 1)(x - 2)
85. -1(2x - 1)(3x + 2)
86. (6x + 5)(x - 1)
87. (3x - 2)(2x + 7)
88. -1(2x + 1)(2x - 5)
89. -1(2x - 3)(5x + 2)
90. 12x 2 - 11x - 5; (4x - 5)(3x + 1)
91. yes; (x + 6)2 92. no; 5x ≠ 2(x)(5)
93. no; -2x ≠ 2(2x)(1)
94. yes; (3x + 2)2 95. no; 8x ≠
2(4x)(2) 96. yes; (x + 7)2 97. yes;
(10x - 9)(10x + 9) 98. No; 2 is
not a perfect square. 99. No; 5
and 10 are not perfect squares.
100. yes; (-12 + x 3)(-12 - x 3)
101. no; terms must be subtracted
102. yes; (10p - 5q)(10p + 5q)
103. (x - 5)(x + 5); difference of 2
squares 104. (x + 10) 2; perfectsquare trinomial 105. (j - k2)(j + k2);
difference of 2 squares
106. (3x - 7)2; perfect-square
trinomial 107. (9x + 8) 2;
perfect-square trinomial
108. (4b 2 - 11c 3)(4b 2 + 11c 3);
difference of 2 squares
109. no; 2(2x + 3)(x + 1)
110. yes
111. no; (b 2 + 9)(b - 3)(b + 3)
112. yes 113. 4(x - 4)(x + 4)
114. 3b 3(b - 4)(b + 2)
115. a 2b 3(a - b)(a + b)
116. t 4 (t 8 + 1)(t 4 + 1)(t 2 + 1)
(t + 1)(t - 1) 117. 5(x + 3)(x + 1)
118. 2x 2(x - 5)(x + 5)
119. 2(s + 4)(t + 4)
120. 5m(5m + 2)(m - 4)
121. 4x(4x 2 + 1)(2x - 3)
122. 6s 2t (s + t 2)
123. 2(m + 3)(m - 3)(5m + 2)
Chapter 9
9-1
Check It Out! 1a. Yes; the second
differences are constant. 1b. Yes;
the function can be written in the
form y = ax 2 + bx + c.
Selected Answers
S97
2a.
y
x
2b.
y
x
13. (1, 8) 15. (-2, -2) 17. (-2, -9)
19. no zeros 21. -8, -2
23. x = 6 25. x = - __12 27. x = 5
29. (-3.5, -12.25) 31. (-2, 5)
33. (1, 4.5) 35. x = 0. 37. 0 39. 2
41. B 43. 2 45. 25 ft; 100 ft
47. y = -2x + 3 49. y = -4x + 2
51. yes
x
y
x
Exercises 1.
y
y
x
y
11. upward; a > 0 13. upward;
a > 0 15. downward; a < 0
17. (-3, -4); minimum: -4 19. D:
all real numbers; R: y ≤ 4 21. D: all
real numbers; R: y ≥ -4 23. yes
25. yes 31. upward; a > 0
33. vertex: (0, -5); minimum: -5
35. D: all real; numbers; R: y ≤ 0
37. D: all real numbers; R: y ≥ -2
39. never 41. always
43. sometimes 45. no 47. yes
49. yes 53. quadratic 55. quadratic
57. neither 59. linear 61b. t ≥ 0
c. 16 ft d. 2 s 65. C 67. yes
71. (-2)4 73. 42 __34 mi
9-2
Check It Out! 1a. no zeros
1b. 3 2a. x = -3 2b. x = 1
3. x = - __14 4. (2, -14) 5. 7 ft
Exercises 3. -1 5. no zeros
7. x = 2 9. x = -2 11. x = - __34
Selected Answers
x
5.
y
x
7. Maximum height: 144 ft at 3 s;
time in the air: 6 s
9.
y
symmetry x = 0 27b. D: {x | 0 ≤
x ≤ 3.16}; R: {y | 0 ≤ x ≤ 50} c. 3.16 s
35a. h(t) = -16t 2 + 45t + 50
b. (1.4, 81.6) 37. A 39. D 41. -1
43. 3; 6 45. none; 3 47. (3, -1)
49. (-1, -16) 51. (-1, 4)
9-4
f (x), h (x) 2a. same width, same
axis of symmetry, opens upward,
vertex is translated 4 units
down 2b. narrower, same axis of
symmetry, opens upward, vertex is
translated 9 units up 2c. wider, same
axis of symmetry, opens upward,
vertex is translated 2 units up
3a. The graph of the ball that is
dropped from a height of 100 ft is
a vertical translation of the graph
of the ball that is dropped from
a height of 16 ft. The y-intercept
of the graph of the ball that is
dropped from 100 ft is 84 units
higher. 3b. The ball that is dropped
from 16 ft reaches the ground in
1 s. The ball that is dropped from
100 ft reaches the ground in 2.5 s.
Exercises 1. f (x), g (x) 3. h (x),
x
)
Check It Out! 1a. f(x), g(x) 1b. g(x),
x
3.
S98
(
2. maximum height: 9 ft at 0.75 s;
time it takes to reach the pool: 1.5 s
y
(0, 0); axis of symmetry x = 0
23. vertex: (3, -5); axis of symmetry
x = 3 25. vertex: (0, -4); axis of
y
9.
13.
15
21. vertex:
19. x = - __12 ; - __12 , - __
4
15. x = 4; (4, -16) 17. x = 0; (0,4)
Exercises 1. minimum 3. yes
x
x
5. no
y
1b.
x
1a.
3a. Because a < 0, the parabola
opens downward. 3b. Because
a > 0, the parabola opens upward.
4a. Vertex: (-2, 5); maximum: 5
4b. Vertex: (3, -1); minimum: -1
5a. D: all real numbers; R: y ≥ 4
5b. D: all real numbers; R: y ≤ 3
y
9-3
Check It Out!
7.
11.
g (x), f (x) 5. same width, same axis
of symmetry, opens upward, vertex
is translated 6 units up 7. wider,
same axis of symmetry, opens
upward, same vertex
9a. h 1(t) = -16t 2 + 16, h 2(t) =
-16t 2 + 256; The graph of h 2 is a
vertical translation of the graph
of h 1. The y-intercept of h 2 is 240
units higher. b. The baseball that
is dropped from 256 ft reaches the
ground in 4 s. The baseball that
is dropped from 16 ft reaches the
ground in 1 s. 11. f(x), g(x) 13. f(x),
h (x), g (x) 19. always 21. never
25. f (x) = 3x 2 - 6 39. D 41. 0
43a. f (x) = x 2 - 7 b. f (x) = -x 2 + 2
c. f (x) = __12 x 2 + 1 45. no correlation
9-5
Check It Out! 1a. x = -4 1b. no
zeros 1c. x = -2 or x = 2 2. 2 s
Exercises 1. zeros, x-intercepts
3. -4, 4 5. 6 7. -2, 4 9. -1
11. no real solutions 13. no real
solutions 15. x = -4 or x = 4
17. x = __12 or x = 5 19. x = -3
21. no real solutions 23. no real
solutions 25. always 27. always
29. never 31a. 4 s b. 10 ft 33. 1.4 s
35. -1, 1 41. C 45. no real solutions
47. x ≈ -1.6 or x ≈ 0.86 49. y =
-3x - 2 51. 27 53. x 11 55. a 3b 3
27b 2
57. ____
6
8a
9-6
Check It Out! 1a. 0, -4 1b. -4, 3
2a. 3 2b. 1, -5 2c. - __53 2d. __13 , 1
3. 1.5 s
Exercises 1. -2, 8 3. -7, -9
5. -11, 0 7. -6, 2 9. 2, 3
11. -8, -2 13. 4 15. 6 17. 8
19. 1 s 21. -4, -7 23. 0, 9
25. - __12 , __13 27. -2, 4 29. -5
31. -2 33. 1 35. 1 37. 1 39. A is
correct 41. 6 m 43. 6 s 45. no
47a. 3 s b. 64 ft c. yes 49. F
51. -5, -1 53. __12 , -3 55. -2, 5
57. 3x 59. f - 4 61. 11 63. -10
65. -7, 7 67. 3, 5
9-7
Check It Out! 1a. ±11 1b. 0 1c. no
real solutions 2a. no real solutions
2b. ± __16 3a. ±9.49 3b. ±5.66 3c. no
real solutions 4. 45 ft
Exercises 1. ±15 3. no real
solutions 5. no real solutions 7. ±5
9. no real solutions 11. ±2
13. ±5.20 15. ±4.47 17. ±13
19. no real solutions 21. no real
13
solutions 23. ± __29 25. ± __58 27. ± __
7
29. ±4.69 31. ±10.20 33. ±7.07
35. 6.1 s 37. a = -6 and b
= -3 or a = 6 and b = 3 39.
about 4.2 ft by 8.4 ft 41. A 43.
sometimes 45a. a must be greater
than 0. b. a must be equal to 0. c.
a must be less than 0. 47. no; x =
√2
±___
, irrational 49. yes; x = ± __12 ,
2
rational 53. H 55. ± __14
8
59. 13 61. 2, 4 63. -2, 7
57. ± __
11
9-8
25
Check It Out! 1a. 36 1b. __
1c. 16
4
2a. -9, -1 2b. 4 ± √
21 3a. - __13 , 2
3b. no real solutions 4. 16.4 ft by
24.4 ft
Study Guide: Review
1. vertex 2. minimum; maximum
3. zero of a function 4. discriminant
of a quadratic equation
5. completing the square 6. Yes; it
is in standard form. 7. No; there
is no ax 2 term. 8. Yes; it is in
standard form. 9. No; a quadratic
function does not have a term to
the third power.
10.
y
Exercises 3. 4 5. -5, -1 7. -6, 5
x
-5 ± 3 √
5
13. no real
9. 1, 9 11. ________
2
solutions 15. 4 ± √
10 17. 7.2 m;
11.2 m 19. 1 21. -2, 12
23. -13, -2 25. -6, 8 27. -2, 3
-1 ± √5
11.
y
x
-15 ± √
105
29. _______
31. _________
33. 4 in.
2
2
7 37. -3, __12 39. -10, 2
35. 1 ± √
49
41. 81 43. __
45. 9 47a. (10 + 2x)
4
(24 + 2x)= 640 b. 3 ft
51. -6 ± 3 √
3 53. -6 55. no real
solutions 57. no real solutions
61a. -16t 2 + 64t + 32 = 0 b. 4
c. ≈4.4 s 63. B 65. B 67. - __32 , __23
12.
x
√
√7
7
, - __23 + ___
71. 0, - __ab
69. - __23 - ___
3
3
77. x 2 - 8x + 16 79. t 2 - 8t + 16
81. 64b 4 - 4 83. ±1 85. ±4 87. ±15
89. ±1.55 91. ±5.10 93. ±1.48
y
13.
y
x
9-9
Check It Out! 1a. 2, - __13 1b. 2, -__15
2. ≈ 0.13, ≈ 3.87 3a. 0 3b. 1 3c. 2
4. No; for the equation 45 =
-16t 2 + 20t + 0, the discriminant is
negative, so the weight will not ring
the bell. 5a. -2, -5 5b. -2, 7
5c. ≈-4.39, ≈2.39
Exercises 1. no 3. __12 , 3 5. -4, -10
1 __
7. -__
, 3 9. ≈-5.45, ≈-0.55
2 2
11. ≈1.14, ≈-1.47 13. ≈-1.85,
≈1.35 15. 1 17. 0 19. 2 21. 0
23. yes 25. -3 27. - __12 29. -3, __32
31. 1, 9 33. ≈0.27, ≈3.73
35. ≈2.78, ≈-0.72 37. 2
39. no 41. -5, 3 43. no real
solutions 45. 2 solutions; -2, __14
47. 1 solution; __23 49. 2 x-intercepts;
7
__
, -3 51. 1 x-intercept; 5 57. A
2
59a. 1 b. -1 c. -1 d. -1 63. -10, 4
65. (r 3 + t)(s 2 + 5)
67. (n 4 - 2)(n - 6) 69. f (x), g (x)
14. upward 15. downward
16. (-2, -4); minimum: -4
17. -5 and 2 18. -1 and 2
19. x = 6; (6, 4) 20. x = -1;
(-1, -18)
21.
y
x
22.
x
y
Selected Answers
S99
23.
y
x
35.
Chapter 10
y
10-1
Check It Out! 1a. bread
1b. cheese and mayonnaise
2. 2001, 2002, and 2005; about
13,000 3. about 18°F 4. Prices
increased from January through
July or August, and then prices
decreased through November.
5. 31.25%
6.
6ERAS$AY
x
24.
x
y
x = -3
36.
y
x
25.
no real solutions
37.
y
(OMEWORK
3LEEPING
3PORTS
x
x
y
26.
A circle graph shows parts of a whole.
38.
x = 1 or x = -1
Exercises 1. one part of a whole
3. 82 animals 5. $15 7. Prices at
stadium A are greater than prices at
stadium B. 9. between weeks 4 and
5 11. 18% 13. purple 15. blue and
green 17. 225,000 19. Friday
21. 3.5 times 23. games 3, 4, and 5
25. Stock Y changed the most
between April and July of 2004.
27. 8 __13 % 31. double line 33. circle
35a. Greece; about 40% b. United
States; about 15% 37. D 41. 19
girls 43. D: {-3, -1, 0, 1, 3}; R: {0,
1, 3}; yes 47. quadratic binomial
40.
10-2
y
(EIGHTM
39.
y
x
4IMES
y
x
x=4
In 2 seconds, the water reaches its
maximum height of 20 meters. It
takes a total of 4 seconds for the
water to reach the ground. 28. g(x),
f (x) 29. The graphs have the same
width. 30. h (x), f(x), g(x) 31. same
width, same axis of symmetry,
opens upward, vertex translated
5 units up 32. narrower, same
axis of symmetry, opens upward,
vertex translated 1 unit down
33. narrower, same axis of
symmetry, opens upward, vertex
translated 3 units up
x = -3 or x = -1
S100
x
7ATER&OUNTAIN
34.
%ATING
x = 1 or x = 5
3CHOOL
27.
/THER
x
y
Selected Answers
y
Check It Out!
1.
x
no real solutions 41. x = -5 or
x = -1 42. x = -7 or x = -2
43. x = -3 or x = 5 44. x = -1 or
x = 2 45. x = -5 46. x = 4.5
47. x 2 + 2x = 48; 6 ft 48. x = -8
or x = 8 49. x = -12 or x = 12
50. no real solutions 51. x = 0
52. x = -5 or x = 5 53. x = - __52 or
x = __52 54. 4 ft 55. x = -8 or x = 6
56. x = -7 or x = 3 57. x = 1 or
x = 5 58. x = 5 ± √
5 59. 16 ft
by 12 ft 60. x = -1 or x = 6
61. x = - __12 or x = 5 62. x = 1
6 ± √8
63. x = ______
64. 1 65. 0 66. 2 67. 2
2
4EMPERATUREª#
3TEM ,EAVES
Key: 1]9 means 19
2.
Interval
Frequency
4–6
5
7–9
4
10–12
4
13–15
2
3.
11a.
6ACATION
.UMBER
Cumulative
Frequency
Interval Frequency
36–38
4
4
39–41
6
10
42–44
5
15
45–47
1
16
b. 10
n
4a.
n n n
,ENGTHDAYS
15a.
Interval
Frequency
160–169.9
2
170–179.9
4
180–189.9
3
Interval
Frequency
Cumulative
Frequency
28–31
2
2
190–199.9
1
32–35
7
9
200–209.9
2
36–39
5
14
210–219.9
1
40–43
3
17
4b. 9
Exercises 1. stem-and-leaf plot
3. !USTIN 3TEM .EW9ORK
"REATHING)NTERVALS
5.
&REQUENCY
19. G 21. 8; 8; 41; 66 23. -2.3
25. 0.5 in. 27. books
10-3
Check It Out! 1a. mean: 9;
median: 8; mode: 8; range: 8
1b. mean: 3.6; median: 3; mode:
none 1c. mean: 15 __16 ; median: 15 __12 ;
mode: 12 and 18; range: 6 2a. mode:
75 2b. Median; the mean is lowered
by the 2 scores of 75, and the mode
is the lowest score.
Exercises 3. mean: 31.5; median:
n
7.
10-4
3.
n
n
n
4IMEMIN
3UMMER 3TEM 7INTER
33.5; mode: 44; range: 32
5. mean: 78.25; median: 78; mode:
78; range: 15
7.
9.
Key: ]2]1 means 21
Ê Ê 7]2] means 27
9.
Interval
Frequency
2.0–2.4
2
2.5–2.9
7
3.0–3.4
5
11. mean: 79.5; median: 82; mode:
none; range: 28 13. mean: 26.875;
median: 28; modes: 19, 31, and 34;
range: 15 15a. mean: 151 b. mean
3.5–3.9
3
17.
21. mean: 5.4; median: 5; mode: 5;
range: 1 23. mean: __12 ; median: __12 ;
mode: none; range: 1 25. mean: -2 __13 ;
median: -2 __12 ; mode: -3; range: 2
27. mean: 51.8; median: 51;
mode: 51; range: 2 31a. mean:
5.6875; median: 5.65; mode: 5.55;
range: 0.4 b. 5.95 m c. mean
37. increase the mean; decrease the
mean 39. sometimes 41. always
43. never 45. B 47. C 51. 32;
Typing speed is 32 words per
minute. 53. length: 5 yd; width: 3 yd
Check It Out! 1. Company D; the
fertilizer from company D appears
to be more effective than the other
fertilizers. 2. Possible answer: taxi
drivers; the drivers could justify
charging higher rates by using
this graph, which seems to show
that gas prices have increased
dramatically. 3. Smith; Smith
might want to show that he or she
got many more votes than Atkins or
Napier. 4. The sample size is much
too small.
Exercises 3a. The vertical scale
does not start at 0, and the
categories on the horizontal scale
are not at equal time intervals.
b. Tourism is decreasing rapidly.
c. someone who wants to run a
campaign to increase tourism
5. The sample size is too small.
7a. The vertical scale does not
start at 0. b. Single men pay
significantly more than single
women. 9a. The sectors of the
graph do not add to 100%.
b. Someone might believe that
half of the state’s spending was for
welfare. c. someone who wants
to justify cutting spending on
welfare 15. B 19. w ≤ 1500
21. b ≤ 20 23. t ≥ -4
10-5
Check It Out! 1. sample space:
{1, 2, 3, 4, 5, 6}; outcome shown: 3
7
13
2. certain 3a. __
3b. __
4a. 99.8%
20
20
4b. 34,930
Exercises 3. sample space: {blue,
red, yellow, green}; outcome shown:
red 5. impossible 7. unlikely
Selected Answers
S101
10-6
41. independent: hours; dependent:
total fee; f (x) = 300 + 8x
⎢
2a. 217 2b. 21
3.
1
2. 0.4 3. __
25
9
23. __15 25. __45
17. __59 19. 70% 21. __
10
27. 4:1 31. __12 35. D 37. B
13
1
41. (4x - 3)(x - 1) 43. __
45. __
10
20
Exercises 1. dependent
3. independent 5. independent
1
7. __18 9. __16 11. __
13. __27
16
Short
sleeve
Small ⎡ 126
Medium 228
Large ⎣ 57
1.
3
b. __16
27. independent 29a. __
20
9
1
2
___
__
__
c. 100 d. 15 31. 15 35. D 37. A
39. 72.9% 41. 80% 43. 48%
5
45. 24 47. wider 49. __35 51. __
26
10-8
Check It Out! 1. 15,600
2a. permutation; 6
2b. combination; 6 3. 362,880
4. 792
Exercises 1. combination 3. 8
5. combination; 6 7. 20,160 9. 35
11. 15,504 13. 441,000
15. combination; 10 17. 120
19. 133,784,560 21. nP r
1
25a. _________
b. 85,810 h 27. J
308,915,776
29. 227,920 31. 168 39. independent:
minutes, t ; dependent: volume
of water in tub, v : v(t) = 15t
S102
Selected Answers
8.
3.
Capacity
F V E
Tetrahedron ⎡ 4
4
6⎤
Cube 6
8 12
Octahedron 8
6 12
Icosahedron ⎣ 20 12 30⎦
At bats
Johnson ⎡ 69
Crabtree 108
Aguirre ⎣ 47
⎢
Hits
22⎤
31
13⎦
b. 52.96 km
17. ⎡ -4
0
-12
12
⎣ 0 -24
⎢
19. ⎡⎣-4.92
21. ⎡ 12 __1
⎢ __12
⎣ -2
-6
16 ⎤
-20
4⎦
1.68⎤⎦
-7 __12 -2⎤
10
-5⎦
Study Guide: Review
1. outcome 2. interquartile range
3. independent events 4. 2003
5. 14 more boys
6. 3TEM ,EAVES
Key: 1]2 means 12
Tally
Frequency
IIII I
15−19
IIII IIII
20−24
III
3
25−29
III
3
6
10
'AS4ANK#APACITIES
n
Km
Day 1 ⎡16.32 ⎤
Day 2 29.76
Day 3 ⎣ 6.88 ⎦
⎢
10−14
9.
5. 1 × 1 7. 2 × 4 9. 3 × 3
11. ⎡ 3 10 ⎤ 13. ⎡-1.4 ⎤
⎢
⎢
⎣-1 2 ⎦
⎣ 0.7 ⎦
15a.
Gas Tank Capacities
⎢
Key: ]12]8 means 128
Ê Ê 4]10] means 104
Exercises
1
15. dependent 17. __18 19. __
12
27
1
b. __
25. dependent
21. __29 23a. __
64
64
36
41 ⎦
Long
sleeve
156⎤
129
78⎦
⎢
10-7
Check It Out! 1a. Independent;
the result of rolling the number
cube the first time does not affect
the result of the second roll.
1b. Dependent; choosing the first
student leaves fewer students to
choose from the second time. 2. __14
8
3. __
87
Check It Out! 1. North West
P ⎡14 19 ⎤
B 23
W ⎣16
$AYSAND
$AYS
#AMP
Extension Answers
Check It Out! 1a. 50% 1b. 33 __13 %
Exercises 1. complement 3. 25%
9
5. __12 7. __23 9. __
11. 1:12 13. __14 15. 50%
10
7. #OMEDY
&REQUENCY
3
9. __
11a. 30% b. 54 13. sample
5
space: {blue, red, yellow}; outcome
shown: blue 15. as likely as not 17.
6
likely 19. __
21a. 5% b. 21 25. as
25
likely as not 27. 1%; 57 29. B 31. B
33. as likely as not 35. unlikely
37a. 7 b. 8 39. $14 41. reflected
across the x-axis 43. mean: 6;
median: 5; mode: 5
n n n
#APACITYGAL
10. mean: 14; median: 12; mode:
12; range: 28 11. Median; the mean
is higher than 4 of the 5 prices; the
mode is the lowest price.
12.
13. The scale on the vertical axis is
too large. This makes the slopes of
the segments less steep.
14. Someone might believe that the
price has been relatively stable,
when in fact it has doubled.
15. 99.5% 16. 24,875 17. 250 18. __12
19. __14 20. __58 21. independent
22. independent 23. dependent
2048
256
24. ____
25. 0 26. ____
27. 60
9555
2401
28. permutation; 604,800
29. combination; 220
30. combination; 1365
Chapter 11
5b.
x
y
11-1
Check It Out! 1a. 80, -160, 320
1b. 216, 162, 121.5 2. 7.8125
3. $1342.18
6. after about 13 yr
Exercises 3. 25, 12.5, 6.25
Exercises 1. no 3. no 17. about
5. 1,000,000,000 7. 4 9. 162, 243,
364.5 11. 2058; 14,406; 100,842
5 ___
5
13. __
, 5 , ___
15. 0.0000000001, or
32 128 512
2023 19. 289 ft 21. yes 23. no
x
35. y = 4.8 (2) 41. -0.125 45. C
47. D 49. 3 51. The value of a is
the y-intercept. 53. 25 55. 9x 2
1
1 × 10 -10 17. 80; 160 19. __13 21. __17 ; __
49
1
__
23. 6; -48 25. 4913 27. yes; 3 29. no
31. no 33a. 1.28 cm b. 40.96 cm
35. -2, -8, -32, -128
3
37. 2, 4, 8, 16 39. 12, 3, __34 , __
16
43a. $3993; $4392.30 b. 1.1
c. $2727.27 45. J 47. x 4, x 5, x 6
49. 1, y, y 2 51. -400 53. the 7th
term 55. b > 10 57. c < - __13
61. f (x) = x 2 + 4
11-2
Check It Out! 1. 3.375 in. 2a. no
2b. yes
3a.
y
x
3b.
y
x
4a.
11-5
Check It Out! 1. y = 1200(1.08)t;
$1904.25 2a. A = 1200(1.00875)4t;
$1379.49 2b. A = 4000(1.0025)12t;
t
$5083.47 3. y = 48,000(0.97) ; 38,783
4a. 1.5625 mg 4b. 0.78125 g
Exercises 1. exponential growth
t
3. y = 300(1.08) ; 441 5. A =
4t
4200(1.007) ; $4965.43 7. y =
t
10(0.84) ; 4.98 mg 9. 5.5 g 11. y =
t
1600(1.03) ; 2150 13. A = 30(1.078)t;
47 members 15. A = 7000(1.0075)4t;
t
$9438.44 17. A = 12,000(1.026) ;
t
$17,635.66 19. y = 58(0.9) ; $24.97
21. growth; 61% 23. decay; 33 __13 %
25. growth; 10% 27. growth; 25%
t
29. y = 58,000,000(1.001) ;
t
58,174,174 31. y = 8200(0.98) ;
t
$7118.63 33. y = 970(1.012) ; 1030
35. B 37. 18 yr 39. A; B 45. D 47. D
49. about 20 yr 51. 100 min, or 1 h
40 min 53. $225,344 55. 16 ft
1a.
x
y
x
Exercises 1. There is no variable
under the square-root sign.
3. x ≥ -6 5. x ≥ 0 7. x ≥ -3
15. 49.96 mi/h 17. x ≥ 0 19. x ≤ __32
21. x ≥ - __53 23. x ≥ 40 25. x ≥ 9
45. A 47. C 49. x ≤ -5 OR x ≥ 5
51. x ≤ -4 OR x ≥ __32
53. D: x ≤ 3; R: y ≤ 4 57a. 2 and 4
b. 3, 1 61. 9x 2 - 6x + 1
63. a 2 - 2ab 2c + b 4c 2 65. 9r 2 - 4s 2
67. A = 42,000(1.0125)4t;
$48,751.69
11-6
z 2 √z
x
p3
q
84.9 ft
Exercises 1. 3x - 6 3. 7 5. 6 √
5
17
6
2 9. 4x 2y √
2y 11. ____
13. ___
7. 18 √
5
7
√
6 √3
√
√x
x
x
√
41 mi; 32 mi 25. 20 27. 9
23. 5 √
29. ⎪x + 1⎥ 31. ⎪x - 3⎥ 33. 20 √
10
3 √
5
√
14
5 37. ____
39. ____
41. ____
35. 8rs √
3
2
3
8s √3
y
√
16 2
5x 2
17. ____
19. _____
21. _____
15. ___
7
3
9
13
y
3b.
2 √
5
exponential
1b.
5a.
x
4b. ____
4c. __5 5. 60 √
2 ft;
4a. ____
7
5y
x
y
y
y3
y
6
3b 3a. __23 3b. __
3c. __
2c. 4a √
2
2
3a.
Check It Out! 1a. 8 1b. 7 1c. 13
1d. ⎪3 - x⎥ 2a. 8 √
2 2b. xy √
x
4b.
1b. 30.98 ft/s 2a. x ≥ __12 2b. x ≥ __53
11-4
x
Check It Out! 1a. 40 ft/s
11-3
Check It Out!
y
Exercises 5. exponential 7. Grapes
cost $1.79/lb; y = 1.79x ; $10.74
11. linear 13. exponential
15. = 6k ; linear 17. linear
x
145
19. y = 0.2(4) 21. linear 33. ___
g
9
9
__
__
35. 5, -5 37. 4 , - 4
quadratic 2. quadratic 3. The oven
temperature decreases by 50°F
every 10 min; y = -5x + 375; 75°F
x √x
y
47. 15x √7
45. -20 √3
43. ____
7
x 3 √x
____
√
49. x 51. 3 53. 36 ; 6 55. √
50 ;
59. √
2 57. √3
20 ; 2 √
5 67. C
5 √
69. C 71. x √
x + 1 73a. ⎪x⎥ b. x 2
c. ⎪x 3⎥ d. x 4 e. ⎪x 5⎥ f. x n; ⎪x n⎥
77. exponential
Selected Answers
S103
11-7
7 1b. 3 √
3
Check It Out! 1a. - √
+ 8 √
1c. 8 √n
5s 2a. 5 √
6
1d. √2s
- 3 √2
2c. 5 √
2b. 12 √3
3y
in.
3. 10 √b
+ 5 √
Exercises 3. 10 √
5 5. 3 √7
2
+ 6 √5a
9. 13 √3 11. - √5x
7. 5 √6a
- 4 √3t
15. 6 √3 17. -3 √
13. 8 √2t
11
√
√
19. -4 √n
21.
7
7
23.
12
2
25. 3 √
7x - 12 √
3x 27. 3 √
5j
31. 12 √7 33. 0 35. 7 √3
29. 2 √3m
37. 7 √
2 41. 2 √
3 + 5 √
5+5
43. 8 √
7x - √
70x 45. 35 √
5k
47. 5 √
3 + 5 √
5 51. 9 53. 18
in.; 8 √
55. 36x 2 57. 16 √3
3 in.;
24 √
3 in. 59. B 61. A 63. √
x (x + 2)
65. 0 67. (x + 2) √
x-1
1
69. 3 √
x + 1 - x √
x + 2 73. __
12
75. x ≥ -3
11-8
Check It Out! 1a. 5 √
2 1b. 63
- 3 √6
2a. 4 √3
1c. 2m √7
2b. 5 √
2 + 4 √
15 2c. 7 √
k - 5 √
7k
3a. 21 - 5 √
2d. 150 - 20 √5
3
3b. 83 + 18 √
2 3c. 11 - 6 √2
√
√
65
21a
3 4a. ____
4b. _____
3d. 17 - √
5
6
8 √
35
4c. _____
7
17. quadratic 18. linear
19. exponential 20. exponential
21. quadratic 22. linear
23. y = 1.5x; 15 h 24. 4.74 cm
25. x ≥ 0 26. x ≥ -4 27. x ≥ 0
28. x ≥ -2 29. x ≥ __43 30. x ≥ -3
18
31. x ≥ __72 32. x ≥ - __
33. x ≥ __34
5
34. x ≥ 1
Extension Answers
36.
35.
x
16
65. 1 67. 0 69. 625 71. -1
63. ___
625
73. 11% 75. x 4
√
33
____
18
21.
27. 3 √
10 29. 8
19.
√
√
√
33. 4 31. 6d 7
5-5 2
35. 2 √
3 - 2 √
5 37. 3 √f + 12 √
3f
39. 75 + 19 √
15 41. 10 - √
2
√
5 √
6
3x
43. 67 + 16 √
3 45. ____
47. ____
x
2
1. square-root function
2. exponential decay 3. common
ratio 4. exponential function
5. 81, 243, 729 6. 48, -96, 192
7. 5, 2.5, 1.25 8. -256, -1024, -4096
9. 7,812,500 10. 19,131,876 11. yes
12. no
y
x
37.
x
Check It Out! 1a. 36 1b. 3 1c. __13
2a. 9 2b. 18 2c. 3 3a. 121 3b. 64
11
3c. 100 4a. 2 4b. __
5a. no solution
2
5b. no solution 5c. 4 6. 8; 3 cm
Selected Answers
38.
y
13.
x
39.
y
x
y
40.
y
x
14.
x
y
41.
y
x
15. y = 9(1.15) ; 24
t
16. y = 24,500(0.96) ; 3182
42.
x
y
x
S104
t
11-9
y
√
3
87. translation 4 units down
1
75. B 77. D
71. 269.5 ft 2 73. ___
+ 4 √5
81. -5 - 2 √
6
79. -4 √3
√
83. 2 - 3 85. 2 √
6 + 2 √5
7 √
2x
51. 2 √y 53. 180 in 2
49. _____
2
cm 2 57. √
55. 6 √
10 - 2 √5
30
61. 3 √
59. -5 - 2 √3
2
63. 134 √
3 + 96 65. x - 2 √xy
+y
π √6
____
+ x 69. 4 s ≈ 1.9 s
67. 3 + 2 √3x
Check It Out! 1a. 3 1b. 0 1c. 2
1d. 12 2a. 11 2b. 3 2c. 4 3a. 8 3b. 1
3c. 81
Exercises 1. 13 3. 5 5. 2 7. 20 9. 7
11. 2 13. 6 15. 8 17. 2 19. 4
25. $9698 27. 4 29. 9 31. 1 33. 27
35. 14 37. 17 39. 20 41. 25 43. 216
45. 64 47. 125 49. 32 51. 113.04 cm 2
8
1
53. __23 55. __14 57. __49 59. ___
61. __
343
27
y
Study Guide: Review
Exercises 1. √
6 3. 125 5. 3 √
30a
√
√
7. 2 6+ 42 9. √
35 - √
21
11. 5 √
3y + 4 √
5y 13. 12 + 7 √
2
17. 81 - 30 √2
15. -5 - 2 √3
√
26
____
2
Exercises 1. No; it does not contain
a variable under the radical sign.
3. -8 5. -144 7. 27 9. 50 11. -2
13. 9 15. 64 17. 16 19. 16 21. __49
23. 100 25. 5 27. 13 29. 6 31. 2
33. no solution 35. 4 37. 2 39. no
solution 41. 48 43. -25 45. 71
47. -8 49. 36 51. -16 53. 8 55. 9
57. 2 59. -5 61. 5 63. 1 65. 1
67. x = 144; 12 in. 69. √
x - 3 = 4; 49
71. x = √
x + 6 ; 3 73. 3 in. by 1 in.
75a. 54.88 joules b. 0 joules
77. 1690 ft 79. x = 25; y = 16
87. A 89. C 95. 2
43.
4. 3 5. 80.625 lb
y
Exercises 3. no 5. yes 9. 4
11. 16 teeth 13. yes 15. no
19. 2 21. 12 yd 23. direct; 8
25. neither 27. inverse; 12
10
29. inverse; 15 31. d = __
n ; inverse
33. neither 41. C 43. C
49. D: {-4, -2, 0, 2, 4}; R: {1, 3, 5};
yes 51. -1, 7 53. 2 √
10 cm
x
44.
y
x
2
2 √
56. _____
57. ____
58.
s
7
4p
2
t
4√
t
10
2b 2
_____
5
3
3 √
+ 2 √3
7 60. 3 √
3 61. 3 √2
59. 9 √
62. √
5t 63. 2 √
2 64. 2 √
3 + 2 √
5
67. √
65. -2 √
5x 66. 10 √6
14
68. 3 √
2 69. 6 √
7x 70. 150
4 √
5
71. 4 √
2 - 4 72. 71 + 16 √
7 73. ____
5
Check It Out! 1a. 0 1b. 1 1c. -4
2a. x = 5; y = 0 2b. x = -4; y = 5
2c. x = -77; y = -15
3a.
x
6OLUMEOFGASMM
3. D: x > 0; R: y > 0; 2.5 mm 3
p+6
67. -2, 0 73. -6
y
5x 2y 4
Check It Out! 1a. - __94 1b. ____
6
p - p - 20
n+4
3m - 15
3a. ______
3b. _________
2. ______
2
3
m-6
2
x
4a.
n + 2n
p + 16p
3x - 15
2w 6
x
______
____
________
4b.
4c.
x5
v 2x 3
x 2 + 5x + 6
5. approximately 0.23
4a. D: x > 0; R: natural
numbers > 10
6h
2x - 4
Exercises 1. ___
3. _____
5. __a6
3
5jk 2
m - 10m
7. 3y -6 9. ________
11. a 3 + 10a 2 +
2
2
a + 6b
2r + 28
15. __12 17. ______
19. b
25a 13. _____
2
r-4
b
3p 8q 2
10y + 20
1
21. ______
23. - _____
25. _______
4
3x - 15
3y + 15
27. 4m 2 - 4m
1
35a.
33. - ___
3
#OPIES
Exercises 1. excluded value 3. -3
5. 4 7. x = -5; y = 0 9. x = -9;
y = -10 15. 0 17. 0 19. x = 4; y = 0
21. x = 3; y = 4 29. 7 39. x = 2; y = 5
41. B 43. C 51. D: x > 2 53. D: x >
- __15 55. I and III; II and IV 59. J
61a. yes b. D: all real numbers
3
c. R: 0 < y ≤ 1 d. no 63. y = ____
+3
x+2
65. -2, 3 67. 0.46875 cm 69. No;
the product xy is not constant.
Check It Out! 1a. -5 1b. 0, -5
m
1c. -3, -4 2a. __
; m ≠ 0 2b. 6p
3
3n
b-5
1
; n ≠ 2 3a. ____
3b. ____
2c. ____
r+5
n-2
b+5
3
3
1
____
____
_____
4b. 4c.
5.
4a. 4+x
0RESSUREATM
p-7
z-1
35. ____
31. __8t ; t ≠ 0 33. ____
p-5
z+1
a-3
65. ±14
b. 3 c. 1 57. F 63. ____
a+5
2
x
12-3
1
29. already simplified; m ≠ 4
3w + 7
5+x
49. 1 51. - ____
53a. __6s
47. _____
3
x+2
2
2
same: ______
. 25. 0 27. - __12 , 4
b +b
12-4
3b.
0RICE
b
2
23a. ______
b. They will be the
b +b
Check It Out! 1a. No; the product
y
5
19. not possible 21. - _____
10 + q
2
1
39. - ____
43. ____
45. __13
37. ____
x-4
12
b+7
Chapter 12
xy is not constant. 1b. Yes; the
product xy is constant. 1c. No; the
equation cannot be written in the
form y = __kx . 2. y = __5x
j-5
c+2
2
15. ____
17. - ____
13. ____
c-4
8+n
j-3
y
4b.
12-1
h
1
; h ≠ -2 11. ____
y ≠ -3 9. ____
h+2
b+1
b
√3
√
√6
10n
3a √2
75. ___
76. _____
77. ___
74. _____
2
3
2n
2
3 79. 64 80. 8 81. 3 82. 25
78. - √
83. -81 84. 100 85. 3 86. no
solution 87. x = 4 88. x = 6
19
89. x = 7 90. x = __
91. x = 12
2
92. x = 3 93. x = 4 94. x = 5
2
Exercises 3. 0, 8 5. __a2 ; a ≠ 0 7. ____
;
y+3
1
12-2
45. 11 46. n 2 47. x + 3 48. 5
49. 6d 50. y 3 √
x 51. 2 √
3
√
5
t
2 √
___
54. __
55. __2
52. 4b 2ab 53.
survive. Its surface-area-to-volume
ratio is greater than for a cactus
with a radius of 6 inches.
x+1
x + 11
The barrel cactus with a radius of
3 inches has less of a chance to
7r
3n 2 - 3n
29. _______
31.
n+8
x2
___________
1
2a
4(4x 2 + 8x - 1)
9
1
___
37.
B
39.
b. ___
236
2m
1
41. ___
43. 1 45a. 64 cm b. 80 cm
16x
x
1
51. __13 53. __
c. 4 47. H 49. ______
2
2
3x + 9x
z
1
57. 12 + 9 + m ≤ 30; m ≤ 9
55. _____
2a + 2
61. x ≠ 3; x = 3 and y = 0
59. 8 √3t
63. x ≠ 0; x = 0 and y = 3 65. x ≠ 0;
x = 0 and y = 0
12-5
Check It Out! 1a. 2 1b. 3y
4b + 12
3
2a. ____
2b. ________
3a. 15f 2h 2
2
a-2
b + 3b - 4
4d - 3
3b. (x - 6)(x + 2)(x + 5) 4a. _____
2
a+8
5
5. __
h or 12.5 min
4b. ____
a-2
24
3d
1
2
Exercises 1. __2y 3. ____
5. ____
x-4
a+1
7. 6x 3y 2z 9. (y + 4)(y - 4)(y + 9)
x+3
260
1
__
13a. ___
11. ____
r b. 6 2 h 15. a - 1
x+2
17. m 19. 3a + 1 21. 36a(3a + 1)
y+2
23. 10xy 3z 27. ______
3(y - 3)
Selected Answers
S105
19
-m - 6m
700
29. ___
31. ________
33a. ___
2
r
21z
2
4 (m - 2 )
3
1
b. 14 h 35. ____
37. ___
7+c
2b 2
8x + 20
43. A
41. __________
(x + 4)(x + 2)
2
3
47. 4x ; 8x ; 8x 49. A 51. D
x - 4y
; x ≠ y and x ≠ -y
53. __________
x+y x-y
(
)(
az + by +cx
)
55. _________
; x ≠ 0, y ≠ 0, and
xyz
z ≠ 0 61. __12 , 4 63. 2; t ≠ ±2
1
65. - ____
; x ≠ ±4
x+4
39. 2; 3 is extraneous. 41. no
solution; 4 is extraneous.
240
43. ___
; t - 2; 40 mi/h
t
1
1
45a. __
= __
+ __1y b. 40 cm
15
24
c. It will increase to 72 cm. 49. F
53. Eddie: 6 h; Luke 3 h; Ryan: 4 h
55. y = -2x and y = __12 x + 4 are
perpendicular. 59. 5
Check It Out! 1a. -2p + 1 - __p3
5
1b. x 2 + __13 - __
2a. k + 5 2b. b - 7
2x
2c. s + 6 3a. 2y + 1 3b. a - 2
13
20
4a. 3m - 5 + _____
4b. y + 6 + ____
m+3
y-3
-7
5a. x 2 - 2x - 4 + ____
x-2
-7
5b. 2p 2 - 2p + 6 + ____
p+1
14
Exercises 1. 2x - __12 3. 7b - __
+ __b8
3
5. 2x + 4 + __3x 7. 2x - 3 9. 2y + 5
11. x + 1 13. c + 3 15. x - 2
-1
-1
17. a + 2 + ____
19. n + 4 + ____
n+4
a+2
-2
21. 4n - 5 + _____
2n + 1
x
19.
x
2
29. 3t + 4 - __2t 31. -4p + 1 + __
3
9. y = __1x
y
7IDTHCM
21. 0 22. 7 23. 0, 1 24. -1, 5
1
25. 5, -5 26. 4, 7 27. __
;
3r
1
r ≠ 0 28. _____
;
2k - 3
2b + 2b
4
_______
x ≠ -6 and x ≠ 5 33. __
π 34.
3
2
4x - 12x
15b
- 3c
36. ____
37. ____
35. _______
2
3
2
2
x
3
45. -20 47. 2x - 5 + ____
x+1
51. 0.5m + 1 57. C 59. B
-2
; x ≠ ±3
and x ≠ 2 30. ____
x+3
x+3
3
____
31. x - 1 ; x ≠ -5 and x ≠ 1 32. ____
;
x-5
-216
43. 2t 2- 6t + 25 + _____
3t + 9
1
; x ≠ -6
k ≠ 0 and k ≠ __32 29. ____
x-2
p
y
20. D: x > 0; R: y > 0
1. rational expression 2. rational
function 3. rational equation
4. inverse variation 5. discontinuous
function 6. Yes; the product xy is
constant. 7. No; the product xy is
not constant.
8. y = - __4x
Study Guide: Review
-10
27. 4k 2 - 4k + 2 + ____
k+1
2
3
b+2
n 2 + 3n + 2
39. ________
38. _______
2
2
2b + 8b
4d
n - n - 42
2
2y
1
61. 3x - __
+ __
x 63. x + 2
2y
√
15
10. -15 11. $13,200 12. -4; x = -4
and y = 0 13. -1; x = -1 and y = 3
14. -3; x = -3 and y = -4 15. __74 ;
x = __74 and y = 5
65. 3 m 67. ____
15
5 - 5 √
2 71. 4(x + 1)
69. 6 √
73. 2k 2 + 5k + 2
16.
12-7
Check It Out! 1a. 2 1b. 1 1c. - __76
2a. -4 2b. -4 2c. 1, 3 3. 22 __29 min
4a. 5; 7 is an extraneous solution.
4b. 1 and 5; no extraneous
solutions. 4c. 4; 0 is an extraneous
solution.
11
3. -24 5. - __83 7. __32 9. __35 11. - __
5
15
4
__
__
13. 19 15. 3, - 3 17. -2, 3 19. -1, __32
21. __12 h, or 30 min 23. - __43 ; 1 is
extraneous. 25. -2 27. 0 29. __4
5
b +8
46. 10x (x - 3) 47. _____
2b
2
8p - 2
3x 2 + 2x - 4
48. _________
49. _________
2
2
x -2
p - 4p + 2
7m + 2
5b - 1
-10
51. _____
52. ______
50. _____
2
2
7-b
10m
x
18
68. 3b 2 + 6b + 8 + ____
b-2
x
5
57. x + 2 58. 3n + 1
56. x - __2x + __
2
36
67. 2n + 7 + ____
n-5
y
2(b + 4)(2b + 7)
4x - 16
59. h + 12 60. 3x + 2 61. m - 6
62. 3m + 4 63. x + 2 64. x + 6
-3
65. p - 2 66. 2x - 1 + ____
x+2
17.
(b + 8)(b + 7)
44. ____________ 45. 10a 2b 2
h 2 + 5h - 1
40
54. __
55. 2n2 - 3n - 5
53. _________
3r
h-5
x
y
x 2 + 2x - 3
12n 3
1
________
40. ____
41. __
42. ____
2
m 43.
3
b-3
n -1
y
Exercises 1. rational equation
Selected Answers
y
Exercises 1. 0.923; 0.385; 2.400
3. 5.0 5. 8.0
3
25. m + 1 + _____
m-1
31. 5 33. __32 35. -4, 3 37. 6 h
3
__
= 0.600; __43 ≈ 1.333 2. 4.8 ft
5
x
14
39. 3x + 4 + ____
x-2
_____
41. 3x + 1 + 2x-2
-1
Extension Answers
35
23. -2x 2 + 6x - 15 + ____
x+3
33. 4t + 3 35. x - 3 37. 3a - 1
y
Check It Out! 1. __45 = 0.800;
12-6
S106
18.
,ENGTHCM
2
x-5
39. ____
3
34
69. -4x 2 + 10x - 17 + ____
x+2
18
12
72. - __
73. - __76 ;
70. - __34 71. __
7
11
0 is extraneous. 74. - __23 ; 1 is
extraneous. 75. - __13 , 1 76. -3 77. ±1
1
78. - __
79. -2; 4 is extraneous.
12
80. 4, 5 81. -12, 1 82. -19 83. 0; 2
is extraneous.
Glossary/Glosario
KEYWORD: MA7 Glossary
A
ENGLISH
absolute value (p. 14) The
absolute value of x is the distance
from zero to x on a number line,
denoted ⎪x⎥.
⎧x
if x ≥ 0
⎩ -x if x < 0
SPANISH
valor absoluto El valor absoluto
de x es la distancia de cero a x
en una recta numérica, y se
expresa ⎪x⎥.
⎧x
si x ≥ 0
⎩ -x si x < 0
EXAMPLES
⎪3⎥ = 3
⎪-3⎥ = 3
⎪x⎥ = ⎨
⎪x⎥ = ⎨
absolute-value equation (p. 148)
An equation that contains
absolute-value expressions.
ecuación de valor absoluto Ecuación
que contiene expresiones de valor
absoluto.
⎪x + 4⎥ = 7
absolute-value function (p. 366)
A function whose rule contains
absolute-value expressions.
función de valor absoluto Función
cuya regla contiene expresiones de
valor absoluto.
y = ⎪x + 4⎥
absolute-value inequality (p. 212)
An inequality that contains
absolute-value expressions.
desigualdad de valor absoluto
Desigualdad que contiene
expresiones de valor absoluto.
⎪x + 4⎥ > 7
acute angle (p. S56) An angle that
measures greater than 0° and less
than 90°.
ángulo agudo Ángulo que mide más
de 0° y menos de 90°.
acute triangle (p. S63) A triangle
with three acute angles.
triángulo acutángulo Triángulo con
tres ángulos agudos.
Addition Property of Equality
(p. 79) For real numbers a, b, and
c, if a = b, then a + c = b + c.
Propiedad de igualdad de la
suma Dados los números reales a, b
y c, si a = b, entonces a + c = b + c.
x-6= 8
+6 +6
−−−− −−−
x
= 14
Addition Property of Inequality
(p. 174) For real numbers
a, b, and c, if a < b, then
a + c < b + c. Also holds true
for >, ≤, ≥, and ≠.
Propiedad de desigualdad de la
suma Dados los números reales a, b
y c, si a < b, entonces a + c < b + c.
Es válido también para >, ≤, ≥ y ≠.
x-6< 8
+6 +6
−−−− −−−
x
< 14
additive inverse (p. 15) The
opposite of a number. Two
numbers are additive inverses if
their sum is zero.
inverso aditivo El opuesto de un
número. Dos números son inversos
aditivos si su suma es cero.
The additive inverse of
5 is -5.
algebraic expression (p. 6) An
expression that contains at least
one variable.
expresión algebraica Expresión que
contiene por lo menos una variable.
algebraic order of operations See
order of operations.
orden algebraico de las operaciones
Ver orden de las operaciones.
The additive inverse of
-5 is 5.
2x + 3y
4x
Glossary/Glosario
S107
ENGLISH
SPANISH
AND (p. 202) A logical operator
representing the intersection of
two sets.
Y Operador lógico que representa
la intersección de dos conjuntos.
angle (p. S56) A figure formed by
two rays with a common endpoint.
ángulo Figura formada por dos
rayos con un extremo común.
EXAMPLES
A = {2, 3, 4, 5} B = {1, 3, 5, 7}
The set of values that are in A
AND B is A B = {3, 5}.
area (p. S61) The number of
nonoverlapping unit squares of a
given size that will exactly cover
the interior of a plane figure.
área Cantidad de cuadrados
unitarios de un determinado
tamaño no superpuestos que
cubren exactamente el interior
de una figura plana.
arithmetic sequence (p. 272)
A sequence whose successive
terms differ by the same nonzero
number d, called the common
difference.
sucesión aritmética Sucesión
cuyos términos sucesivos difieren
en el mismo número distinto de
cero d, denominado diferencia
común.
Associative Property of Addition
(p. 46) For all numbers a, b, and c,
a + b + c = (a + b) + c
= a + (b + c).
Propiedad asociativa de la suma
Dados tres números cualesquiera
a, b y c, a + b + c = (a + b) + c
= a + (b + c).
Associative Property of
Multiplication (p. 46) For all
numbers a, b, and c, a · b · c =
(a · b) · c = a · (b · c).
Propiedad asociativa de la
multiplicación Dados tres números
cualesquiera a, b y c, a · b · c =
(a · b) · c = a · (b · c).
asymptote (p. 858) A line that a
graph gets closer to as the value
of a variable becomes extremely
large or small.
asíntota Línea recta a la cual se
aproxima una gráfica a medida
que el valor de una variable
se hace sumamente grande o
pequeño.
x
Ó
The area is 10 square units.
4,
7,
10,
promedio Ver media.
axis of a coordinate plane (p. 54)
One of two perpendicular number
lines, called the x-axis and the
y-axis, used to define the location
of a point in a coordinate plane.
eje de un plano cartesiano
Una de las dos rectas numéricas
perpendiculares, denominadas eje
x y eje y, utilizadas para definir la
ubicación de un punto en un
plano cartesiano.
axis of symmetry (p. 366, p. 600)
A line that divides a plane figure
or a graph into two congruent
reflected halves.
eje de simetría Línea que divide
una figura plana o una gráfica en
dos mitades reflejadas congruentes.
5 + 3 + 7 = (5 + 3) + 7 =
5 + (3 + 7)
5 · 3 · 7 = (5 · 3) · 7 =
5 · (3 · 7)
Þ
{
asymptote
Ý
ä
ä
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݈ÃʜvÊÃޓ“iÌÀÞ
Þ
{ ÞÊNÝN
Ó
Ý
Ó
ä
Ó
{
Glossary/Glosario
{
އ>݈Ã
{
S108
16, …
+3+3 +3 +3
d=3
{
average See mean.
13,
Ó
{
B
ENGLISH
back-to-back stem-and-leaf
plot (p. 687) A graph used to
organize and compare two sets of
data so that the frequencies can
be compared. See also stem-andleaf plot.
SPANISH
diagrama doble de tallo y hojas
Gráfica utilizada para organizar
y comparar dos conjuntos de
datos para poder comparar las
frecuencias. Ver también
diagrama de tallo y hojas.
EXAMPLES
Data set A: 9, 12, 14, 16, 23, 27
Data set B: 6, 8, 10, 13, 15, 16, 21
Set A
Set B
9 0 68
642 1 0356
37 2 1
Key: ⎪2⎥ 1 means 21
7 ⎪2⎥ means 27
gráfica de barras Gráfica con
barras horizontales o verticales
para mostrar datos.
-՘ˆ}…̽ÃÊ/À>ÛiÊ/ˆ“i
̜Ê*>˜iÌÃ
{nää
xäää
ÓÈää
À˜
ÌÕ
->
Ìi
«ˆ
>À
Ã
À
ÇÈä
Õ
>
ÀÌ
…
{äää
Îäää
Óäää
£äää xää
/ˆ“iʭî
bar graph (p. 678) A graph that
uses vertical or horizontal bars to
display data.
*>˜iÌ
base of a power (p. 26) The
number in a power that is used as
a factor.
base de una potencia Número de
una potencia que se utiliza como
factor.
base of an exponential
function (p. 772) The value of b in
a function of the form f (x) = ab x,
where a and b are real numbers
with a ≠ 0, b > 0, and b ≠ 1.
base de una función exponencial
Valor de b en una función del tipo
f(x) = ab x, donde a y b son
números reales con a ≠ 0,
b > 0 y b ≠ 1.
biased sample (p. 709) A sample
that does not fairly represent the
population.
muestra no representativa
Muestra que no representa
adecuadamente una
población.
To find out about the exercise
habits of average Americans, a
fitness magazine surveyed its
readers about how often they
exercise. The population is all
Americans and the sample is
readers of the fitness magazine.
This sample will likely be biased
because readers of fitness
magazines may exercise more
often than other people do.
binomial (p. 477) A polynomial
with two terms.
binomio Polinomio con dos
términos.
x+y
2a 2 + 3
4m 3n 2 + 6mn 4
boundary line (p. 414) A line that
divides a coordinate plane into
two half-planes.
línea de límite Línea que divide
un plano cartesiano en dos
semiplanos.
3 4 = 3 · 3 · 3 · 3 = 81
3 is the base.
In the function f (x) = 5(2) ,
the base is 2.
x
Î
Þ
œÕ˜`>ÀÞʏˆ˜i
Ý
Î
ä
Î
Î
Glossary/Glosario
S109
ENGLISH
box-and-whisker plot (p. 695) A
method of showing how data is
distributed by using the median,
quartiles, and minimum and
maximum values; also called a
box plot.
SPANISH
gráfica de mediana y rango Método
para mostrar la distribución de datos
utilizando la mediana, los cuartiles
y los valores mínimo y máximo;
también llamado gráfica de caja.
EXAMPLES
&IRSTQUARTILE
-INIMUM
ä
Ó
{
4HIRDQUARTILE
-EDIAN
È
n
£ä
£Ó
-AXIMUM
£{
C
Cartesian coordinate system
See coordinate plane.
sistema de coordenadas
cartesianas Ver plano cartesiano.
center of a circle (p. S62) The
point inside a circle that is the
same distance from every point
on the circle.
centro de un círculo Punto dentro
de un círculo que se encuentra a la
misma distancia de todos los
puntos del círculo.
central angle of a circle (p. 681)
An angle whose vertex is the
center of a circle.
ángulo central de un círculo Ángulo
cuyo vértice es el centro de un
círculo.
circle (p. S62) The set of points in
a plane that are a fixed distance
from a given point called the
center of the circle.
círculo Conjunto de puntos en
un plano que se encuentran a
una distancia fija de un punto
determinado denominado
centro del círculo.
circle graph (p. 680) A way to
display data by using a circle
divided into non-overlapping
sectors.
gráfica circular Forma de mostrar
datos mediante un círculo dividido
en sectores no superpuestos.
,iÈ`i˜ÌÃʜvÊiÃ>]Ê<
Èx³
£Î¯
{xqÈ{
Óǯ
1˜`iÀÊ
£n
£™¯
££¯
Îä¯
£nqÓ{
Óxq{{
circumference (p. S62) The
distance around a circle.
circunferencia Distancia alrededor
de un círculo.
ˆÀVՓviÀi˜Vi
closure (p. 37) A set of numbers
is said to be closed, or to have
closure, under a given operation if
the result of the operation on any
two numbers in the set is also in
the set.
cerradura Se dice que un
conjunto de números es cerrado,
o tiene cerradura, respecto de
una operación determinada, si el
resultado de la operación entre
dos números cualesquiera del
conjunto también está en el
conjunto.
The set of integers is closed
under addition because the
sum of any two integers is also
an integer.
The set of whole numbers is
not closed under subtraction
because the difference of any
two whole numbers may not
be another whole number; for
example, 2 - 4 = -2.
coefficient (p. 48) A number
multiplied by a variable.
coeficiente Número multiplicado
por una variable.
In the expression 2x + 3y, 2 is
the coefficient of x and 3 is the
coefficient of y.
S110
Glossary/Glosario
ENGLISH
SPANISH
EXAMPLES
combination (p. 737) A selection
of a group of objects in which
order is not important. The
number of combinations of r
objects chosen from a group of n
objects is denoted nCr.
combinación Selección de un grupo
de objetos en la cual el orden no
es importante. El número de
combinaciones de r objetos
elegidos de un grupo de n objetos
se expresa así: nCr.
commission (p. 133) Money
paid to a person or company for
making a sale, usually a percent of
the sale amount.
comisión Dinero que se paga a una
persona o empresa por realizar una
venta; generalmente se trata de un
porcentaje del total de la venta.
common difference (p. 272) In an
arithmetic sequence, the nonzero
constant difference of any term
and the previous term.
diferencia común En una sucesión
aritmética, diferencia constante
distinta de cero entre cualquier
término y el término anterior.
In the arithmetic sequence 3,
5, 7, 9, 11, …, the common
difference is 2.
common factor (p. 525) A factor
that is common to all terms of
an expression or to two or more
expressions.
factor común Factor que es común
a todos los términos de una
expresión o a dos o más
expresiones.
Expression: 4x 2 + 16x 3 - 8x
Common factor: 4x
Expressions: 12 and 18
Common factors: 2, 3, and 6
common ratio (p. 766) In a
geometric sequence, the constant
ratio of any term and the previous
term.
razón común En una sucesión
geométrica, la razón constante
entre cualquier término y el
término anterior.
Commutative Property of
Addition (p. 46) For any two
numbers a and b, a + b = b + a.
Propiedad conmutativa de la
suma Dados dos números
cualesquiera a y b, a + b = b + a.
Commutative Property of
Multiplication (p. 46) For any two
numbers a and b, a · b = b · a.
Propiedad conmutativa de la
multiplicación Dados dos números
cualesquiera a y b, a · b = b · a.
complement of an event (p. 721)
All outcomes in the sample
space that are not in an event E,
−
denoted E.
complemento de un suceso
Todos los resultados en el espacio
muestral que no están en el
−
suceso E, y se expresan E.
complementary angles (p. S57)
Two angles whose measures have
a sum of 90°.
ángulos complementarios Dos
ángulos cuyas medidas suman 90°.
For objects A, B, C, and D,
there are 6 different
combinations of 2 objects.
AB, AC, AD, BC, BD, CD
In the geometric sequence
32, 16, 8, 4, 2, . . ., the
1
common ratio is __
.
2
3+4=4+3=7
3 · 4 = 4 · 3 = 12
In the experiment of
rolling a number cube, the
complement of rolling a 3 is
rolling a 1, 2, 4, 5, or 6.
ÎÇÂ
xÎÂ
completing the square (p. 645) A
process used to form a perfectsquare trinomial. To complete
()
2
the square of x 2 + bx, add __b2 .
completar el cuadrado Proceso
utilizado para formar un trinomio
cuadrado perfecto. Para completar
el cuadrado de x 2 + bx, hay que
()
2
sumar __b2 .
x 2 + 6x +
( ) = 9.
6
Add _
2
2
x 2 + 6x + 9
Glossary/Glosario
S111
ENGLISH
SPANISH
composite figure (p. 83) A plane
figure made up of triangles,
rectangles, trapezoids, circles,
and other simple shapes, or a
three-dimensional figure made
up of prisms, cones, pyramids,
cylinders, and other simple threedimensional figures.
figura compuesta Figura plana
compuesta por triángulos,
rectángulos, trapecios, círculos
y otras figuras simples, o figura
tridimensional compuesta por
prismas, conos, pirámides, cilindros
y otras figuras tridimensionales
simples.
compound event (p. 737) An
event made up of two or more
simple events.
suceso compuesto Suceso formado
por dos o más sucesos simples.
compound inequality (p. 202) Two
inequalities that are combined
into one statement by the word
and or or.
desigualdad compuesta Dos
desigualdades unidas en un
enunciado por la palabra y u o.
EXAMPLES
In the experiment of tossing
a coin and rolling a number
cube, the event of the coin
landing heads and the
number cube landing on 3.
x ≥ 2 AND x < 6 (also
written 2 ≤ x < 6)
ä
A = P(1 +
)
r nt
__
n
, where A is the
final amount, P is the principal, r
is the interest rate expressed as a
decimal, n is the number of times
interest is compounded, and t is
the time.
interés compuesto Intereses
ganados o pagados sobre el capital
y los intereses ya devengados. La
fórmula de interés compuesto es
r
A = P(1 + __
n ) , donde A es la
nt
cantidad final, P es el capital, r
es la tasa de interés expresada
como un decimal, n es la cantidad
de veces que se capitaliza el
interés y t es el tiempo.
compound statement (p. 201) Two
statements that are connected by
the word and or or.
enunciado compuesto Dos
enunciados unidos por la palabra
y u o.
cone (p. 874, p. S64) A threedimensional figure with a circular
base and a curved surface that
connects the base to a point
called the vertex.
cono Figura tridimensional con
una base circular y una superficie
lateral curva que conecta la base
con un punto denominado vértice.
congruent (p. S59) Having the
same size and shape, denoted
by .
congruente Que tiene el mismo
tamaño y la misma forma, expresado
por .
conjugate of an irrational
number (p. 821) The conjugate of
is
a number in the form a + √b
.
a - √b
conjugado de un número irracional
El conjugado de un número en la
.
forma a + √
b es a - √b
S112
Glossary/Glosario
{
È
n
x < 2 OR x > 6
ä
compound interest (p. 782)
Interest earned or paid on both
the principal and previously
earned interest. The formula
for compound interest is
Ó
Ó
{
È
n
If $100 is put into an
account with an interest
rate of 5% compounded
monthly, then after 2 years,
the account will have
(
100 1 +
0.05 12·2
____
) = $110.49.
12
The sky is blue and the grass is
green.
I will drive to school or I will
take the bus.
+
*
,
−− −−
PQ RS
-
The conjugate of 1 + √
2 is
1 - √
2.
SPANISH
consistent system (p. 406)
A system of equations or
inequalities that has at least one
solution.
sistema consistente Sistema de
ecuaciones o desigualdades que
tiene por lo menos una solución.
constant (p. 6) A value that does
not change.
constante Valor que no cambia.
constant of variation (p. 326) The
constant k in direct and inverse
variation equations.
constante de variación La constante
k en ecuaciones de variación directa
e inversa.
continuous graph (p. 231) A graph
made up of connected lines or
curves.
gráfica continua Gráfica compuesta
por líneas rectas o curvas
conectadas.
EXAMPLES
⎧x + y = 6
⎨
⎩x - y = 4
solution: (5, 1)
3, 0, π
y = 5x
constant of variation
˜}iˆµÕi½ÃÊi>ÀÌÊ,>Ìi
Þ
i>ÀÌÊÀ>Ìi
ENGLISH
Ý
/ˆ“i
contradiction (p. 101) An
equation that has no solutions.
contradicción Ecuación que no tiene
soluciones.
conversion factor (p. 115) The
ratio of two equal quantities, each
measured in different units.
factor de conversión Razón entre
dos cantidades iguales, cada una
medida en unidades diferentes.
coordinate (p. 54) A number used
to identify the location of a point.
On a number line, one coordinate
is used. On a coordinate plane,
two coordinates are used, called
the x-coordinate and the
y-coordinate.
coordenada Número utilizado
para identificar la ubicación
de un punto. En una recta
numérica se utiliza una
coordenada. En un plano
cartesiano se utilizan dos
coordenadas, denominadas
coordenada x y coordenada y.
x+1=x
1=0✗
12 inches
_
1 foot
A
{ Î Ó £
ä
£
Ó
Î
{
x
È
The coordinate of A is 2.
{
Þ
Ó
Ý
{
ä
Ó
Ó
{
The coordinates of B are
(-2, 3).
coordinate plane (p. 54) A plane
that is divided into four regions
by a horizontal line called the
x-axis and a vertical line called
the y-axis.
plano cartesiano Plano dividido
en cuatro regiones por una línea
horizontal denominada eje x y una
línea vertical denominada eje y.
correlation (p. 262) A measure of
the strength and direction of the
relationship between two
variables or data sets.
correlación Medida de la
fuerza y dirección de la
relación entre dos variables
o conjuntos de datos.
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i}>̈ÛiÊVœÀÀi>̈œ˜
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Glossary/Glosario
S113
ENGLISH
SPANISH
EXAMPLES
corresponding angles of
polygons (p. 121) Angles in the
same position in two different
polygons that have the same
number of angles.
ángulos correspondientes de los
polígonos Ángulos que tienen la
misma posición relativa en dos
polígonos diferentes que tienen
el mismo número de ángulos.
corresponding sides of
polygons (p. 121) Sides in the
same position in two different
polygons that have the same
number of sides.
lados correspondientes de los
polígonos Lados que tienen la
misma posición en dos polígonos
diferentes que tienen el mismo
número de lados.
cosine (p. 908) In a right triangle,
the cosine of angle A is the ratio
of the length of the leg adjacent
to angle A to the length of the
hypotenuse.
coseno En un triángulo rectángulo,
el coseno del ángulo A es la
razón entre la longitud del cateto
adyacente al ángulo A y la longitud
de la hipotenusa.
counterexample (p. S76) An
example that proves that a
conjecture or statement is false.
contraejemplo Ejemplo que
demuestra que una conjetura o
enunciado es falso.
cross products (p. 115) In the
c
statement __ab = __
, bc and ad are the
d
cross products.
productos cruzados En el
c
enunciado __ab = __
, bc y ad son
d
productos cruzados.
Cross Product Property (p. 115)
For any real numbers a, b, c, and
c
d, where b ≠ 0 and d ≠ 0, if __ab = __
,
d
then ad = bc.
Propiedad de productos cruzados
Dados los números reales a, b, c
c
y d, donde b ≠ 0 y d ≠ 0, si __ab = __
,
d
entonces ad = bc.
cube (p. S66) A prism with six
square faces.
cubo Prisma con seis caras
cuadradas.
cube in numeration (p. 26) The
third power of a number.
cubo en numeración Tercera
potencia de un número.
cube root (p. 832) A number,
3
written as √
x
, whose cube is x.
raíz cúbica Número, expresado
3
como √
x
, cuyo cubo es x.
cubic polynomial (p. 477) A
polynomial of degree 3.
polinomio cúbico Polinomio de
grado 3.
x 3 + 4x 2 - 6x + 2
cumulative frequency (p. 689) The
frequency of all data values that
are less than or equal to a given
value.
frecuencia acumulativa
Frecuencia de todos los valores
de los datos que son menores
que o iguales a un valor dado.
For the data set 2, 2, 3, 5, 5, 6,
7, 7, 8, 8, 8, 9, the cumulative
frequency table is shown below.
Glossary/Glosario
∠A and ∠D are corresponding angles.
−−
−−
AB and DE are corresponding sides.
…Þ«œÌi˜ÕÃi
>`>Vi˜Ì
adjacent
cos A = _________
hypotenuse
_1 = _3
2
6
Cross products: 2 · 3 = 6
and: 1 · 6 = 6
_
10 , then 4x = 60,
If 4 = _
x
6
so x = 15.
8 is the cube of 2.
3
√
64 = 4, because 4 3 = 64;
4 is the cube root of 64.
Data
2
3
5
6
7
8
9
S114
Frequency
2
1
2
1
2
3
1
Cumulative
Frequency
2
3
5
6
8
11
12
ENGLISH
cylinder (p. S64) A threedimensional figure with two
parallel congruent circular
bases and a curved surface
that connects the bases.
SPANISH
EXAMPLES
cilindro Figura tridimensional con
dos bases circulares congruentes
paralelas y una superficie lateral
curva que conecta las bases.
D
data (p. 678) Information
gathered from a survey or
experiment.
datos Información reunida en una
encuesta o experimento.
degree measure of an angle
(p. S56) A unit of angle measure;
1
one degree is ___
of a circle.
360
medida en grados de un ángulo
Unidad de medida de los ángulos;
1
un grado es ___
de un círculo.
360
degree of a monomial (p. 476)
The sum of the exponents of the
variables in the monomial.
grado de un monomio Suma de
los exponentes de las variables del
monomio.
degree of a polynomial (p. 476)
The degree of the term of the
polynomial with the greatest
degree.
grado de un polinomio Grado
del término del polinomio con el
grado máximo.
dependent events (p. 726)
Events for which the occurrence
or nonoccurrence of one event
affects the probability of the other
event.
sucesos dependientes Dos sucesos
son dependientes si el hecho de
que uno de ellos ocurra o no afecta
la probabilidad del otro suceso.
From a bag containing 3 red
marbles and 2 blue marbles,
drawing a red marble, and then
drawing a blue marble without
replacing the first marble.
dependent system (p. 407) A
system of equations that has
infinitely many solutions.
sistema dependiente Sistema de
ecuaciones que tiene infinitamente
muchas soluciones.
⎧x + y = 2
⎨
⎩ 2x + 2y = 4
dependent variable (p. 246) The
output of a function; a variable
whose value depends on the value
of the input, or independent
variable.
variable dependiente Salida de una
función; variable cuyo valor depende
del valor de la entrada, o variable
independiente.
diameter (p. S62) A segment that
has endpoints on the circle and
that passes through the center of
the circle; also the length of that
segment.
diámetro Segmento que
atraviesa el centro de un círculo
y cuyos extremos están sobre
la circunferencia; longitud de
dicho segmento.
difference of two cubes (p. 564) A
polynomial of the form a 3 - b 3,
which may be written as the
product (a - b)(a 2 + ab + b 2).
diferencia de dos cubos Polinomio
del tipo a 3 - b 3, que se puede
expresar como el producto
(a - b)(a 2 + ab + b 2).
x 3 - 8 = (x - 2)(x 2 + 2x + 4)
difference of two squares (p. 503)
A polynomial of the form a 2 - b 2,
which may be written as the
product (a + b)(a - b).
diferencia de dos cuadrados
Polinomio del tipo a 2 - b 2, que se
puede expresar como el producto
(a + b)(a - b).
x 2 - 4 = (x + 2)(x - 2)
4x 2y 5z 3 Degree: 2 + 5 + 3 = 10
5 = 5x 0 Degree: 0
3x 2y 2 + 4xy 5 - 12x 3y 2
Degree 4 Degree 6 Degree 5
Degree 6
For y = 2x + 1, y is the
dependent variable.
input: x output: y
Glossary/Glosario
S115
ENGLISH
SPANISH
direct variation (p. 326) A
linear relationship between two
variables, x and y, that can be
written in the form y = kx, where
k is a nonzero constant.
EXAMPLES
variación directa Relación lineal
entre dos variables, x e y, que puede
expresarse en la forma y = kx, donde
k es una constante distinta de cero.
{
Þ
Ó
Ý
{ Ó
Ó
{
{
y = 2x
discontinuous function (p. 858) A
function whose graph has one or
more jumps, breaks, or holes.
función discontinua Función cuya
gráfica tiene uno o más saltos,
interrupciones u hoyos.
Þ
{
Ý
ä
{
descuento Cantidad por la que se
reduce un precio original.
discrete graph (p. 231) A graph
made up of unconnected points.
gráfica discreta Gráfica compuesta
de puntos no conectados.
Theme Park Attendance
People
discount (p. 139) An amount by
which an original price is reduced.
{
Years
discriminant (p. 654) The
discriminant of the quadratic
equation ax 2 + bx + c = 0 is
b 2 - 4ac.
discriminante El discriminante
de la ecuación cuadrática
ax 2 + bx + c = 0 es b 2 - 4ac.
Distance Formula (p. 642) In a
coordinate plane, the distance
from (x 1, y 1) to (x 2, y 2) is
Fórmula de distancia En un plano
cartesiano, la distancia desde (x 1, y 1)
hasta (x 2, y 2) es
d=
√(
x2 - x1 2 + y2 - y1 2.
)
(
)
d=
√(
The discriminant of
2x 2 - 5x - 3 is
(-5) 2 - 4(2)(-3) or 49.
(
)
­Ó]Êx®
{
­£]Ê£®
x2 - x1 2 + y2 - y1 2.
)
Þ
{
Ó
Ó
Ý
ä
Ó
{
The distance from (2, 5) to (-1, 1) is
(-1 - 2)2 + (1 - 5)2
d = √
=
(-3) 2 + (-4) 2
√
= √
9 + 16 = √
25 = 5.
Distributive Property (p. 47) For
all real numbers a, b, and c,
a(b + c) = ab + ac, and
(b + c)a = ba + ca.
Propiedad distributiva Dados los
números reales a, b y c,
a(b + c) = ab + ac, y :
(b + c)a = ba + ca.
Division Property of Equality
(p. 86) For real numbers a, b,
and c, where c ≠ 0, if a = b,
then __ac = __bc .
Propiedad de igualdad de la
división Dados los números reales
a, b y c, donde c ≠ 0, si a = b,
entonces __ac = __bc .
S116
Glossary/Glosario
3(4 + 5) = 3 · 4 + 3 · 5
(4 + 5)3 = 4 · 3 + 5 · 3
4x = 12
4x = _
12
_
4
4
x=3
ENGLISH
SPANISH
Division Property of Inequality
(p. 180) If both sides of an
inequality are divided by the
same positive quantity, the new
inequality will have the same
solution set. If both sides of an
inequality are divided by the
same negative quantity, the new
inequality will have the same
solution set if the inequality
symbol is reversed.
Propiedad de desigualdad de la
división Cuando ambos lados de una
desigualdad se dividen entre el mismo
número positivo, la nueva desigualdad
tiene el mismo conjunto solución.
Cuando ambos lados de una
desigualdad se dividen entra el
mismo número negativo, la nueva
desigualdad tiene el mismo conjunto
solución si se invierte el símbolo de
desigualdad.
domain (p. 236) The set of all
possible input values of a relation
or function.
dominio Conjunto de valores de
entrada de una función o relación.
EXAMPLES
4x ≥ 12
4x ≥ _
12
_
4
4
x≥3
-4x ≥ 12
4x ≥ 12
-4
-4
x ≤ -3
_ _
The domain of the function
f (x) = √
x is x ≥ 0.
E
element Each member in a set or
matrix. See also entry.
elemento Cada miembro en un
conjunto o matriz. Ver también
entrada.
elimination method (p. 397) A
method used to solve systems of
equations in which one variable
is eliminated by adding or
subtracting two equations of the
system.
eliminación Método utilizado para
resolver sistemas de ecuaciones
por el cual se elimina una variable
sumando o restando dos ecuaciones
del sistema.
empty set (p. 102) A set with no
elements.
conjunto vacío Conjunto sin
elementos.
The solution set of ⎪x⎥ < 0 is
the empty set, { }, or .
entry (p. 746) Each value in a
matrix; also called an element.
entrada Cada valor de una matriz,
también denominado elemento.
3 is the entry in the first row
and second column of
⎡2 3⎤
A=⎢
, denoted a 12.
⎣0 1⎦
equally likely outcomes (p. 720)
Outcomes are equally likely if
they have the same probability of
occurring. If an experiment has n
equally likely outcomes, then the
1
probability of each outcome is __
n.
resultados igualmente probables Los
resultados son igualmente probables
si tienen la misma probabilidad de
ocurrir. Si un experimento tiene n
resultados igualmente probables,
entonces la probabilidad de cada
1
resultado es __
n.
If a fair coin is tossed, then
P(heads) = P(tails) = 1 .
2
So the outcome “heads”
and the oucome “tails” are
equally likely.
equation (p. 77) A mathematical
statement that two expressions
are equivalent.
ecuación Enunciado matemático
que indica que dos expresiones son
equivalentes.
x+4=7
2+3=6-1
(x - 1)2 + (y + 2)2 = 4
equilateral triangle (p. S63) A
triangle with three congruent
sides.
triángulo equilátero Triángulo con
tres lados congruentes.
equivalent ratios (p. 114) Ratios
that name the same comparison.
razones equivalentes Razones que
expresan la misma comparación.
_
_1 and _2 are equivalent ratios.
2
4
Glossary/Glosario
S117
ENGLISH
SPANISH
EXAMPLES
evaluate (p. 7) To find the value
of an algebraic expression by
substituting a number for each
variable and simplifying by using
the order of operations.
evaluar Calcular el valor de una
expresión algebraica sustituyendo
cada variable por un número y
simplificando mediante el orden de
las operaciones.
Evaluate 2x + 7 for x = 3.
2x + 7
2(3) + 7
6+7
13
event (p. 713) An outcome or
set of outcomes in a probability
experiment.
suceso Resultado o conjunto de
resultados en un experimento de
probabilidad.
In the experiment of rolling
a number cube, the event
“an odd number” consists of
the outcomes 1, 3, and 5.
excluded values (p. 858) Values
of x for which a function or
expression is not defined.
valores excluidos Valores de x para
los cuales no está definida una
función o expresión.
experiment (p. 713) An operation,
process, or activity in which
outcomes can be used to estimate
probability.
experimento Una operación,
proceso o actividad en la que se
usan los resultados para estimar
una probabilidad.
experimental probability (p. 714)
The ratio of the number of times
an event occurs to the number of
trials, or times, that an activity is
performed.
probabilidad experimental
Razón entre la cantidad de
veces que ocurre un suceso
y la cantidad de pruebas,
o veces, que se realiza una
actividad.
The excluded values of
(x + 2)
f (x) = __
(x - 1)(x + 4)
are x = 1 and x = -4,
which would make the
denominator equal to 0.
Tossing a coin 10 times and
noting the number of heads.
Kendra attempted 27 free
throws and made 16 of them.
The probability that she will
make her next free throw can
be estimated by
P(free throw) ≈
16 ≈ 0.59.
number made
__
=_
27
number attempted
exponent (p. 26) The number that
indicates how many times the
base in a power is used as a factor.
exponente Número que indica la
cantidad de veces que la base de
una potencia se utiliza como factor.
exponential decay (p. 783) An
exponential function of the form
f (x) = ab x in which 0 < b < 1.
If r is the rate of decay, then the
function can be written
t
y = a (1 - r) , where a is the initial
amount and t is the time.
decremento exponencial Función
exponencial del tipo f (x) = ab x
en la cual 0 < b < 1. Si r es la tasa
decremental, entonces la función
se puede expresar como
t
y = a (1 - r) ,donde a es la
cantidad inicial y t es el tiempo.
3 4 = 3 · 3 · 3 · 3 = 81
4 is the exponent.
()
1
f (x) = 3 _
2
x
Þ
Ý
exponential expression
An algebraic expression in which
the variable is in an exponent
with a fixed number as the base.
expresión exponencial Expresión
algebraica en la que la variable está
en un exponente y que tiene un
número fijo como base.
exponential function (p. 772) A
function of the form f (x) = ab x,
where a and b are real numbers
with a ≠ 0, b > 0, and b ≠ 1.
función exponencial Función del
tipo f (x) = ab x, donde a y b son
números reales con a ≠ 0, b > 0
y b ≠ 1.
2 x+1
f (x) = 3 · 4 x
Þ
Ý
S118
Glossary/Glosario
ENGLISH
SPANISH
EXAMPLES
exponential growth (p. 781) An
exponential function of the form
f (x) = ab x in which b > 1. If r
is the rate of growth, then the
function can be written
t
y = a(1 + r) , where a is the initial
amount and t is the time.
crecimiento exponencial Función
exponencial del tipo f (x) = ab x
en la que b > 1. Si r es la tasa de
crecimiento, entonces la función se
t
puede expresar como y = a(1 + r) ,
donde a es la cantidad inicial y t es el
tiempo.
expression (p. 6) A mathematical
phrase that contains operations,
numbers, and/or variables.
expresión Frase matemática que
contiene operaciones, números y/o
variables.
extraneous solution (p. 824) A
solution of a derived equation
that is not a solution of the
original equation.
solución extraña Solución de una
ecuación derivada que no es una
solución de la ecuación original.
To solve √
x = -2, square
both sides; x = 4.
4 = -2 is false; so 4
Check √
is an extraneous solution.
factor A number or expression
that is multiplied by another
number or expression to get a
product. See also factoring.
factor Número o expresión que
se multiplica por otro número o
expresión para obtener un
producto. Ver también factoreo.
12 = 3 · 4
3 and 4 are factors of 12.
factorial (p. 738) If n is a positive
integer, then n factorial, written n!,
is n · (n - 1) · (n - 2) · … · 2 · 1.
The factorial of 0 is defined to
be 1.
factorial Si n es un entero positivo,
entonces el factorial de n, expresado
como n!, es n · (n - 1) · (n - 2) · …
· 2 · 1. Por definición, el factorial de
0 será 1.
factoring (p. 524) The process
of writing a number or algebraic
expression as a product.
factorización Proceso por el que
se expresa un número o expresión
algebraica como un producto.
fair (p. 720) When all outcomes
of an experiment are equally
likely.
justo Cuando todos los resultados When tossing a fair coin, heads
de un experimento son igualmente and tails are equally likely.
Each has a probability of __12 .
probables.
family of functions (p. 357) A set
of functions whose graphs have
basic characteristics in common.
Functions in the same family are
transformations of their parent
function.
familia de funciones Conjunto de
funciones cuyas gráficas tienen
características básicas en común.
Las funciones de la misma familia
son transformaciones de su
función madre.
f (x) = 2 x
Þ
Ó
Ý
Ó ä
Ó
6x + 1
F
x 2 - 1 = (x - 1)(x + 1)
(x - 1) and (x + 1) are
factors of x 2 - 1.
7! = 7 · 6 · 5 · 4 · 3 · 2 · 1
= 5040
x 2 - 4x - 21 = (x - 7)(x + 3)
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n
Þ
ÊÞÊÊÎÝÓ
ÊÞÊÊ­ÝÊÊÓ®Ó
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{
ÊÞÊÊÝÓ
Ó
Ý
{
Ó
ä
Ó
{
Glossary/Glosario
S119
ENGLISH
first differences (p. 590) The
differences between y-values of
a function for evenly spaced
x-values.
SPANISH
EXAMPLES
primeras diferencias
Diferencias entre
los valores de y de una
función para valores
de x espaciados
uniformemente.
Constant change in x-values
+1
+1
+1
+1
x
0
1
2
3
4
y = x2
0
1
4
9
16
+1
+3
+5
+7
First differences
first quartile (p. 695) The median
of the lower half of a data set,
denoted Q 1. Also called lower
quartile.
primer cuartil Mediana de la mitad
inferior de un conjunto de datos,
expresada como Q 1. También se
llama cuartil inferior.
FOIL (p. 493) A mnemonic
(memory) device for a method of
multiplying two binomials:
Multiply the First terms.
Multiply the Outer terms.
Multiply the Inner terms.
Multiply the Last terms.
FOIL Regla mnemotécnica para
recordar el método de multiplicación
de dos binomios:
Multiplicar los términos Primeros
F
L
(First).
Multiplicar los términos Externos (x + 2)(x - 3) = x 2 - 3x + 2x - 6
= x2 - x - 6
(Outer).
I
Multiplicar los términos Internos
O
(Inner).
Multiplicar los términos Últimos
(Last).
formula (p. 107) A literal equation
that states a rule for a relationship
among quantities.
fórmula Ecuación literal que
establece una regla para una relación
entre cantidades.
fractional exponent See rational
exponent.
exponente fraccionario Ver
exponente racional.
frequency (p. 688, p. S71) The
number of times the value appears
in the data set.
frecuencia Cantidad de veces que
aparece el valor en un conjunto
de datos.
frequency table (p. 688) A table
that lists the number of times, or
frequency, that each
data value occurs.
tabla de frecuencia Tabla
que enumera la cantidad
de veces que ocurre cada
valor de datos, o la
frecuencia.
function (p. 237) A relation in
which every input is paired with
exactly one output.
función Una relación en la que
cada entrada corresponde
exactamente a una salida.
Lower half
Upper half
18, 23, 28, 49, 36, 42
First quartile
A = πr 2
In the data set 5, 6, 6, 7, 8,
9, the data value 6 has a
frequency of 2.
Data set: 1, 1, 2, 2, 3, 4, 5, 5, 5, 6, 6, 6, 6
Frequency table:
Data
1
2
3
4
5
6
Frequency
2
2
1
1
3
4
È
x
Ó
£
S120
Glossary/Glosario
{
£
ä
ENGLISH
SPANISH
function notation (p. 246) If x is
the independent variable and y is
the dependent variable, then the
function notation for y is f (x),
read “f of x,” where f names the
function.
notación de función Si x es la
variable independiente e y es la
variable dependiente, entonces
la notación de función para y es
f (x), que se lee “f de x,” donde f
nombra la función.
function rule (p. 246) An algebraic
expression that defines a
function.
regla de función Expresión
algebraica que define una
función.
Fundamental Counting
Principle (p. 736) For n items, if
there are m 1 ways to choose a first
item, m 2 ways to choose a second
item after the first item has been
chosen, and so on, then there are
m 1 · m 2 · … · m n ways to choose
n items.
Principio fundamental de conteo
Dados n elementos, si existen
m 1 formas de elegir un primer
elemento, m 2 formas de elegir
un segundo elemento después
de haber elegido el primero, y así
sucesivamente, entonces existen
m 1 · m 2 · … · m n formas de elegir
n elementos.
EXAMPLES
equation: y = 2x
function notation: f(x) = 2x
f (x) = 2x 2 + 3x - 7
function rule
If there are 4 colors of shirts,
3 colors of pants, and 2 colors
of shoes, then there are
4 · 3 · 2 = 24 possible outfits.
G
geometric sequence (p. 766) A
sequence in which the ratio of
successive terms is a constant r,
called the common ratio, where
r ≠ 0 and r ≠ 1.
sucesión geométrica Sucesión en
la que la razón de los términos
sucesivos es una constante r,
denominada razón común,
donde r ≠ 0 y r ≠ 1.
graph of a function (p. 252) The
set of points in a coordinate plane
with coordinates (x, y), where x is
in the domain of the function
f and y = f (x).
gráfica de una función Conjunto
de los puntos de un plano
cartesiano con coordenadas
(x, y), donde x está en el
dominio de la función f e
y = f (x).
1,
2,
4,
8,
16, …
·2 ·2 ·2 ·2
{
r=2
Þ
Þ
Ó
Ý
{
Ó
ä
Ó
Ý
n
{
ä
{
Ó
{
{
n
{
n
Þ
graph of a system of linear
inequalities (p. 421) The region
in a coordinate plane consisting
of points whose coordinates are
solutions to all of the inequalities
in the system.
gráfica de un sistema de
desigualdades lineales Región de
un plano cartesiano que consta
de puntos cuyas coordenadas
son soluciones de todas las
desigualdades del sistema.
graph of an inequality in one
variable (p. 169) The set of
points on a number line that are
solutions of the inequality.
gráfica de una desigualdad en una
variable Conjunto de los puntos de
una recta numérica que representan
soluciones de la desigualdad.
graph of an inequality in two
variables (p. 414) The set of
points in a coordinate plane
whose coordinates (x, y) are
solutions of the inequality.
gráfica de una desigualdad en dos
variables Conjunto de los puntos
de un plano cartesiano cuyas
coordenadas (x, y) son soluciones
de la desigualdad.
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Ó
ä
Ó
Ý
Ó
Ó
x≥2
{ Î Ó £
ä
£
Ó
Î
{
x
È
y≤x+1
Î
Þ
Ý
Î
ä
Î
Î
Glossary/Glosario
S121
ENGLISH
SPANISH
graph of an ordered pair (p. 54)
For the ordered pair (x, y), the
point in a coordinate plane that
is a horizontal distance of x units
from the origin and a vertical
distance of y units from the
origin.
gráfica de un par ordenado Dado
el par ordenado (x, y), punto en un
plano cartesiano que está a una
distancia horizontal de x unidades
desde el origen y a una distancia
vertical de y unidades desde el
origen.
greatest common factor (GCF)
(p. 525) The product of the
greatest integer and the greatest
power of each variable that
divide evenly into each term.
máximo común divisor (MCD)
Producto del entero mayor y la
potencia mayor de cada variable
que divide exactamente cada
término de la expresión.
grouping symbols (p. 40) Symbols
such as parentheses ( ), brackets
[ ], and braces { } that separate
part of an expression. A fraction
bar, absolute-value symbols, and
radical symbols may also be used
as grouping symbols.
símbolos de agrupación Símbolos
tales como paréntesis ( ), corchetes
[ ] y llaves { } que separan parte
de una expresión. La barra de
fracciones, los símbolos de valor
absoluto y los símbolos de radical
también se pueden utilizar como
símbolos de agrupación.
EXAMPLES
Þ
{
Ó
Ý
{
ä
Ó
Ó
{
Ó
{
-
(2, -4)
The GCF of 4x 3y and 6x 2y is
2x 2y.
The GCF of 27 and 45 is 9.
⎧
⎫
6 + ⎨3 - ⎡⎣(4 - 3) + 2⎤⎦ + 1⎬ - 5
⎧⎩
⎫
⎩
⎭
6 + ⎨3 - ⎡⎣1 + 2⎤⎦ + 1⎬ - 5
6 + {3 - 3 + 1 } - 5
6+1-5
2
⎭
H
half-life (p. 783) The half-life of a
substance is the time it takes for
one-half of the substance to decay
into another substance.
vida media La vida media de
una sustancia es el tiempo que
tarda la mitad de la sustancia en
desintegrarse y transformarse en
otra sustancia.
half-plane (p. 414) The part of the
coordinate plane on one side of a
line, which may include the line.
semiplano La parte del plano
cartesiano de un lado de una línea,
que puede incluir la línea.
Carbon-14 has a half-life of
5730 years, so 5 g of an initial
amount of 10 g will remain
after 5730 years.
Þ
Î
Ý
ä
Î
Î
Î
where s is one-half the perimeter,
or s = __12 (a + b + c).
histogram (p. 688) A bar graph
used to display data grouped in
class intervals. The width of each
bar is proportional to the class
interval, and the area of each bar
is proportional to the frequency.
S122
Glossary/Glosario
fórmula de Herón Un triángulo con
longitudes de lado a, b y c tiene un
(s - a)(s - b)(s - c) ,
área A = √s
donde s es la mitad del perímetro
ó s = __12 (a + b + c).
histograma Gráfica de barras
utilizada para mostrar datos
agrupados en intervalos de clases.
El ancho de cada barra es
proporcional al intervalo de clase
y el área de cada barra es
proporcional a la frecuencia.
-Ì>À̈˜}Ê->>ÀˆiÃ
ÀiµÕi˜VÞ
Heron’s Formula (p. 810) A
triangle with side lengths a, b, and
c has area
A = √
s(s - a)(s - b)(s - c) ,
{ä
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Óä
£ä
ä
n
n
n
n
->>ÀÞÊÀ>˜}iʭ̅œÕÃ>˜`Êf®
ENGLISH
horizontal line (p. 312) A line
described by the equation
y = b, where b is the y-intercept.
SPANISH
línea horizontal Línea descrita
por la ecuación y = b, donde b
es la intersección con el eje y.
EXAMPLES
y=4
Þ
Ó
Ý
{ Ó ä
hypotenuse (p. S68) The side
opposite the right angle in a right
triangle.
hipotenusa Lado opuesto al ángulo
recto de un triángulo rectángulo.
Ó
{
…Þ«œÌi˜ÕÃi
I
3=3
2(x - 1) = 2x - 2
identity (p. 101) An equation
that is true for all values of the
variables.
identidad Ecuación verdadera para
todos los valores de las variables.
inclusive events (p. 734) Events
that have one or more outcomes
in common.
sucesos inclusivos Sucesos que
tienen uno o más resultados en
común.
inconsistent system (p. 406)
A system of equations or
inequalities that has no solution.
sistema inconsistente Sistema de
ecuaciones o desigualdades que
no tiene solución.
independent events (p. 726)
Events for which the occurrence
or nonoccurrence of one event
does not affect the probability of
the other event.
sucesos independientes Dos sucesos
son independientes si el hecho de
que se produzca o no uno de ellos
no afecta la probabilidad del otro
suceso.
independent system (p. 407)
A system of equations that has
exactly one solution.
sistema independiente Sistema
de ecuaciones que tiene sólo una
solución.
independent variable (p. 246)
The input of a function; a variable
whose value determines the
value of the output, or dependent
variable.
variable independiente Entrada de
una función; variable cuyo valor
determina el valor de la salida, o
variable dependiente.
For y = 2x + 1, x is the
independent variable.
n
index (p. 832) In the radical √
x,
which represents the nth root of
x, n is the index. In the radical √
x,
the index is understood to be 2.
n
índice En el radical √
x , que
representa la enésima raíz de x, n
es el índice. En el radical √
x , se da
por sentado que el índice es 2.
3
The radical √
8 has an
index of 3.
indirect measurement (p. 122) A
method of measurement that uses
formulas, similar figures, and/or
proportions.
medición indirecta Método
de medición en el que se usan
fórmulas, figuras semejantes
y/o proporciones.
In the experiment of rolling a
number cube, rolling an even
number and rolling a number
less than 3 are inclusive events
because both contain the
outcome 2.
⎧x + y = 0
⎨
⎩x + y = 1
From a bag containing 3 red
marbles and 2 blue marbles,
drawing a red marble,
replacing it, and then
drawing a blue marble.
⎧x + y = 7
⎨
⎩x - y = 1
Solution: (4, 3)
Glossary/Glosario
S123
ENGLISH
SPANISH
EXAMPLES
inequality (p. 168) A statement
that compares two expressions by
using one of the following signs:
<, >, ≤, ≥, or ≠.
desigualdad Enunciado que
compara dos expresiones utilizando
uno de los siguientes signos:
<, >, ≤, ≥, o ≠.
x≥2
input (p. 55) A value that is
substituted for the independent
variable in a relation or function.
entrada Valor que sustituye a la
variable independiente en una
relación o función.
input-output table A table that
displays input values of a function
or expression together with the
corresponding outputs.
tabla de entrada y salida Tabla
que muestra los valores de entrada
de una función o expresión junto
con las correspondientes salidas.
integer (p. 34) A member of the
set of whole numbers and their
opposites.
entero Miembro del conjunto de
números cabales y sus opuestos.
intercept See x-intercept and
y-intercept.
intersección Ver intersección con el
eje x e intersección con el eje y.
interest (p. 133) The amount of
money charged for borrowing
money or the amount of money
earned when saving or investing
money. See also compound
interest, simple interest.
interés Cantidad de dinero que se
cobra por prestar dinero o cantidad
de dinero que se gana cuando se
ahorra o invierte dinero. Ver también
interés compuesto, interés simple.
interquartile range (IQR)
(p. 695) The difference of the third
(upper) and first (lower) quartiles
in a data set, representing the
middle half of the data.
rango entre cuartiles Diferencia
entre el tercer cuartil (superior) y
el primer cuartil (inferior) de un
conjunto de datos, que representa
la mitad central de los datos.
intersection (p. 203) The
intersection of two sets is the
set of all elements that are
common to both sets, denoted
by .
intersección de conjuntos La
intersección de dos conjuntos es el A = {1, 2, 3, 4}
B = {1, 3, 5, 7, 9}
conjunto de todos los elementos
A B = {1, 3}
que son comunes a ambos
conjuntos, expresado por .
inverse operations Operations
that undo each other.
operaciones inversas Operaciones
que se anulan entre sí.
inverse variation (p. 851) A
relationship between two
variables, x and y, that can be
written in the form y = __kx , where k
is a nonzero constant and x ≠ 0.
variación inversa Relación entre
dos variables, x e y, que puede
expresarse en la forma y = __kx , donde
k es una constante distinta
de cero y x ≠ 0.
irrational number (p. 34) A real
number that cannot be expressed
as the ratio of two integers.
número irracional Número real que
no se puede expresar como una
razón de enteros.
S124
Glossary/Glosario
{ Î Ó £
ä
£
Ó
Î
{
x
È
For the function f (x) = x + 5,
the input 3 produces an output
of 8.
Input
x
1
2
3
Output
y
4
7
10 13
4
… -3, -2, -1, 0, 1, 2, 3, …
Lower half
Upper half
18, 23, 28, 29, 36, 42
First quartile Third quartile
Interquartile range:
36 - 23 = 13
Addition and subtraction are
inverse operations:
5 + 3 = 8, 8 - 3 = 5
Multiplication and division are
inverse operations:
2 · 3 = 6, 6 ÷ 3 = 2
8
y=_
x
√2
, π, e
ENGLISH
SPANISH
EXAMPLES
isolate the variable (p. 77) To
isolate a variable in an equation,
use inverse operations on both
sides until the variable appears by
itself on one side of the equation
and does not appear on the other
side.
despejar la variable Para despejar
la variable de una ecuación, utiliza
operaciones inversas en ambos lados
hasta que la variable aparezca sola
en uno de los lados de la ecuación y
no aparezca en el otro lado.
10 = 6 - 2x
-6 -6
−− −−−−−−
4=
-2x
4 = -2x
-2
-2
-2 = x
isosceles triangle (p. S63)
A triangle with at least two
congruent sides.
triángulo isósceles Triángulo
que tiene al menos dos lados
congruentes.
_ _
L
leading coefficient (p. 477) The
coefficient of the first term of a
polynomial in standard form.
coeficiente principal Coeficiente del
primer término de un polinomio en
forma estándar.
least common denominator
(LCD) (p. 887) The least common
multiple of the denominators of
two or more given fractions.
mínimo común denominador
(MCD) Mínimo común múltiplo de
los denominadores de dos o más
fracciones dadas.
least common multiple (LCM)
(p. 886) The product of the
smallest positive number and the
lowest power of each variable that
divide evenly into each term.
mínimo común múltiplo (MCM) El
producto del número positivo
más pequeño y la menor potencia
de cada variable que divide
exactamente cada término.
leg of a right triangle (p. S68)
One of the two sides of a right
triangle that form the right angle.
cateto de un triángulo
rectángulo Uno de los dos lados de
un triángulo rectángulo que forman
el ángulo recto.
3x 2 + 7x - 2
Leading coefficient: 3
5 is 12.
3 and _
The LCD of _
4
6
The LCM of 10 and 18 is 90.
i}
i}
like radicals (p. 811) Radical
terms having the same radicand
and index.
radicales semejantes Términos
radicales que tienen el mismo
radicando e índice.
3 √
2x and √2x
like terms (p. 47) Terms with the
same variables raised to the same
exponents.
términos semejantes Términos con
las mismas variables elevadas a los
mismos exponentes.
3a 3b 2 and 7a 3b 2
line (p. S56) An undefined term in
geometry, a line is a straight path
that has no thickness and extends
forever in two directions.
línea Término indefinido en
geometría, una línea es un trazo
recto que no tiene grosor y se
extiende infinitamente.
line graph (p. 679) A graph that
uses line segments to show how
data changes.
gráfica lineal Gráfica que se
vale de segmentos de recta para
mostrar cambios en los datos.
Ű
-VœÀi
>Àœ˜½ÃÊ6ˆ`iœÊ>“iÊ-VœÀiÃ
£Óää
nää
{ää
ä
£
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Î
{
x
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>“iʘՓLiÀ
Glossary/Glosario
S125
ENGLISH
SPANISH
EXAMPLES
linear equation in one variable
(p. 298) An equation that can be
written in the form ax = b where
a and b are constants and a ≠ 0.
ecuación lineal en una variable
Ecuación que puede expresarse en
la forma ax = b donde a y b son
constantes y a ≠ 0.
x+1=7
linear equation in two variables
(p. 298) An equation that can be
written in the form Ax + By = C
where A, B, and C are constants
and A and B are not both 0.
ecuación lineal en dos variables
Ecuación que puede expresarse en
la forma Ax + By = C donde A, B y
C son constantes y A y B no son
ambas 0.
2x + 3y = 6
linear function (p. 296) A function
that can be written in the form
y = mx + b, where x is the
independent variable and m and
b are real numbers. Its graph is a
line.
función lineal Función que puede
expresarse en la forma y = mx + b,
donde x es la variable independiente
y m y b son números reales. Su
gráfica es una línea.
linear inequality in one variable
(p. 414) An inequality that can be
written in one of the following
forms: ax < b, ax > b, ax ≤ b,
ax ≥ b, or ax ≠ b, where a and b
are constants and a ≠ 0.
desigualdad lineal en una variable
Desigualdad que puede expresarse
de una de las siguientes formas:
ax < b, ax > b, ax ≤ b, ax ≥ b o
ax ≠ b, donde a y b son constantes
y a ≠ 0.
3x - 5 ≤ 2(x + 4)
linear inequality in two
variables (p. 414) An inequality
that can be written in one of the
following forms: Ax + By < C,
Ax + By > C, Ax + By ≤ C,
Ax + By ≥ C, or Ax + By ≠ C,
where A, B, and C are constants
and A and B are not both 0.
desigualdad lineal en dos variables
Desigualdad que puede expresarse
de una de las siguientes formas:
Ax + By < C, Ax + By > C, Ax + By
≤ C, Ax + By ≥ C o Ax + By ≠ C,
donde A, B y C son constantes y A y
B no son ambas 0.
2x + 3y > 6
literal equation (p. 108) An
equation that contains two or
more variables.
ecuación literal Ecuación que
contiene dos o más variables.
lower quartile See first quartile.
cuartil inferior Ver primer cuartil.
y=x-1
{
Þ
Ó
Ý
{ Ó ä
Ó
{
{
d = rt
1h b + b
A=_
( 1 2)
2
M
mapping diagram (p. 236)
A diagram that shows the
relationship of elements in the
domain to elements in the range
of a relation or function.
diagrama de correspondencia
Diagrama que muestra la relación
entre los elementos del dominio
y los elementos del rango de una
función.
markup (p. 139) The amount by
which a wholesale cost is increased.
margen de ganancia Cantidad que
se agrega a un costo mayorista.
matrix (p. 746) A rectangular
array of numbers.
matriz Arreglo rectangular de
números.
>««ˆ˜}ʈ>}À>“
œ“>ˆ˜
Ó
Glossary/Glosario
⎡ 1
⎢-2
⎣ 7
S126
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0
3⎤
2 -5
-6
3⎦
ENGLISH
maximum of a function (p. 592)
The y-value of the highest point
on the graph of the function.
SPANISH
EXAMPLES
máximo de una función Valor
de y del punto más alto en la
gráfica de la función.
­ä]ÊÓ®
The maximum of the function is 2.
mean (p. 694) The sum of all the
values in a data set divided by the
number of data values. Also called
the average.
media Suma de todos los valores
de un conjunto de datos dividida
entre el número de valores de
datos. También llamada promedio.
measure of an angle (p. S56)
Angles are measured in degrees. A
1
degree is ___
of a complete circle.
360
medida de un ángulo Los ángulos
se miden en grados. Un grado es
1
___
de un círculo completo.
360
measure of central tendency
(p. 694) A measure that describes
the center of a data set.
medida de tendencia dominante
Medida que describe el centro de
un conjunto de datos.
median (p. 694) For an ordered
data set with an odd number of
values, the median is the middle
value. For an ordered data set
with an even number of values,
the median is the average of the
two middle values.
mediana Dado un conjunto de
datos ordenado con un número
impar de valores, la mediana es el
valor medio. Dado un conjunto
de datos con un número par de
valores, la mediana es el promedio
de los dos valores medios.
minimum of a function (p. 592)
The y-value of the lowest point on
the graph of the function.
mínimo de una función Valor de
y del punto más bajo en la gráfica
de la función.
Data set: 4, 6, 7, 8, 10
4 + 6 + 7 + 8 + 10
Mean: __
5
35 = 7
=_
5
ÓÈ°nÂ
mean, median, or mode
8,
9,
9,
12,
15
Median: 9
4,
6,
7,
10,
10,
12
7 + 10
Median: _ = 8.5
2
­ä]ÊÓ®
The minimum of the function
is -2.
mode (p. 694) The value or values
that occur most frequently in a
data set; if all values occur with
the same frequency, the data set is
said to have no mode.
moda El valor o los valores que se
presentan con mayor frecuencia
en un conjunto de datos. Si todos
los valores se presentan con la
misma frecuencia, se dice que el
conjunto de datos no tiene moda.
monomial (p. 476) A number or a
product of numbers and variables
with whole-number exponents, or
a polynomial with one term.
monomio Número o producto de
números y variables con exponentes
de números cabales, o polinomio
con un término.
Multiplication Property of
Equality (p. 86) If a, b, and c are
real numbers and a = b, then
ac = bc.
Propiedad de igualdad de la
multiplicación Si a, b y c son
números reales y a = b,
entonces ac = bc.
Data set: 3, 6, 8, 8, 10 Mode: 8
Data set: 2, 5, 5, 7, 7 Modes: 5
and 7
Data set: 2, 3, 6, 9, 11 No mode
3x 2 y 4
1x =7
_
3
1
_
(3) x = (3)(7)
3
x = 21
( )
Glossary/Glosario
S127
ENGLISH
SPANISH
Multiplication Property of
Inequality (p. 180) If both sides
of an inequality are multiplied by
the same positive quantity, the
new inequality will have the same
solution set.
If both sides of an inequality are
multiplied by the same negative
quantity, the new inequality
will have the solution set if the
inequality symbol is reversed.
Propiedad de desigualdad de la
multiplicación Si ambos lados de
una desigualdad se multiplican
por el mismo número positivo,
la nueva desigualdad tendrá el
mismo conjunto solución.
Si ambos lados de una desigualdad
se multiplican por el mismo número
negativo, la nueva desigualdad
tendrá el mismo conjunto solución si
se invierte el símbolo de desigualdad.
multiplicative inverse (p. 21) The
reciprocal of the number.
inverso multiplicativo Recíproco de
un número.
mutually exclusive events (p. 734)
Two events are mutually exclusive
if they cannot both occur in the
same trial of an experiment.
sucesos mutuamente excluyentes
Dos sucesos son mutuamente
excluyentes si ambos no pueden
ocurrir en la misma prueba de un
experimento.
EXAMPLES
1x >7
_
3
1
(3) _ x > (3)(7)
3
x > 21
( )
-x ≤ 2
(-1)(-x) ≥ (-1)(2)
x ≥ -2
The multiplicative inverse
of 5 is __15 .
In the experiment of rolling
a number cube, rolling a 3
and rolling an even number
are mutually exclusive
events.
N
natural number (p. 34) A counting
number.
número natural Número que se
utiliza para contar.
negative correlation (p. 263)
Two data sets have a negative
correlation if one set of data
values increases as the other set
decreases.
correlación negativa Dos conjuntos
de datos tienen una correlación
negativa si un conjunto de valores de
datos aumenta a medida que el otro
conjunto disminuye.
negative exponent (p. 446) For
any nonzero real number x and
1
any integer n, x -n = __
.
xn
exponente negativo Para cualquier
número real distinto de cero x y
1
cualquier entero n, x -n = __
.
xn
negative number A number that is
less than zero. Negative numbers
lie to the left of zero on a number
line.
número negativo Número menor
que cero. Los números negativos
se ubican a la izquierda del cero
en una recta numérica.
negative square root (p. 32) The
opposite of the principal square
root of a number a, written as - √a
.
raíz cuadrada negativa Opuesto de la
raíz cuadrada principal de un número
a, que se expresa como - √a
.
net (p. S67) A diagram of the
faces of a three-dimensional
figure arranged in such a way that
the diagram can be folded to form
the three-dimensional figure.
plantilla Diagrama de las caras de
una figura tridimensional que se
puede plegar para formar la figura
tridimensional.
1, 2, 3, 4, 5, 6, …
Þ
Ý
1 ; 3 -2 = _
1
x -2 = _
x2
32
-2 is a negative number.
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S128
Glossary/Glosario
sin correlación Dos conjuntos
de datos no tienen correlación si
no existe una relación entre los
conjuntos de valores.
{
The negative square root
of 9 is - √
9 = -3.
£äʓ
£äʓ
Èʓ
Èʓ
no correlation (p. 263) Two data
sets have no correlation if there
is no relationship between the
sets of values.
Î
Þ
Ý
ENGLISH
SPANISH
EXAMPLES
n th root (p. 832) The nth root
n
of1 a number a, written as √
a
or
__
a n , is a number that is equal to a
when it is raised to the nth power.
enésima raíz La enésima raíz de un
1
__
n
número a, que se escribe √
a o a n,
es un número igual a a cuando se
eleva a la enésima potencia.
number line (p. 14) A line used to
represent the real numbers.
recta numérica Línea utilizada para
representar los números reales.
numerical expression (p. 6) An
expression that contains only
numbers and operations.
expresión numérica Expresión que
contiene únicamente números y
operaciones.
5
√
32 = 2, because 2 5 = 32.
{ Î Ó £
ä
£
Ó
Î
{
x
È
2 · 3 + (4 - 6)
O
obtuse angle (p. S56) An angle
that measures greater than 90°
and less than 180°.
ángulo obtuso Ángulo que mide más
de 90° y menos de 180°.
obtuse triangle (p. S63) A triangle
with one obtuse angle.
triángulo obtusángulo Triángulo con
un ángulo obtuso.
odds (p. 722) A comparison
of favorable and unfavorable
outcomes. The odds in favor
of an event are the ratio of the
number of favorable outcomes
to the number of unfavorable
outcomes. The odds against an
event are the ratio of the number
of unfavorable outcomes to the
number of favorable outcomes.
probabilidades a favor y en contra
Comparación de los resultados
favorables y desfavorables. Las
probabilidades a favor de un suceso
son la razón entre la cantidad de
resultados favorables y la cantidad
de resultados desfavorables. Las
probabilidades en contra de
un suceso son la razón entre
la cantidad de resultados
desfavorables y la cantidad
de resultados favorables.
opposite (p. 15) The opposite of
a number a, denoted -a, is the
number that is the same distance
from zero as a, on the opposite
side of the number line. The sum
of opposites is 0.
opuesto El opuesto de un número
a, expresado -a, es el número
que se encuentra a la misma
distancia de cero que a, del lado
opuesto de la recta numérica. La
suma de los opuestos es 0.
opposite reciprocal (p. 352) The
opposite of the reciprocal of a
number. The opposite reciprocal
of any nonzero number a is - __a1 .
recíproco opuesto Opuesto
del recíproco de un número.
El recíproco opuesto de a
es - __a1 .
OR (p. 202) A logical operator
representing the union of two
sets.
O Operador lógico que
representa la unión de dos
conjuntos.
The odds in favor of rolling a 3
on a number cube are 1 : 5.
The odds against rolling a 3 on
a number cube are 5 : 1.
xÊ՘ˆÌÃ
È x { Î Ó £
xÊ՘ˆÌÃ
ä
£
Ó
Î
{
x
È
5 and -5 are opposites.
3.
2 is - _
The opposite reciprocal of _
3
2
A = {2, 3, 4, 5} B = {1, 3, 5, 7}
The set of values that are in
A OR B is A B = {1, 2, 3, 4, 5, 7}.
Glossary/Glosario
S129
ENGLISH
SPANISH
EXAMPLES
order of operations (p. 40)
A process for evaluating
expressions:
First, perform operations in
parentheses or other grouping
symbols.
Second, evaluate powers and
roots.
Third, perform all multiplication
and division from left to right.
Fourth, perform all addition and
subtraction from left to right.
orden de las operaciones Regla
para evaluar las expresiones:
Primero, realizar las operaciones
entre paréntesis u otros símbolos
de agrupación.
Segundo, evaluar las potencias y
las raíces.
Tercero, realizar todas las
multiplicaciones y divisiones de
izquierda a derecha.
Cuarto, realizar todas las sumas y
restas de izquierda a derecha.
ordered pair (p. 54) A pair of
numbers (x, y) that can be used
to locate a point on a coordinate
plane. The first number x indicates
the distance to the left or right of
the origin, and the second number
y indicates the distance above or
below the origin.
par ordenado Par de números (x, y)
que se pueden utilizar para ubicar
un punto en un plano cartesiano. El
primer número, x, indica la distancia
a la izquierda o derecha del origen
y el segundo número, y, indica la
distancia hacia arriba o hacia abajo
del origen.
origin (p. 54) The intersection of
the x- and y-axes in a coordinate
plane. The coordinates of the
origin are (0, 0).
origen Intersección de los ejes
x e y en un plano cartesiano. Las
coordenadas de origen son (0, 0).
outcome (p. 713) A possible result
of a probability experiment.
resultado Resultado posible de un
experimento de probabilidad.
outlier (p. 695) A data value that
is far removed from the rest of the
data.
valor extremo Valor de
datos que está muy alejado
del resto de los datos.
output (p. 55) The result of
substituting a value for a variable
in a function.
salida Resultado de la sustitución
de una variable por un valor en
una función.
2 + 3 2 - (7 + 5) ÷ 4 · 3
2 + 3 2 - 12 ÷ 4 · 3 Add inside
parentheses.
2 + 9 - 12 ÷ 4 · 3 Evaluate the
power.
2+9-3·3
Divide.
2+9-9
Multiply.
11 - 9
Add.
2
Subtract.
{
Þ
Ó
Ý
{
Ó
ä
Ó
{
The coordinates of B
are (-2, 3).
œÀˆ}ˆ˜
ä
In the experiment of rolling
a number cube, the possible
outcomes are 1, 2, 3, 4, 5, and 6.
-OSTOFDATA -EAN
/UTLIER
For the function f (x) = x 2 + 1,
the input 3 produces an output
of 10.
P
parabola (p. 591) The shape of the
graph of a quadratic function.
parábola Forma de la gráfica de una
función cuadrática.
parallel lines (p. 349, p. S56) Lines
in the same plane that do not
intersect.
líneas paralelas Líneas en el mismo
plano que no se cruzan.
parallelogram (p. S63) A
quadrilateral with two pairs of
parallel sides.
paralelogramo Cuadrilátero con dos
pares de lados paralelos.
S130
Glossary/Glosario
À
Ã
ENGLISH
SPANISH
EXAMPLES
parent function (p. 357) The
simplest function with the
defining characteristics of the
family. Functions in the same
family are transformations of their
parent function.
función madre La función más
básica que tiene las características
distintivas de una familia. Las
funciones de la misma familia son
transformaciones de su función
madre.
Pascal’s triangle (p. 570) A
triangular arrangement of
numbers in which every row
starts and ends with 1 and each
other number is the sum of the
two numbers above it.
triángulo de Pascal Arreglo
triangular de números en el cual
cada fila comienza y termina con
1 y los demás números son la suma
de los dos valores que están arriba
de cada uno.
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
percent (p. 127) A ratio that
compares a number to 100.
porcentaje Razón que compara un
número con 100.
17 = 17%
_
100
percent change (p. 138) An
increase or decrease given as a
percent of the original amount.
See also percent decrease, percent
increase.
porcentaje de cambio Incremento
o disminución dada como un
porcentaje de la cantidad original. Ver
también porcentaje de disminución,
porcentaje de incremento.
percent decrease (p. 138) A
decrease given as a percent of the
original amount.
porcentaje de disminución
Disminución dada como un
porcentaje de la cantidad original.
If an item that costs $8.00 is
marked down to $6.00, the
amount of the decrease is
$2.00, so the percent decrease is
2.00
____
= 0.25 = 25%.
8.00
percent increase (p. 138) An
increase given as a percent of the
original amount.
porcentaje de incremento
Incremento dado como un
porcentaje de la cantidad
original.
If an item’s wholesale cost of
$8.00 is marked up to $12.00,
the amount of the increase is
$4.00, so the percent increase
4.00
is ____
= 0.5 = 50%.
8.00
perfect square (p. 32) A number
whose positive square root is a
whole number.
cuadrado perfecto Número cuya
raíz cuadrada positiva es un número
cabal.
36 is a perfect square
36 = 6.
because √
perfect-square trinomial (p. 501)
A trinomial whose factored form
is the square of a binomial. A
perfect-square trinomial has the
2
form a 2 - 2ab + b 2 = (a - b) or
2
2
2
a + 2ab + b = (a + b) .
trinomio cuadrado perfecto Trinomio
cuya forma factorizada es el
cuadrado de un binomio. Un
trinomio cuadrado perfecto tiene
2
la forma a 2 - 2ab + b 2 = (a - b)
2
2
2
o a + 2ab + b = (a + b) .
x 2 + 6x + 9 is a perfectsquare trinomial, because
x 2 + 6x + 9 = (x + 3) 2.
perimeter (p. S60) The sum of
the side lengths of a closed plane
figure.
£nÊvÌ
perímetro Suma de las longitudes
de los lados de una figura plana
ÈvÌ
cerrada.
Perimeter = 18 + 6 + 18 + 6 = 48 ft
permutation (p. 737) An
arrangement of a group of objects
in which order is important.
permutación Arreglo de un grupo
de objetos en el cual el orden es
importante.
f (x) = x 2 is the parent
function for g (x) = x 2 + 4
and h (x) = (5x + 2)2 - 3.
For objects A, B, C, and
D, there are 12 different
permutations of 2 objects.
AB, AC, AD, BC, BD, CD
BA, CA, DA, CB, DB, DC
Glossary/Glosario
S131
ENGLISH
SPANISH
perpendicular Intersecting to form
90° angles.
perpendicular Que se cruza para
formar ángulos de 90°.
perpendicular lines (p. 351,
p. S56) Lines that intersect at 90°
angles.
líneas perpendiculares Líneas que se
cruzan en ángulos de 90°.
plane (p. S56) An undefined term
in geometry, it is a flat surface
that has no thickness and extends
forever in all directions.
plano Término indefinido en
geometría; un plano es una
superficie plana que no tiene grosor
y se extiende infinitamente en todas
direcciones.
EXAMPLES
˜
“
˜
“
plane R of plane ABC
point (p. S56) An undefined term
in geometry, it names a location
and has no size.
punto Término indefinido en
geometría que denomina una
ubicación y no tiene tamaño.
point-slope form (p. 342) The
point-slope form of a linear
equation is y - y 1 = m(x - x 1),
where m is the slope and (x 1, y 1)
is a point on the line.
forma de punto y pendiente La
forma de punto y pendiente de una
ecuación lineal es y - y 1 = m(x - x 1),
donde m es la pendiente y (x 1, y 1) es
un punto en la línea.
polygon (p. S58) A closed plane
figure formed by three or more
segments such that each segment
intersects exactly two other
segments only at their endpoints
and no two segments with a
common endpoint are collinear.
polígono Figura plana cerrada
formada por tres o más segmentos
tal que cada segmento se cruza
únicamente con otros dos
segmentos sólo en sus extremos y
ningún segmento con un extremo
común a otro es colineal con éste.
polynomial (p. 476) A monomial
or a sum or difference of
monomials.
polinomio Monomio o suma o
diferencia de monomios.
polynomial long division (p. 893)
A method of dividing one
polynomial by another.
división larga polinomial
Método por el que se divide
un polinomio entre otro.
positive correlation (p. 263)
Two data sets have a positive
correlation if both sets of data
values increase.
correlación positiva (p. 264)
Dos conjuntos de datos tienen
correlación positiva si los valores
de ambos conjuntos de datos
aumentan.
positive number A number greater
than zero.
número positivo Número mayor
que cero.
S132
Glossary/Glosario
*
point P
y - 3 = 2(x - 3)
2x 2 + 3xy - 7y 2
x+1
x + 2 x 2 + 3x + 5
-(x 2 + 2x)
−−−−−−−
x+5
-(x + 2)
−−−−−−
3
x 2+ 3x + 5
3
__
=x+1+_
x+2
x +2
Þ
Ý
2 is a positive number.
{ Î Ó £
ä
£
Ó
Î
{
ENGLISH
SPANISH
EXAMPLES
positive square root (p. 32) The
positive square root of a number,
indicated by the radical sign.
raíz cuadrada positiva Raíz cuadrada
positiva de un número, expresada
por el signo de radical.
The positive square root of
36 is √
36 = 6.
power (p. 26) An expression
written with a base and an
exponent or the value of such an
expression.
potencia Expresión escrita con una
base y un exponente o el valor de
dicha expresión.
Power of a Power Property
(p. 462) If a is any nonzero real
number and m and n are integers,
n
then (a m) = a mn.
Propiedad de la potencia de una
potencia Dado un número real
a distinto de cero y los números
n
enteros m y n, entonces (a m) = a mn.
Power of a Product Property
(p. 463) If a and b are any nonzero
real numbers and n is any integer,
n
then (ab) = a nb n.
Propiedad de la potencia de un
producto Dados los números reales
a y b distintos de cero y un número
n
entero n, entonces (ab) = a nb n.
Power of a Quotient Property
(p. 469, p. 470) If a and b are any
nonzero real numbers and n is an
Propiedad de la potencia de un
cociente Dados los números reales a
y b distintos de cero y un número
integer, then
(b)
a n
__
n
a
= __
.
bn
entero n, entonces
(b)
a n
__
n
a
= __
.
bn
2 3 = 8, so 8 is the third
power of 2.
(6 7)4 = 6 7·4
= 6 28
(2 · 4)3 = 2 3 · 4 3
= 8 · 64
= 512
(_35 ) = _53 · _53 · _53 · _53
4
·3·3·3
= 3__
5·5·5·5
34
=_
54
prediction (p. 715) An estimate or
guess about something that has
not yet happened.
predicción Estimación o suposición
sobre algo que todavía no ha
sucedido.
prime factorization (p. 524) A
representation of a number or
a polynomial as a product of
primes.
factorización prima Representación
de un número o de un polinomio
como producto de números primos.
The prime factorization of
60 is 2 · 2 · 3 · 5
prime number (p. 524) A whole
number greater than 1 that has
exactly two factors, itself and 1.
número primo Número cabal mayor
que 1 que es divisible únicamente
entre sí mismo y entre 1.
5 is prime because its only
factors are 5 and 1.
principal (p. 133) An amount of
money borrowed or invested.
capital Cantidad de dinero que se
pide prestado o se invierte.
prism (p. 874, p. S64) A
polyhedron formed by two
parallel congruent polygonal
bases connected by faces that are
parallelograms.
prisma Poliedro formado por dos
bases poligonales congruentes y
paralelas conectadas por caras
laterales que son paralelogramos.
probability (p. 713) A number
from 0 to 1 (or 0% to 100%) that
is the measure of how likely an
event is to occur.
probabilidad Número entre 0 y 1
(o entre 0% y 100%) que describe
cuán probable es que ocurra un
suceso.
Product of Powers Property
(p. 460) If a is any nonzero real
number and m and n are integers,
then a m · a n = a m+n.
Propiedad del producto de potencias
Dado un número real a distinto de
cero y los números enteros m y n,
entonces a m · a n = a m+n.
A bag contains 3 red marbles
and 4 blue marbles. The
probability of randomly
choosing a red marble is __37 .
6 7 · 6 4 = 6 7+4
= 6 11
Glossary/Glosario
S133
ENGLISH
SPANISH
EXAMPLES
Product Property of Square
Roots (p. 806) For a ≥ 0 and
b ≥ 0, √
ab = √
a · √
b.
Propiedad del producto de raíces
cuadradas Dados a ≥ 0 y
.
b ≥ 0, √
ab = √a
· √b
proportion (p. 114) A statement
c
that two ratios are equal; __ab = __
.
d
proporción Ecuación que establece
c
que dos razones son iguales; __ab = __
.
d
pyramid (p. 874, p. S64) A
polyhedron formed by a polygonal
base and triangular lateral faces
that meet at a common vertex.
pirámide Poliedro formado por
una base poligonal y caras laterales
triangulares que se encuentran en
un vértice común.
Pythagorean Theorem (p. S68) If a
right triangle has legs of lengths a
and b and a hypotenuse of length
c, then a 2 + b 2 = c 2.
Teorema de Pitágoras Dado un
triángulo rectángulo con catetos de
longitudes a y b y una hipotenusa de
longitud c, entonces a 2 + b 2 = c 2.
√
9 · 25 = √
9 · √
25
= 3 · 5 = 15
4
2 =_
_
3
6
£ÎÊV“
xÊV“
£ÓÊV“
5 2 + 12 2 = 13 2
25 + 144 = 169
Pythagorean triple (p. 519) A set
of three nonzero whole numbers
a, b, and c such that a 2 + b 2 = c 2.
Tripleta de Pitágoras Conjunto de
tres números cabales distintos de
cero a, b y c tal que a 2 + b 2 = c 2.
The numbers 3, 4, and 5
form a Pythagorean triple
because 3 2 + 4 2 = 5 2.
Q
quadrant (p. 54) One of the four
regions into which the x- and
y-axes divide the coordinate
plane.
cuadrante Una de las cuatro
regiones en las que los ejes x e y
dividen el plano cartesiano.
+Õ>`À>˜ÌÊ
+Õ>`À>˜ÌÊ
ä
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quadratic equation (p. 622) An
equation that can be written in
the form ax 2 + bx + c = 0, where
a, b, and c are real numbers and
a ≠ 0.
ecuación cuadrática Ecuación
que se puede expresar como
ax 2 + bx + c = 0, donde a, b y c
son números reales y a ≠ 0.
Quadratic Formula (p. 652)
fórmula cuadrática La fórmula
-b ± √
b 2 - 4ac
-b ± √
b 2 - 4ac
The formula x = ____________
,
2a
which gives solutions, or roots, of
equations in the form
ax 2 + bx + c = 0, where a ≠ 0.
x = ____________
, que da
2a
soluciones, o raíces, para
las ecuaciones del tipo
ax 2 + bx + c = 0, donde
a ≠ 0.
quadratic function (p. 590) A
function that can be written in the
form f (x) = ax 2 + bx + c, where
a, b, and c are real numbers and
a ≠ 0.
función cuadrática Función
que se puede expresar como
f (x) = ax 2 + bx + c, donde a,
b y c son números reales
y a ≠ 0.
S134
Glossary/Glosario
x 2 + 3x - 4 = 0
x2 - 9 = 0
The solutions of 2x 2 - 5x - 3 = 0
are given by
(-5)2 - 4 (2)(-3)
-(-5) ± √
x = ___
2(2)
5 ± √
25 + 24
5±7
= __ = _
4
4
1.
x = 3 or x = - _
2
f (x) = x 2 - 6x + 8
ENGLISH
SPANISH
quadratic polynomial (p. 477) A
polynomial of degree 2.
polinomio cuadrático Polinomio de
grado 2.
quartile (p. 695) The median of
the upper or lower half of a data
set. See also first quartile, third
quartile.
cuartil La mediana de la mitad
superior o inferior de un conjunto
de datos. Ver también primer
cuartil, tercer cuartil.
Quotient of Powers Property
(p. 467) If a is a nonzero real
number and m and n are integers,
am
then ___
= a m-n.
an
Propiedad del cociente de
potencias Dado un número real
a distinto de cero y los números
am
enteros m y n, entonces ___
= a m-n.
an
Quotient Property of Square
Roots (p. 806) For a ≥ 0 and
Propiedad del cociente de raíces
cuadradas Dados a ≥ 0 y
a
= ___
.
b > 0, __
b
a
= ___
.
b > 0, __
b
√a
√b
√a
EXAMPLES
x 2 - 6x + 8
&IRSTQUARTILE
-INIMUM
ä
Ó
{
4HIRDQUARTILE
-EDIAN
È
n
£ä
-AXIMUM
£Ó
£{
6 7 = 6 7-4 = 6 3
_
64
√
9
9 =_
3
_
=_
25
√
25
5
√b
R
radical equation (p. 822) An
equation that contains a variable
within a radical.
ecuación radical Ecuación que
contiene una variable dentro de un
radical.
radical expression (p. 805) An
expression that contains a radical
sign.
expresión radical Expresión que
contiene un signo de radical.
radical symbol (p. 32) The
symbol √ used to denote a
root. The symbol is used alone
to indicate a square root or with
n
an index, √, to indicate the nth
root.
símbolo de radical Símbolo √
que se utiliza para expresar una
raíz. Puede utilizarse solo para
indicar una raíz cuadrada, o con un
n
índice, √, para indicar la enésima
raíz.
radicand (p. 805) The expression
under a radical sign.
radicando Número o expresión
debajo del signo de radical.
radius (p. S62) A segment whose
endpoints are the center of a
circle and a point on the circle;
the distance from the center of a
circle to any point on the circle.
radio Segmento cuyos extremos son
el centro de un círculo y un punto de
la circunferencia; distancia desde el
centro de un círculo hasta cualquier
punto de la circunferencia.
random sample (p. 703) A sample
selected from a population so that
each member of the population
has an equal chance of being
selected.
muestra aleatoria Muestra
seleccionada de una población
tal que cada miembro de ésta
tenga igual probabilidad de ser
seleccionada.
Mr. Hansen chose a random
sample of the class by writing
each student’s name on a slip
of paper, mixing up the slips,
and drawing five slips without
looking.
range of a data set (p. 694) The
difference of the greatest and least
values in the data set.
rango de un conjunto de datos
La diferencia del mayor y menor
valor en un conjunto de datos.
The data set {3, 3, 5, 7, 8, 10,
11, 11, 12} has a range of
12 - 3 = 9.
√
x+3+4=7
√
x+3+4
√
36 = 6
3
√
27 = 3
Expression: √x + 3
Radicand: x + 3
,>`ˆÕÃ
Glossary/Glosario
S135
ENGLISH
SPANISH
EXAMPLES
range of a function or relation
(p. 236) The set of output values of
a function or relation.
rango de una función o relación
Conjunto de todos los valores de
salida posibles de una función o
relación.
rate (p. 114) A ratio that
compares two quantities
measured in different units.
tasa Razón que compara dos
cantidades medidas en diferentes
unidades.
rate of change (p. 310) A ratio
that compares the amount of
change in a dependent variable
to the amount of change in an
independent variable.
tasa de cambio Razón que compara
la cantidad de cambio de la variable
dependiente con la cantidad
de cambio de la variable
independiente.
The range of y = x 2 is y ≥ 0.
55 miles = 55mi/h
_
1 hour
The cost of mailing a letter
increased from 22 cents in
1985 to 25 cents in 1988.
During this period, the rate of
change was
change in cost
25 - 21
___________
= _________
= __3
change in year
1988 - 1985
3
= 1 cent per year.
ratio (p. 114) A comparison of
two quantities by division.
razón Comparación de dos
cantidades mediante una división.
rational equation (p. 900) An
equation that contains one or
more rational expressions.
ecuación racional Ecuación que
contiene una o más expresiones
racionales.
rational exponent (p. 832) An
exponent that can be expressed
m
as __
n such that if m and n are
exponente racional Exponente que
m
se puede expresar como __
n tal que si
m y n son números enteros,
n
n
m
integers, then b n = √b
= ( √
b) .
m
__
m
1 or 1 : 2
_
2
x+2
__
=6
2
x + 3x - 1
__1
6
64 6 = √
64
n
n
m
) .
entonces b n = √b
= ( √b
m
__
m
rational expression (p. 866)
An algebraic expression whose
numerator and denominator
are polynomials and whose
denominator has a degree ≥ 1.
expresión racional Expresión
algebraica cuyo numerador y
denominador son polinomios y cuyo
denominador tiene un grado ≥ 1.
rational function (p. 858) A
function whose rule can be
written as a rational expression.
función racional Función cuya
regla se puede expresar como una
expresión racional.
x+2
f(x) = __
x 2 + 3x - 1
rational number (p. 34) A number
that can be written in the form __ab ,
where a and b are integers and
b ≠ 0.
número racional Número que se
puede expresar como __ab , donde a y b
son números enteros y b ≠ 0.
−
2, 0
3, 1.75, 0.3, - _
3
rationalizing the denominator
(p. 818) A method of rewriting a
fraction by multiplying by another
fraction that is equivalent to 1
in order to remove radical terms
from the denominator.
racionalizar el denominador Método
que consiste en escribir nuevamente
una fracción multiplicándola por
otra fracción equivalente a 1 a fin de
eliminar los términos radicales del
denominador.
√
√
2
2
1 ·_
_
=_
2
√
2 √
2
ray (p. S56) A part of a line that
starts at an endpoint and extends
forever in one direction.
rayo Parte de una recta que
comienza en un extremo y se
extiende infinitamente en una
dirección.
S136
Glossary/Glosario
x+2
__
x 2 + 3x - 1
ENGLISH
real number (p. 34) A rational or
irrational number. Every point on
the number line represents a real
number.
SPANISH
número real Número racional o
irracional. Cada punto de la recta
numérica representa un número
real.
EXAMPLES
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recíproco Dado el número real
a ≠ 0, el recíproco de a es __a1 . El
producto de los recíprocos es 1.
rectangle (p. S63) A quadrilateral
with four right angles.
rectángulo Cuadrilátero con cuatro
ángulos rectos.
rectangular prism (p. 874) A prism
whose bases are rectangles.
prisma rectangular Prisma cuyas
bases son rectángulos.
rectangular pyramid (p. 874)
A pyramid whose base is a
rectangle.
pirámide rectangular Pirámide cuya
base es un rectángulo.
reflection (p. 359, p. S69) A
transformation that reflects, or
“flips,” a graph or figure across a
line, called the line of reflection.
reflexión Transformación en la
que una gráfica o figura se refleja
o se invierte sobre una línea,
denominada la línea de reflexión.
regular polygon (p. S58) A
polygon that is both equilateral
and equiangular.
polígono regular Polígono equilátero
de ángulos iguales.
relation (p. 236) A set of ordered
pairs.
relación Conjunto de pares
ordenados.
repeating decimal (p. 34) A
rational number in decimal form
that has a block of one or more
digits that repeat continuously.
decimal periódico Número racional
en forma decimal que tiene un
bloque de uno o más dígitos que se
repite continuamente.
replacement set (p. 8) A set of
numbers that can be substituted
for a variable.
conjunto de reemplazo Conjunto de
números que pueden sustituir una
variable.
rhombus (p. S63) A quadrilateral
with four congruent sides.
rombo Cuadrilátero con cuatro
lados congruentes.
right angle (p. S56) An angle that
measures 90°.
ángulo recto Ángulo que mide 90°.
rise (p. 311) The difference in the
y-values of two points on a line.
distancia vertical Diferencia entre
los valores de y de dos puntos de
una línea.
ÊÊȖ££Ê
е
еÊ
е
ÊȖÓÊ
Ê
ä
ÚÚÊxÊÊÊ
{°x
reciprocal (p. 21) For a real
number a ≠ 0, the reciprocal of a
is __a1 . The product of reciprocals
is 1.
£ÇÊ
еÊ
ÊȖе
Ó
7…œiÊ Õ“LiÀÃÊ­ϓ®
£
ÀÀ>̈œ˜>Ê ՓLiÀÃ
ÊÊÊ
ÊÚÚÚ
棊
££
û
™
Number
Reciprocal
2
1
__
1
1
-1
-1
0
No reciprocal
2
Ī
Ī
Ī
⎧
⎫
⎨(0, 5), (0, 4), (2, 3), (4, 0)⎬
⎩
⎭
− − −−
−
1.3, 0.6, 2.14, 6.773
For the points (3, -1) and
(6, 5), the rise is 5 - (-1) = 6.
Glossary/Glosario
S137
ENGLISH
rotation (p. 358, p. S69) A
transformation that rotates or
turns a figure about a point called
the center of rotation.
SPANISH
EXAMPLES
rotación Transformación que rota
o gira una figura sobre un punto
llamado centro de rotación.
Ī
Ī
Ī
Ī
run (p. 311) The difference in the
x-values of two points on a line.
distancia horizontal Diferencia
entre los valores de x de dos
puntos de una línea.
For the points (3, -1) and
(6, 5), the run is 6 - 3 = 3.
S
sales tax (p. 134) A percent of the
cost of an item that is charged by
governments to raise money.
impuesto sobre la venta Porcentaje
del costo de un artículo que cobran
los gobiernos para recaudar dinero.
sample space (p. 713) The set
of all possible outcomes of a
probability experiment.
espacio muestral Conjunto de
todos los resultados posibles de un
experimento de probabilidad.
scale (p. 116) The ratio between
two corresponding measurements.
escala Razón entre dos medidas
correspondientes.
scale drawing (p. 116) A drawing
that uses a scale to represent an
object as smaller or larger than
the actual object.
dibujo a escala Dibujo que utiliza
una escala para representar un
objeto como más pequeño o más
grande que el objeto original.
scale factor (p. 123) The
multiplier used on each
dimension to change one
figure into a similar figure.
factor de escala El multiplicador
utilizado en cada dimensión para
transformar una figura en una
figura semejante.
In the experiment of rolling
a number cube, the sample
space is {1, 2, 3, 4, 5, 6}.
1 cm : 5 mi
A blueprint is an example of
a scale drawing.
Èʈ˜°
{ʈ˜°
Óʈ˜°
Îʈ˜°
3 = 1.5
Scale factor: _
2
scale model (p. 116) A threedimensional model that uses a
scale to represent an object as
smaller or larger than the actual
object.
modelo a escala Modelo
tridimensional que utiliza una escala
para representar un objeto como
más pequeño o más grande que el
objeto real.
scalene triangle (p. S63) A triangle
with no congruent sides.
triángulo escaleno Triángulo sin
lados congruentes.
scatter plot (p. 262) A graph with
points plotted to show a possible
relationship between two sets of
data.
diagrama de dispersión Gráfica con
puntos que se usa para demostrar
una relación posible entre dos
conjuntos de datos.
Þ
n
È
{
Ó
Ý
ä
S138
Glossary/Glosario
Ó
{
È
n
ENGLISH
SPANISH
scientific notation (p. 453) A
method of writing very large or
very small numbers, by using
powers of 10, in the form m × 10 n,
where 1 ≤ m < 10 and n is an
integer.
notación científica Método que
consiste en escribir números muy
grandes o muy pequeños utilizando
potencias de 10 del tipo m × 10 n,
donde 1 ≤ m < 10 y n es un número
entero.
second differences (p. 590)
Differences between first
differences of a function.
segundas diferencias Diferencias
entre las primeras diferencias de
una función.
EXAMPLES
12,560,000,000,000 =
1.256 × 10 13
0.0000075 = 7.5 × 10 -6
Constant change in x-values
+1 +1 +1 +1
x
0
1
2
3
4
y = x2
0
1
4
9
16
First differences
+1 +3 +5 +7
Second differences
sequence (p. 272) A list of numbers
that often form a pattern.
sucesión Lista de números que
generalmente forman un patrón.
set-builder notation (p. 168) A
notation for a set that uses a rule
to describe the properties of the
elements of the set.
notación de conjuntos Notación
para un conjunto que se vale de una
regla para describir las propiedades
de los elementos del conjunto.
similar (p. 121) Two figures are
similar if they have the same
shape but not necessarily the
same size.
semejantes Dos figuras con
la misma forma pero no
necesariamente del mismo
tamaño.
similarity statement (p. 121) A
statement that indicates that
two polygons are similar by
listing the vertices in the order of
correspondence.
enunciado de semejanza Enunciado
que indica que dos polígonos son
semejantes enumerando los vértices
en orden de correspondencia.
+2 +2 +2
1, 2, 4, 8, 16, …
{x | x > 3} is read “The set of
all x such that x is greater
than 3.”
È
x
x°{
{
£Ó
£ä
£ä°n
n
quadrilateral ABCD ∼
quadrilateral EFGH
simple event (p. 737) An event
consisting of only one outcome.
suceso simple Suceso que tiene
sólo un resultado.
simple interest (p. 133) A fixed
percent of the principal. For
principal P, interest rate r, and
time t in years, the simple interest
is I = Prt.
interés simple Porcentaje fijo del
capital. Dado el capital P, la tasa de
interés r y el tiempo t expresado en
años, el interés simple es I = Prt.
In the experiment of rolling
a number cube, the event
consisting of the outcome 3
is a simple event.
If $100 is put into an account
with a simple interest rate of
5%, then after 2 years, the
account will have earned
I = 100 · 0.05 · 2 = $10 in
interest.
Glossary/Glosario
S139
ENGLISH
SPANISH
EXAMPLES
simplest form of a square root
expression (p. 805) A square root
expression is in simplest form
if it meets the following
criteria:
1. No perfect squares are in the
radicand.
2. No fractions are in the
radicand.
3. No square roots appear in the
denominator of a fraction.
forma simplificada de una expresión
de raíz cuadrada Una expresión
de raíz cuadrada está en forma
simplificada si reúne los siguientes
requisitos:
1. No hay cuadrados perfectos en
el radicando.
2. No hay fracciones en el
radicando.
3. No aparecen raíces cuadradas en
el denominador de una fracción.
See also rationalizing the
denominator.
Ver también racionalizar el
denominador.
simplest form of a rational
expression (p. 867) A rational
expression is in simplest form if
the numerator and denominator
have no common factors.
x - 1)(x + 1)
forma simplificada de una expresión _
x 2 - 1 = (__
2
racional Una expresión racional
x +x-2
(x + 1)(x + 2)
está en forma simplificada cuando
x
-1
=_
el numerador y el denominador no
x+2
tienen factores comunes.
Not Simplest
Form
Simplest
Form
√
180
6 √
5
√216a b
6ab √
6
2 2
√
7
_
√
2
√
14
_
2
Simplest form
simplest form of an exponential
expression (p. 460) An
exponential expression is in
simplest form if it meets the
following criteria:
1. There are no negative
exponents.
2. The same base does not appear
more than once in a product or
quotient.
3. No powers, products, or
quotients are raised to powers.
4. Numerical coefficients in
a quotient do not have any
common factor other than 1.
forma simplificada de una expresión
exponencial Una expresión
exponencial está en forma
simplificada si reúne los siguientes
requisitos:
1. No hay exponentes negativos.
2. La misma base no aparece más
de una vez en un producto o
cociente.
3. No se elevan a potencias
productos, cocientes ni potencias.
4. Los coeficientes numéricos en un
cociente no tienen ningún factor
común que no sea 1.
simplify (p. 40) To perform all
indicated operations.
simplificar Realizar todas las
operaciones indicadas.
simulation (p. 712) A model of
an experiment, often one that
would be too difficult or timeconsuming to actually perform.
simulación Modelo de un
experimento; generalmente se
recurre a la simulación cuando
realizar dicho experimento sería
demasiado difícil o llevaría mucho
tiempo.
sine (p. 908) In a right triangle,
the ratio of the length of the leg
opposite ∠A to the length of the
hypotenuse.
seno En un triángulo rectángulo,
razón entre la longitud del cateto
opuesto a ∠A y la longitud de la
hipotenusa.
Not Simplest
Form
Simplest
Form
78 · 74
7 12
(x 2)-4 · x 5
1
_
x3
a 5b 9
_
(ab)4
ab 5
13 - 20 + 8
-7 + 8
1
œ««œÃˆÌi
…Þ«œÌi˜ÕÃi
opposite
sin A = __
hypotenuse
S140
Glossary/Glosario
ENGLISH
slope (p. 311) A measure of the
steepness of a line. If (x 1, y 1) and
(x 2, y 2) are any two points on the
line, the slope of the line, known
as m, is represented by the
y2 - y1
equation m = _____
x2 - x1 .
SPANISH
pendiente Medida de la inclinación
de una línea. Dados dos puntos
(x 1, y 1) y (x 2, y 2) en una línea, la
pendiente de la línea, denominada
m, se representa con la ecuación
y2 - y1
m = _____
x2 - x1 .
EXAMPLES
{
Þ
Ó
­Ó]ÊÓ®
­Ó]Ê£®
ä
{
Ý
Ó
{
Ó
{
_
y -y
3
-1 - 2 = _
m = x2 - x1 = _
4
-2 - 2
1
2
slope-intercept form (p. 335) The
slope-intercept form of a linear
equation is y = mx + b, where
m is the slope and b is the
y-intercept.
forma de pendiente-intersección
La forma de pendiente-intersección
de una ecuación lineal es
y = mx + b, donde m es la pendiente
y b es la intersección con el eje y.
solution of a linear equation in
two variables (p. 245) An ordered
pair or ordered pairs that make
the equation true.
solución de una ecuación lineal en
dos variables Un par ordenado o
pares ordenados que hacen que la
ecuación sea verdadera.
Equation: x + y = 6
Solution: (4, 2) (one possible
solution)
solution of a linear inequality in
two variables (p. 414) An ordered
pair or ordered pairs that make
the inequality true.
solución de una desigualdad lineal
en dos variables Un par ordenado
o pares ordenados que hacen que
la desigualdad sea verdadera.
Inequality: x + y < 6
Solution: (3, 1) (one possible
solution)
solution of a system of linear
equations (p. 383) Any ordered
pair that satisfies all the equations
in a system.
solución de un sistema de
ecuaciones lineales Cualquier
par ordenado que resuelva todas
las ecuaciones de un sistema.
solution of a system of linear
inequalities (p. 421) Any
ordered pair that satisfies all the
inequalities in a system.
solución de un sistema de
desigualdades lineales Cualquier
par ordenado que resuelva todas
las desigualdades de un sistema.
y = -2x + 4
The slope is -2.
The y-intercept is 4.
⎧x + y = -1
⎨
⎩ -x + y = -3
Solution: (1, -2)
⎧y ≤ x + 1
⎨
⎩ y < -x + 4
Þ
­Ó]£®ÊˆÃʈ˜Ê̅iÊ
œÛiÀ>««ˆ˜}Ê
Å>`i`ÊÀi}ˆœ˜Ã]
ÜʈÌʈÃÊ>Ê܏Ṏœ˜°
Ó
Ó
ä
Ó
Ý
Ó
solution of an equation in one
variable (p. 77) A value or values
that make the equation true.
solución de una ecuación en una
variable Valor o valores que hacen
que la ecuación sea verdadera.
Equation: x + 2 = 6
Solution: x = 4
solution of an inequality in one
variable (p. 168) A value or values
that make the inequality true.
solución de una desigualdad en una
variable Valor o valores que hacen
que la desigualdad sea verdadera.
Inequality: x + 2 < 6
Solution: x < 4
solution set (p. 77) The set of
values that make a statement
true.
conjunto solución Conjunto de
valores que hacen verdadero un
enunciado.
Inequality: x + 3 ≥ 5
Solution set: {x | x ≥ 2}
{ Î Ó £
ä
£
Ó
Î
{
x
È
Glossary/Glosario
S141
ENGLISH
SPANISH
EXAMPLES
square (p. S63) A quadrilateral
with four congruent sides and
four right angles.
cuadrado Cuadrilátero con cuatro
lados congruentes y cuatro ángulos
rectos.
square in numeration (p. 26) The
second power of a number.
cuadrado en numeración La segunda
potencia de un número.
square root (p. 32) A number that
is multiplied to itself to form a
product is called a square root of
that product.
raíz cuadrada El número que se
multiplica por sí mismo para formar
un producto se denomina la raíz
cuadrada de ese producto.
square-root function (p. 798) A
function whose rule contains a
variable under a square-root sign.
función de raíz cuadrada Función
cuya regla contiene una variable
bajo un signo de raíz cuadrada.
-5
y = √3x
standard form of a linear equation
(p. 298) Ax + By = C, where A, B,
and C are real numbers.
forma estándar de una ecuación
lineal Ax + By = C, donde A, B y C
son números reales.
2x + 3y = 6
standard form of a polynomial
(p. 477) A polynomial in one
variable is written in standard form
when the terms are in order from
greatest degree to least degree.
forma estándar de un polinomio Un
polinomio de una variable se
expresa en forma estándar cuando
los términos se ordenan de mayor a
menor grado.
standard form of a quadratic
equation (p. 622) ax 2 + bx + c = 0,
where a, b, and c are real numbers
and a ≠ 0.
forma estándar de una ecuación
cuadrática ax 2 + bx + c = 0, donde
a, b y c son números reales y a ≠ 0.
stem-and-leaf plot (p. 687) A
graph used to organize and
display data by dividing each data
value into two parts, a stem and
a leaf.
diagrama de tallo y hojas Gráfica
utilizada para organizar y mostrar
datos dividiendo cada valor de datos
en dos partes, un tallo y una hoja.
substitution method (p. 390) A
method used to solve systems of
equations by solving an equation
for one variable and substituting
the resulting expression into the
other equation(s).
sustitución Método utilizado para
resolver sistemas de ecuaciones
resolviendo una ecuación para una
variable y sustituyendo la expresión
resultante en las demás ecuaciones.
Subtraction Property of Equality
(p. 79) If a, b, and c are real
numbers and a = b, then
a - c = b - c.
Propiedad de igualdad de la resta Si
a, b y c son números reales y a = b,
entonces a - c = b - c.
x+6= 8
-6 -6
−−−− −−
x
= 2
Subtraction Property of
Inequality (p. 174) For real
numbers a, b, and c, if a < b, then
a - c < b - c. Also holds true for
>, ≤, ≥, and ≠.
Propiedad de desigualdad de la resta
Dados los números reales a, b y c,
si a < b, entonces a - c < b - c.
Es válido también para >, ≤, ≥ y ≠.
x+6< 8
-6 -6
−−−− −−
x
< 2
S142
Glossary/Glosario
16 is the square of 4.
√
16 = 4, because
4 2 = 4 · 4 = 16.
4x 5 - 2x 4 + x 2 - x + 1
2x 2 + 3x - 1 = 0
-Ìi“
Î
{
x
i>ÛiÃ
ÓÊÎÊ{Ê{ÊÇʙ
äÊ£ÊxÊÇÊÇÊÇÊn
£ÊÓÊÓÊÎ
iÞ\ÊÎ]Óʓi>˜ÃÊΰÓ
ENGLISH
SPANISH
EXAMPLES
supplementary angles (p. S57)
Two angles whose measures have
a sum of 180°.
ángulos suplementarios Dos ángulos
cuyas medidas suman 180°.
surface area (p. S67) The total
area of all faces and curved
surfaces of a three-dimensional
figure.
área total Área total de todas las
caras y superficies curvas de una
figura tridimensional.
Îäc
£xäc
£ÓÊV“
ÈÊV“
nÊV“
Surface area
= 2(8)(12) + 2(8)(6) + 2(12)(6)
= 432 cm 2
system of linear equations
(p. 383) A system of equations
in which all of the equations are
linear.
sistema de ecuaciones lineales
Sistema de ecuaciones en el que
todas las ecuaciones son lineales.
⎧2x + 3y = -1
⎨
⎩ x - 3y = 4
system of linear inequalities
(p. 421) A system of inequalities in
two or more variables in which all
of the inequalities are linear.
sistema de desigualdades lineales
Sistema de desigualdades en dos
o más variables en el que todas las
desigualdades son lineales.
⎧2x + 3y > -1
⎨
⎩ x - 3y ≤ 4
T
tangent (p. 908) In a right
triangle, the ratio of the length of
the leg opposite ∠A to the length
of the leg adjacent to ∠A.
tangente En un triángulo
rectángulo, razón entre la longitud
del cateto opuesto a ∠A y la longitud
del cateto adyacente a ∠A.
œ««œÃˆÌi
>`>Vi˜Ì
tan A =
term of an expression (p. 47) The
parts of the expression that are
added or subtracted.
término de una expresión Parte de
una expresión que debe sumarse o
restarse.
term of a sequence (p. 272)
An element or number in the
sequence.
término de una sucesión Elemento o
número de una sucesión.
terminating decimal (p. 34) A
rational number in decimal form
that has a finite number of digits
after the decimal point.
decimal finito Número racional en
forma decimal que tien un número
finito de dígitos después del punto
decimal.
theoretical probability (p. 720)
The ratio of the number of equally
likely outcomes in an event to
the total number of possible
outcomes.
probabilidad teórica Razón entre el
número de resultados igualmente
probables de un suceso y el número
total de resultados posibles.
opposite
_
adjacent
3x 2 + 6x - 8
Term Term Term
5 is the third term in the
sequence 1, 3, 5, 7, …
1.5, 2.75, 4.0
In the experiment of rolling a
number cube, the theoretical
probability of rolling an odd
number is __36 = __12 .
Glossary/Glosario
S143
ENGLISH
SPANISH
third quartile (p. 695) The median
of the upper half of a data set.
Also called upper quartile.
tercer cuartil La mediana de la
mitad superior de un conjunto de
datos. También se llama cuartil
superior.
tip (p. 134) An amount of money
added to a bill for service; usually
a percent of the bill.
propina Cantidad que se agrega a una
factura por servicios; generalmente,
un porcentaje de la factura.
transformation (p. 357, p. S69)
A change in the position, size, or
shape of a figure or graph.
transformación Cambio en la
posición, tamaño o forma de una
figura o gráfica.
EXAMPLES
Lower half
18, 23, 28,
Upper half
49, 36, 42
Third quartile
Ī
*Àiˆ“>}i
“>}i
Ī
̱
ÊÊÊÊÊÊ̱ĪĪ
ĪÊÊÊ
translation (p. 357, p. S69) A
transformation that shifts or
slides every point of a figure or
graph the same distance in the
same direction.
traslación Transformación en la
que todos los puntos de una figura
o gráfica se mueven la misma
distancia en la misma dirección.
trapezoid (p. S63) A quadrilateral
with exactly one pair of parallel
sides.
trapecio Cuadrilátero con sólo un
par de lados paralelos.
tree diagram (p. 736) A branching
diagram that shows all possible
combinations or outcomes of an
experiment.
diagrama de árbol Diagrama
con ramificaciones que muestra
todas las combinaciones o
resultados posibles de un
experimento.
Ī
Ī
Ī
Ī
Ī
(
4
The tree diagram shows the
possible outcomes when
tossing a coin and rolling a
number cube.
línea de tendencia Línea en
un diagrama de dispersión que
sirve para mostrar la correlación
entre conjuntos de datos más
claramente.
՘`‡À>ˆÃiÀ
£Óää
œ˜iÞÊÀ>ˆÃi`Ê­f®
trend line (p. 265) A line on a
scatter plot that helps show the
correlation between data sets
more clearly.
£äää
nää
Èää
{ää
Óää
ä
trial (p. 713) In probability, a
single repetition or observation of
an experiment.
prueba En probabilidad, una
sola repetición u observación
de un experimento.
triangle (p. 209) A three-sided
polygon.
triángulo Polígono de tres lados.
S144
Glossary/Glosario
xä £ää £xä Óää
,œÃÊ܏`Ê
In the experiment of rolling
a number cube, each roll is
one trial.
ENGLISH
SPANISH
EXAMPLES
triangular prism (p. 874) A prism
whose bases are triangles.
prisma triangular Prisma cuyas
bases son triángulos.
triangular pyramid (p. 874) A
pyramid whose base is a
triangle.
pirámide triangular Pirámide cuya
base es un triángulo.
trigonometric ratio (p. 908) Ratio
of the lengths of two sides of a
right triangle.
razón trigonométrica Razón entre
dos lados de un triángulo rectángulo.
"ASES
V
L
>
a , cos A = _
b , tan A = _
a
sin A = _
c
c
b
trinomial (p. 477) A polynomial
with three terms.
trinomio Polinomio con tres
términos.
4x 2 + 3xy - 5y 2
U
union (p. 204) The union of two
sets is the set of all elements that
are in either set, denoted by .
unión La unión de dos conjuntos es
el conjunto de todos los elementos
que se encuentran en ambos
conjuntos, expresado por .
A = {1, 2, 3, 4}
B = {1, 3, 5, 7, 9}
A B = {1, 2, 3, 4, 5, 7, 9}
unit rate (p. 114) A rate in which
the second quantity in the
comparison is one unit.
tasa unitaria Tasa en la que la
segunda cantidad de la comparación
es una unidad.
30 mi = 30 mi/h
_
1h
unlike radicals (p. 811) Radicals
with a different quantity under
the radical.
radicales distintos Radicales con
cantidades diferentes debajo del
signo de radical.
2 and 2 √
3
2 √
unlike terms Terms with different
variables or the same variables
raised to different powers.
términos distintos Términos con
variables diferentes o las mismas
variables elevadas a potencias
diferentes.
4xy 2 and 6x 2y
upper quartile See third quartile.
cuartil superior Ver tercer cuartil.
V
value of a function (p. 247)
The result of replacing the
independent variable with a
number and simplifying.
valor de una función Resultado
de reemplazar la variable
independiente por un número y
luego simplificar.
The value of the function
f (x) = x + 1 for x = 3 is 4.
value of a variable (p. 7) A
number used to replace a variable
to make an equation true.
valor de una variable Número
utilizado para reemplazar una
variable y hacer que una
ecuación sea verdadera.
In the equation x + 1 = 4,
the value of x is 3.
Glossary/Glosario
S145
ENGLISH
SPANISH
EXAMPLES
value of an expression (p. 7) The
result of replacing the variables in
an expression with numbers and
simplifying.
valor de una expresión Resultado
de reemplazar las variables de una
expresión por un número y luego
simplificar.
The value of the expression
x + 1 for x = 3 is 4.
variable (p. 6) A symbol used
to represent a quantity that can
change.
variable Símbolo utilizado para
representar una cantidad que
puede cambiar.
In the expression 2x + 3, x is
the variable.
Venn diagram (p. S48) A diagram
used to show relationships
between sets.
diagrama de Venn Diagrama
utilizado para mostrar la
relación entre conjuntos.
À>˜`Ê
À>˜`Ê
œÌ…
iˆÌ…iÀ\Ê£x
vertex of a cone (p. S64) The
point opposite the base of the
cone.
vértice de un cono Punto opuesto
a la base del cono.
vertex of a parabola (p. 592) The
highest or lowest point on the
parabola.
vértice de una parábola Punto más
alto o más bajo de una parábola.
6iÀÌiÝ
­ä]ÊÓ®
The vertex is (0, -2).
vertex of an absolute-value
graph (p. 366) The point on the
axis of symmetry of the graph.
vértice de una gráfica de valor
absoluto Punto en el eje de simetría
de la gráfica.
{
Þ
ÞÊNÝN
Ó
6iÀÌiÝ
{
vertical angles (p. S57) The
nonadjacent angles formed by
two intersecting lines.
ángulos opuestos por el vértice
Ángulos no adyacentes formados
por dos líneas que se cruzan.
Ý
ä
Ó
Ó
Ó
{
£
Î {
∠1 and ∠3 are vertical angles.
∠2 and ∠4 are vertical angles.
vertical line (p. 312) A line whose
equation is x = a, where a is the
x-intercept.
línea vertical Línea cuya ecuación
es x = a, donde a es la intersección
con el eje x.
Þ
x
{
Î
Ó
£
x {ÎÓ £
£
S146
Glossary/Glosario
ÝÊÊÓ
£ Ó Î { x
Ý
ENGLISH
SPANISH
vertical-line test (p. 243) A test
used to determine whether a
relation is a function. If any
vertical line crosses the graph of
a relation more than once, the
relation is not a function.
prueba de la línea vertical Prueba
utilizada para determinar si una
relación es una función. Si una
línea vertical corta la gráfica de una
relación más de una vez, la relación
no es una función.
volume (p. S66) The number of
nonoverlapping unit cubes of a
given size that will exactly fill the
interior of a three-dimensional
figure.
volumen Cantidad de cubos
unitarios no superpuestos de un
determinado tamaño que llenan
exactamente el interior de una
figura tridimensional.
EXAMPLES
x
Þ
x
x
Ý
x
Function
Not a function
{ÊvÌ
ÎÊvÌ
£ÓÊvÌ
Volume = (3)(4)(12) = 144 ft 3
W
whole number (p. 34) The set of
natural numbers and zero.
número cabal Conjunto de los
números naturales y cero.
0, 1, 2, 3, 4, 5, …
X
x-axis (p. 54) The horizontal axis
in a coordinate plane.
eje x Eje horizontal en un plano
cartesiano.
݇>݈Ã
ä
x-coordinate (p. 54) The first
number in an ordered pair, which
indicates the horizontal distance
of a point from the origin on the
coordinate plane.
coordenada x Primer número de un
par ordenado, que indica la distancia
horizontal de un punto desde el
origen en un plano cartesiano.
{
Þ
Ó
Ý
{ Ó ä
݇VœœÀ`ˆ˜>Ìi Ó
*
Ó
{
­Ó]Êή {
x-intercept (p. 303) The
x-coordinate(s) of the point(s)
where a graph intersects the
x-axis.
intersección con el eje x
Coordenada(s) x de uno o más
puntos donde una gráfica corta el
eje x.
Þ
{
­Ó]Êä®
Ó
ä
Ý
{
Ó
The x-intercept is 2.
Y
y-axis (p. 54) The vertical axis in a
coordinate plane.
އ>݈Ã
eje y Eje vertical en un plano
cartesiano.
ä
Glossary/Glosario
S147
ENGLISH
SPANISH
y-coordinate (p. 54) The second
number in an ordered pair, which
indicates the vertical distance
of a point from the origin on the
coordinate plane.
coordenada y Segundo número
de un par ordenado, que indica la
distancia vertical de un punto desde
el origen en un plano cartesiano.
EXAMPLES
Þ
{
Ó
Ý
{
Ó
*
ä
Ó
{
އVœœÀ`ˆ˜>Ìi
Ó
­Ó]Êή {
y-intercept (p. 303) The
y-coordinate(s) of the point(s)
where a graph intersects the
y-axis.
intersección con el eje y
Coordenada(s) y de uno o más
puntos donde una gráfica corta el
eje y.
Þ
{
­ä]ÊÓ®
Ý
Ó
ä
Ó
Ó
The y-intercept is 2.
Z
zero exponent (p. 446) For any
nonzero real number x, x 0 = 1.
exponente cero Dado un número
real distinto de cero x, x 0 = 1.
zero of a function (p. 599) For
the function f, any number x such
that f (x) = 0.
cero de una función Dada la función
f, todo número x tal que f (x) = 0.
50 = 1
Ó
£
x { ÎÓ £
£
­Î]Êä®
Ó
£ Ó Î { x
­£]Êä®
Î
{
x
The zeros are -3 and 1.
Zero Product Property (p. 630) For
real numbers p and q, if pq = 0,
then p = 0 or q = 0.
S148
Glossary/Glosario
Propiedad del producto cero Dados
los números reales p y q, si pq = 0,
entonces p = 0 o q = 0.
If (x - 1)(x +2) = 0,
then x - 1 = 0 or x + 2 = 0.
so x = 1 or x = -2.
Index
A
Aaron, Hank, 42
Absolute error, S55
Absolute value, 14, 148
equations, 148–149
functions, 366–367
inequalities, 212–214
Accuracy, S54
Acute angles, S56
Acute triangles, S59
Addition
of decimals, Z12–Z13
of fractions, Z30–Z31
with like denominators, Z30–Z31
with unlike denominators, Z30–Z31
of polynomials, 484–486
modeling, 482–483
properties of, 46
of radical expressions, 811–813
of rational expressions, 885–888
with like denominators, 885
with unlike denominators, 887
of real numbers, 14–17
solving equations by, 77–79
solving inequalities by, 174–177
Addition Property of Equality, 79,
86
Addition Property of Inequality,
174
Additive inverses, 15
Agriculture, 659
Air Force Academy, 425
Air Force One, 250
Albers, Josef, 30
Algebra Lab, see also Technology Lab
Compound Events, 734–735
Explore the Axis of Symmetry, 598
Explore Changes in Population,
144–145
Explore Constant Changes, 318–319
Explore Properties of Exponents,
458–459
Model Completing the Square, 644
Model Equations with Variables on
Both Sides, 99
Model Factoring, 530
Model Factorization of Trinomials,
538–539
Model Growth and Decay, 780
Model Inverse Variation, 850
Model One-Step Equations, 76
Model Polynomial Addition and
Subtraction, 482–483
Model Polynomial Division, 892
Model Polynomial Multiplication,
490–491
Model Systems of Linear Equations,
389
Model Variable Relationships, 244
Simulations, 712
Truth Tables and Compound
Statements, 201
Vertical-Line Test, 243
Algebra tiles, 76, 99, 482–483,
490–491, 530, 538–539, 892
Algebraic expressions, 6, 7, 8, 10,
38–43, 72, 244
All of the Above, 842–843
Altitude sickness, 346
Amusement Parks, 809
Angle(s), S56
acute, S56
central, 681
classifying, S56
complementary, S57
corresponding, 121
naming, S56
obtuse, S56
right, S56
straight, S56
supplementary, S57
using a protractor to measure, S56
vertical, S57
Anglerfish, 81
Animals, 184
Animals Link, 184
Annulus, 537
Answers, choosing combinations of,
916–917
Applications
Agriculture, 659
Amusement Parks, 809
Animals, 184
Aquatics, 624
Archaeology, 118, 786
Archery, 604
Architecture, 602, 810
Art, 30, 545
Astronomy, 10, 330, 454, 455, 461,
465, 472, 802
Athletics, 277, 409, 626
Automobiles, 691
Aviation, 86, 395, 908
Basketball, 733
Biology, 16, 29, 89, 97, 105, 118, 131,
206, 306, 307, 449, 450, 455, 465,
626, 690, 869, 871
Business, 18, 58, 98, 133, 136, 191,
195, 360, 402, 408, 419, 423, 424,
486, 698, 793, 863
Camping, 183
Carpentry, 514
Chemistry, 117, 132, 202, 207, 402,
456, 472, 691
City Planning, 562
Communication, 150, 191, 456, 857
Construction, 109, 151, 316, 546, 870,
909
Consumer application, 102, 182, 240,
310, 337, 638
Consumer Economics, 88, 96, 103,
177, 393, 394, 400, 401, 416, 793,
835
Contests, 777
Data Collection, 234, 316, 617
Decorating, 119
Design, 31
Diving, 24, 909
Earth Science, 88
Ecology, 267
Economics, 88, 96, 103, 177, 267, 317,
468, 835
Education, 24, 184, 198
Electricity, 604, 610, 855
Employment, 142
Engineering, 177, 604
Entertainment, 23, 30, 37, 111, 119,
131, 192, 199, 276, 300, 361, 388,
410, 455, 506, 640, 692, 732, 749,
883
Environment, 330
Environmental Science, 118, 306, 324
Farming, 425
Finance, 80, 88, 109, 118, 133, 137,
395, 535, 782, 795, 835, 864
Fitness, 79, 339, 387, 814, 890
Fund-raising, 265
Games, 633
Gardening, 118, 190, 553
Gemology, 861
Geography, 19, 464, 472
Geology, 80, 81, 410, 802
Geometry, 10, 30, 36, 43, 44, 45, 50,
57, 81, 88, 96, 104, 109, 120, 183,
192, 197, 199, 240, 302, 350, 351,
353, 354, 355, 395, 402, 419, 464,
465, 473, 479, 480, 487, 488, 489,
497, 498, 499, 505, 509, 514, 529,
536, 537, 545, 552, 553, 563, 571,
626, 634, 635, 639, 640, 641, 648,
649, 651, 725, 733, 770, 801, 812,
813, 814, 815, 819, 820, 821, 825,
826, 827, 835, 871, 872, 898, 899
Health, 177, 178, 240, 455
Hiking, 748
History, 97, 707, 741
Hobbies, 124, 362, 419, 649, 657
Home Economics, 856
Landscaping, 387
Law Enforcement, 801
Logic, 707
Manufacturing, 118, 150, 447
Marine Biology, 596
Math History, 251, 506, 570, 810
Measurement, 122, 301, 345, 456,
562, 770
Mechanics, 855, 857
Medicine, 449, 481
Meteorology, 10, 17, 110, 206, 207,
827
Military, 425
Money, 394
Music, 206, 496, 528, 853
Navigation, 909
Number Sense, 528, 529
Index
S149
Number Theory, 37, 276, 634, 640
Nutrition, 87, 88, 130, 142, 240
Oceanography, 256
Personal Finance, 307, 531, 788
Pet Care, 795
Photography, 487, 497
Physical Science, 302, 465, 769
Physics, 478, 535, 553, 569, 616, 618,
634, 640, 655, 776, 820, 827, 854
Population, 120
Probability, 881, 882
Problem-Solving, 28, 33, 94, 175–176,
255, 343–344, 385, 503–504,
559–560, 607–608, 647–648, 729,
791–792, 901–902
Quality Control, 715
Real Estate, 125
Recreation, 22, 87, 151, 198, 234, 240,
276, 317, 394, 425, 808, 888
Recycling, 8
Remodeling, 545
School, 81, 197, 362, 386, 419, 731
Science, 118, 346, 464, 532
Shipping, 275
Solar Energy, 898
Space Shuttle, 150
Sports, 42, 44, 50, 104, 107, 110, 119,
151, 170, 176, 178, 207, 234, 306,
410, 471, 498, 509, 596, 625, 632,
658, 690, 696, 697, 698, 716, 717,
768, 769, 776, 807
Statistics, 82, 88, 455, 775
Technology, 29, 136, 457, 514, 526,
742, 749, 777
Temperature, 151
Transportation, 96, 118, 177, 207,
250, 257, 267, 300, 301, 331, 480,
827
Travel, 18, 36, 90, 104, 183, 274, 275,
304, 315, 610, 855, 889, 890, 904
Wages, 301, 329
Waterfalls, 625
Weather, 23, 690, 691, 697
Winter Sports, 856
Approximating solutions, 91,
637–638
Aquatics, 624
Archaeology, 118, 786
Archery, 604
Architecture, 602, 810
Are You Ready?, 3, 73, 165, 227, 293,
379, 443, 521, 587, 673, 763, 847
Area
of a circle, Z4
of composite figures, 83
in the coordinate plane, 309
estimating, S61
of a parallelogram, S61
of a rectangle, Z4, 83, S61
of a square, Z4, 83, S61
surface, see Surface area
of a trapezoid, S61
of a triangle, Z4, 83, S61
Arguments, writing convincing, 381
S150
Index
Arithmetic sequences, 272–274
finding the nth term of, 273
Art, 30, 545
Art Link, 30, 545
Assessment
Chapter Test, 66, 156, 220, 284, 372,
434, 514, 578, 666, 754, 840, 914
College Entrance Exam Practice
ACT, 157, 285, 435, 579
SAT, 67, 373, 515
SAT Mathematics Subject Tests, 667,
755, 841, 915
SAT Student-Produced Responses,
221
Cumulative Assessment, 70–71,
160–161, 224–225, 288–289,
376–377, 438–439, 518–519,
582–583, 670–671, 758–759,
844–845, 918–919
Multi-Step Test Prep, 38, 60, 112, 146,
186, 210, 260, 278, 332, 364, 412,
428, 474, 508, 556, 572, 620, 660,
710, 744, 796, 830, 876, 906
Multi-Step Test Prep questions are
also found in every exercise set.
Some examples are: 10, 18, 24,
30, 36
Ready to Go On?, 39, 61, 113, 147,
187, 211, 261, 279, 333, 365, 413,
429, 475, 509, 557, 573, 621, 661,
711, 745, 797, 831, 877, 907
Standardized Test Prep, 70–71,
160–161, 224–225, 288–289,
376–377, 438–439, 518–519,
582–583, 670–671, 758–759,
844–845, 918–919
Study Guide: Preview, 4, 74, 166, 228,
294, 380, 444, 522, 588, 674, 764,
848
Study Guide: Review, 62–65, 152–155,
216–219, 280–283, 368–371,
430–433, 510–513, 574–577,
662–665, 750–753, 836–839,
910–913
Test Prep
Test Prep questions are found
in every exercise set. Some
examples: 11, 19, 25, 31, 37
Test Tackler
Any Question Type
Read the Problem for
Understanding, 436–437
Spatial Reasoning, 756–757
Translate Words to Math,
580–581
Use a Diagram, 516–517
Extended Response
Explain Your Reasoning, 668–669
Understand the Scores, 286–287
Gridded Response
Fill in Answer Grids Correctly,
68–69
Multiple Choice
Choose Combinations of
Answers, 916–917
Eliminate Answer Choices,
158–159
None of the Above or All of the
Above, 842–843
Recognize Distractors, 374–375
Short Response
Understand Short Response
Scores, 222–223
Associative Properties of Addition
and Multiplication, 46, S78
Astronomy, 10, 330, 454, 455, 461,
465, 472, 802
Astronomy Link, 10, 330
Asymptote(s), 858
graphing rational functions using, 860
identifying, 859
Athletics, 277, 409, 626
Atoms, 456
Automobiles, 691
Automobiles Link, 691
Aviation, 86, 395, 908
Axes, 54
Axis of symmetry, 366
of an absolute-value graph, 366
of a parabola, 600
exploring, 598
finding
by using the formula, 601
by using zeros, 600
through vertex of a parabola, 598
B
Back-to-back stem-and-leaf plot,
687
Bald eagles, 871
Bamboo, 307
Bar graphs, 676–677, 678
Bases of geometric figures
of a cone, S64
of a cylinder, S64
of a polyhedron, S64
Bases of numbers, Z20, 26
Basketball, 733
Bias, sampling and, 708–709, S73
Biased samples, 709
Binomial(s), 477
division of polynomials by, using long
division for, 894–895
opposite, 534, 868
special products of, 501–505
Biology, 16, 29, 89, 97, 105, 118, 131,
206, 306, 307, 449, 450, 455, 465,
626, 690, 869, 871
Biology Link, 105, 307, 450, 626, 871
Blood loss, 450
Box-and-whisker plot, 695
Boyle’s law, 854
Braces, 40
Brackets, 40
Business, 18, 58, 98, 133, 136, 191, 195,
360, 402, 408, 419, 423, 424, 486,
698, 793, 863
C
Calculator, see Graphing calculator
Camping, 183
Career Path
Applied Sciences major, 388
Biology major, 106
Biostatistics major, 743
Culinary Arts program, 200
Data mining major, 347
Environmental Sciences major, 547
Carpentry, 514
Cartesian plane, 58
Caution!, 27, 48, 86, 133, 182, 213,
214, 297, 304, 310, 311, 392, 407,
423, 447, 463, 532, 551, 566, 590,
593, 601, 616, 720, 768, 775, 807,
867, 886
Center of dilation, S70
Central angles, 681
Central tendency, measure of, 694, S72
Change(s)
constant, exploring, 318–319
percent, 138
in population, exploring, 144–145
rate of, see Rate of change
Changing dimensions, 53, 123, 779
Chapter Test, 66, 156, 220, 284, 372,
434, 514, 578, 666, 754, 840, 914,
see also Assessment
Charts, reading and interpreting, 675
Cheetahs, 105
Chemistry, 117, 132, 202, 207, 402,
456, 472, 691
Chemistry Link, 207, 456
Ch’in Chiu-Shao, 402
Choosing
combinations of answers, 916–917
factoring methods, 566–568
models
graphing data for, 789–790
using patterns for, 790
Circle(s), Z3, S62
area of, Z4, S62
center of a, S62
circumference of, Z3, S62
diameter of, S62
radius of, S62
Circle graphs, 676–677, 680
Circumference, Z3
City Planning, 562
Classic problems, solving, 404–405
Closure, 37, S78
Cluster, data, S71
Clustering, Z10
Coefficients, 48
leading, of polynomials, 477
opposite, 397
College Entrance Exam Practice,
see also Assessment
ACT, 157, 285, 435, 579
SAT, 67, 373, 515
SAT Mathematics Subject Tests, 667,
755, 841, 915
SAT Student-Produced Responses, 221
Combinations
of answers, choosing, 916–917
defined, 737
and permutations, 736–739
Combining like radicals, 811
Combining like terms, 48
Commission, 133
Common difference, 272
Common denominator, Z28–Z29
Common ratio, 766
Communicating math
choose, 547, 657
compare, 11, 141, 170, 182, 199, 234,
411, 471, 496, 650, 651, 787, 800,
826, 834, 899
construct, 706
create, 240, 241, 301, 692
define, 527
describe, 19, 31, 50, 56, 79, 82, 89,
129, 131, 142, 190, 193, 205, 215,
234, 238, 241, 257, 268, 301, 316,
323, 324, 339, 352, 360, 362, 363,
409, 410, 419, 486, 526, 536, 562,
603, 605, 616, 618, 624, 639, 640,
649, 657, 683, 685, 697, 784, 794,
802, 820, 855, 864, 898
determine, 25, 411, 641, 856
explain, 8, 17, 19, 22, 24, 30, 42, 43,
44, 45, 50, 57, 80, 82, 88, 95, 104,
105, 109, 110, 117, 119, 125, 129,
131, 135, 136, 151, 172, 173, 177,
178, 183, 184, 197, 199, 200, 207,
208, 215, 232, 238, 240, 242, 248,
250, 256, 257, 267, 268, 274, 275,
276, 302, 317, 324, 330, 331, 339,
346, 354, 355, 360, 385, 386, 388,
395, 401, 402, 403, 410, 411, 417,
420, 425, 426, 450, 455, 456, 457,
463, 465, 472, 478, 480, 481, 488,
498, 506, 507, 527, 528, 534, 536,
537, 543, 545, 553, 554, 563, 570,
571, 609, 610, 611, 617, 618, 626,
633, 634, 639, 640, 650, 658, 659,
684, 685, 686, 689, 691, 692, 696,
698, 704, 705, 706, 715, 724, 725,
731, 732, 739, 741, 742, 748, 770,
771, 784, 785, 794, 801, 802, 809,
814, 818, 828, 834, 856, 864, 872,
881, 883, 888, 890, 898, 903, 905
express, 28
find, 106, 529, 546, 547, 554, 510,
617, 634, 640, 641, 898
give (an) example(s), 29, 56, 119, 185,
232, 242, 250, 480, 499, 507, 568,
618, 686, 703, 715, 730, 803, 813,
814, 834, 872
identify, 35, 486, 785, 864, 871
list, 425, 699, 856
make, 640, 691, 705, 829
name, 123, 173, 248, 305, 419, 682,
854
Reading and Writing Math, 5, 75,
167, 229, 295, 381, 445, 523, 589,
675, 765, 849, see also Reading
Strategies; Study Strategies; Writing
Strategies
show, 80, 81, 82, 88, 89, 97, 104, 118,
120, 136, 142, 177, 178, 185, 355,
536, 546, 553, 570, 596, 742, 808
tell, 36, 49, 87, 90, 103, 234, 325, 417,
454, 596, 605, 616, 648, 717, 723,
776, 813, 828, 862
write, 8, 9, 98, 105, 130, 308, 339,
387, 498, 553, 564, 571, 597, 635,
770, 785, 809, 865, 869, 891
Write About It
Write About It questions are found
in every exercise set. Some
examples: 9, 19, 24, 29, 31
Communication, 150, 191, 456, 857
Commutative Properties of
Addition and Multiplication, 46,
S78
Compare rational numbers, S50
Compatible numbers, Z10, 46
Complement of an event, 721
Complementary angles, S57
Completing the square, 645–648,
857
modeling, 644
procedure for, 645
solving quadratic equations by, 646,
656
Complex fractions, 884
Composite figures, 83
areas of, 83
Composite numbers, Z17–Z18
Compound events, 734–735, 737
Compound inequalities, 202–205
Compound interest, 782
Compound statements, 201
Computer-animated films, 749
Conclusion, S76
Conditional statements, S76
Cones, 874, S64
surface area of, 500, S67
volume of, 500, S66
Congruence, S59
Congruence statements, S59
Conjecture, S76
making a, 318, 319, 356, 612, 628,
644, 804, 850, 873
Conjugates, 821
rationalizing denominators using, 821
Index
S151
Connecting Algebra
to Data Analysis, 271, 676–677,
708–709
to Geometry, 52–53, 83, 209, 309,
500, 642–643, 779, 874
to Number Theory, 404–405, 565
Consistent systems, 406
Constant, 6
of variation, 326, 851
Constant changes, exploring,
318–319
Construction, 109, 151, 316, 546, 870,
909
Consumer application, 102, 182, 240,
310, 337, 638
Consumer Economics, 88, 96, 103,
177, 267, 317, 393, 394, 400, 401,
416, 468, 793, 835
Contact lenses, 178
Contests, 777
Continuous graphs, 231
Contradictions
equations as, 101
inequalities as, 196
Convenience sample, 709
Conversion factors, 115, 589
Converting between probabilities
and odds, 722
Convincing arguments/
explanations, writing, 381
Coordinate plane, Z7, 54
area in the, 309
distance in the, 642–643, 802
reflections in the, S69
rotations in the, S69
transformations in the, S69
translations in the, S69
Countdown to Testing, C4–C27
Correlation, 262
Corresponding angles, 121, S63
Corresponding sides, 121, S63
Cosine, 908
Counterexamples, S76
Crash test dummies, 480
Create a table to evaluate
expressions, 12–13
Critical Thinking
Critical Thinking questions are found in
every exercise set. Some examples:
11, 18, 23, 24, 30
Cross products, 115
solving rational equations by using, 900
Cross Products Property, 115
Cube(s) (geometric figure)
surface area of, S67
volume of, 779, S66
Cubes, difference of, 564
Cubic functions, S75
solving related equations, S75
Cubic polynomials, 477
Cumulative Assessment, see
Assessment
S152
Index
Cumulative frequency, 689
Cylinders, 874, S64
surface area of, 500, S67
volume of, 500, S66
D
da Vinci, Leonardo, 604
Data
displaying, 678–682
graphing, to choose a model, 789–790
organizing, 678–682
Data analysis
Connecting Algebra to, 271, 676–677,
708–709
Data Collection, 234, 316, 617
Data distributions, 694–696
Death Valley National Park, 18
Decay
exponential, see Exponential decay
modeling, 780
Decimals
addition of, Z12–Z13
division of, Z14–Z16
multiplication of, Z14–Z16
repeating, Z25, 34
subtraction of, Z12–Z13
terminating, Z25, 34
writing as percents, Z27
writing fractions as, Z25–Z27
writing percents as, Z27
Decorating, 119
Deductive reasoning, S77
Degrees
of monomials, 476
of polynomials, 476
Denominators
like, see Like denominators
rationalizing, 818
using conjugates, 821
unlike, see Unlike denominators
Dependent events, 726–730
probability of, 729
Dependent systems, 407
Dependent variables, 246, 247, 248,
249, 250
Descartes, Rene, 58
Design, 31
Devon Island, 10
Diagrams
ladder, 524
reading and interpreting, 675
tree, Z5, 736
using, 516–517
Venn, S48
Diameter, S62
Diepolder Cave, 24
Difference(s)
first, 590
of cubes, 564
second, 590
of two squares, 503, 560
Dilations, S70
Dimensions, changing, 53, 123, 779
Direct variation, 326–329
Discontinuous functions, 858
Discount, 139
Discrete graphs, 231
Discriminant, 654
Quadratic Formula and, 652–657
Displaying data, 678–682
Distance Formula, 642–643, 802
Distracters, recognizing, 374–375
Distributions, data, 694–696
Distributive Property, 47, S78
Diving, 24, 909
Diving Link, 24
Divisibility rules, Z17
Division
of decimals, Z14–Z16
of fractions, Z32–Z33
long, see Long division
of polynomials, 893–897
by binomials, using long division for,
894–895
modeling, 892
of radical expressions, 816–818
of rational expressions, 878–881
of real numbers, 20–22
of signed numbers, 20
solving equations by, 84–87
solving inequalities by, 180–182
by zero, 21
Division properties of exponents,
467–471
Division Property of Equality, 86
Division Property of Inequality, 180,
181
Domain, 236, 237, 238, 239, 240, 241,
242, 248, 249, 250, 251, 252, 253,
255, 256, 259, 260, 261, 815, 857
of absolute-value functions, 366–367
of linear functions, 299
of quadratic functions, 593
reasonable, 248, 249, 250, 251, 255,
261, 283, 284, 299, 304, 596, 853,
856, 861, 863, 864
of square-root functions, 799–800
Double-bar graphs, 679
Double-line graphs, 680
Dow Jones Industrial Average
(DJIA), 17
Draw a diagram, S40
Drawing three-dimensional figures,
S65
Drum Corps International, 528
E
Eagles, 871
Earned run average (ERA), 110
Earth Science, 88
Ecology, 267
Ecology Link, 267
Economics, 88, 96, 103, 177, 267, 317,
393, 394, 400, 401, 416, 468, 793, 835
Edges of a polyhedron, S64
Education, 24, 184, 198
Electricity Link, 820
Element of a set, S78
Elimination, 397
solving systems of linear equations by,
397–401
Ellipsis, 272
Employment, 142
Empty set, 102, S78
as solution set, 102
Engineering, 177, 604, 610, 855
Engineering Link, 604
Entertainment, 23, 30, 37, 111, 119,
131, 192, 199, 276, 300, 361, 388,
410, 455, 506, 640, 692, 732, 749,
883
Entry of matrix, 746–747
Environment, 330
Environmental Science, 118, 306, 324
Equality
Power Property of, 822
properties of, 79, 86
Equally likely, 720
Equation(s)
defined, 77
finding slope from, 322
linear, see Linear equations
literal, 108
model
one-step, 76
with variables on both sides, 99
quadratic, see Quadratic equations
radical, see Radical equations
rational, see Rational equations
solutions of, 77
solving
absolute-value, 148–149
by addition, 77–79
by division, 84–87
by graphing, 91
multi-step, 92–95
by multiplication, 84–87
by subtraction, 77–79
two-step, 92–95
with variables on both sides,
100–103
systems of, see Systems of linear
equations
Equilateral triangles, S59
Equivalent fractions, Z23–Z24
writing, with least common
denominator, Z29
Equivalent ratios, 114
Equivalents, common, 127
Error Analysis, 18, 58, 80, 88, 119, 136,
151, 172, 184, 199, 215, 241, 250,
257, 268, 324, 339, 346, 402, 411,
420, 425, 450, 465, 481, 488, 506,
537, 553, 563, 570, 610, 634, 640,
650, 691, 706, 724, 786, 794, 814,
828, 864, 883, 890, 898
Escape velocity, 802
Estimating, Z9–Z11
by clustering, Z10
irrational numbers, 33
overestimates, Z10
solutions using the Quadratic Formula,
653
underestimates, Z10
using compatible numbers, Z10
with percents, 134
Estimation, 30, 50, 110, 130, 142, 178,
185, 250, 258, 268, 307, 316, 354,
396, 426, 465, 499, 545, 570, 596,
640, 697, 717, 787, 802, 828, 856, 898
Evaluating
expressions, 7
functions, 247
Event(s), 713
compound, 734–735, 737
dependent, see Dependent events
inclusive, 734
independent, see Independent events
mutually exclusive, 734
simple, 737
Exam, final, preparing for your, 849
Expanded form of a number, S50
Excluded values, 848, 858
Experiment, 713
Experimental probability, 713–715
defined, 714
Explanations
convincing, writing, 381
for your reasoning in extended
responses, 668–669
Exploring
axis of symmetry of a parabola, 598
changes in population, 144–145
constant changes, 318–319
properties of exponents, 458–459
roots, zeros, and x-intercepts, 628–629
Exponent(s), Z20, 26
division properties of, 467–471
integer, see Integer exponents
multiplication properties of, 460–463
negative, 446
powers and, 26–28
properties of
exploring, 458–459
using patterns to find, 458–459
rational, 832–834
reading, 27
writing prime factorizations with, Z20
zero, 446
Exponential decay, 781–784
defined, 783
Exponential expressions, simplifying,
460
Exponential functions, 772–775, 796
general form of, 791
graphs of, 775
Exponential growth, 781–784
Exponential models, 789–792
Expression(s)
algebraic, 6
create a table to evaluate, 12–13
exponential, simplifying, 460
numerical, 6
radical, see Radical expressions
rational, see Rational expressions
simplifying, 46–49
square-root, see Square-root
expressions
variables and, 6–8
Extended Response, 71, 161, 225,
242, 286–287, 289, 302, 377, 436,
437, 439, 489, 519, 529, 583, 659,
668–669, 671, 759, 845, 891, 919
Explain Your Reasoning, 668–669
Understand the Scores, 286–287
Extension
Absolute-Value Functions, 366–367
Matrices, 746–747
Rational Exponents, 832–834
Solving Absolute-Value Equations,
148–149
Solving Absolute-Value Inequalities,
212–214
Trigonometric Ratios, 908–909
Extra Practice, S4–S39
Extraneous solutions, 824–825, 902
F
Faces of a polyhedron, S64
Factor(s), Z17, 524–525
Factor tree, Z19, 524
Factorial, 738
Factoring
ax 2 + bx + c, 548–551
composite numbers, Z19–Z20
by greatest common factor, 531–534
by grouping, 533–534
modeling, 530
with opposites, 534
polynomials, 531–571
methods for, 568
solving quadratic equations by,
630–633, 656
special products, 558–561
trinomials, 866
x 2 + bx + c, 540–543
Factoring methods, choosing,
566–568
Factorization
prime, Z19–Z20, 524
writing with exponents, Z20
of trinomials, modeling, 538–539
Fair, 720
Families of functions, 357, 612, 862
of linear functions, 356, 862
of quadratic functions, 612, 862
of rational functions, 862
of square-root functions, 862
Index
S153
Farming, 425
Fibonacci sequence, 276
Field properties, S78
Figure(s)
reading and interpreting, 675
solid, representing, 874
Final exam, preparing for your, 849
Finance, 80, 88, 109, 118, 133, 137,
395, 535, 782, 795, 835, 864
Find a pattern, S44
Finding the nth term of an
arithmetic sequence, 273
Finding the nth term of a
geometric sequence, 767
First coordinates, 236
First differences, 590
First quartile values, 695
Fitness, 79, 339, 387, 814, 890
FOIL method, 493, 540, 817
Formula(s), 107
area, 83
axis of symmetry of a parabola, 601
combinations, 739
compound interest, 782
distance, 642–643
experimental probability, 714
exponential decay, 783
exponential growth, 781
half-life, 783
Heron’s, 810
geometry, Z3–Z4
Midpoint, S68
nth term of an arithmetic sequence, 273
nth term of a geometric sequence, 767
permutations, 738
probability of dependent events, 729
probability of independent events, 727
Quadratic, 652
remembering, 765
simple interest, 133
slope, 320
solving for a variable, 108
theoretical probability, 720
Foundation plan, 875
Fractals, 770, 865
Fraction(s)
addition of, Z30–Z31
complex, 884
division of, Z32–Z33
equivalent, see Equivalent fractions
multiplication of, Z32–Z33
simplest form, Z23
subtraction of, Z30–Z31
writing as decimals, Z25–Z27
Frequency, 688, S71
cumulative, 689
line plots and, S71
histograms and, 687–689
Frequency table, 688
S154
Index
Function(s)
absolute-value, see Absolute-value
functions
defined, 237
discontinuous, 858
evaluating, 247
exponential, see Exponential functions
families of, 357, 612, 862
general forms of, 791
geometric sequences as, 767
graphing, 252–256
introduction to, 54–56
linear, see Linear functions
parent, see Parent functions
quadratic, see Quadratic functions
radical, see Radical functions
rational, see Rational functions
relations and, 236–238
square-root, see Square-root functions
writing, 245–248
zeros of, 599
Function notation, 246
Function rules, 246
connecting to tables and graphs, 259
Function table, 55–56, 259
Fund-raising, 265
Fundamental Counting Principle,
736
G
Galilei, Galileo, 251
Gallium, 207
Games, 633
Gap (in data), S71
Gardening, 118, 190, 553
GCF, see Greatest common factor
Gemology, 861
General forms of functions, 791
Geodes, 410
Geography, 19, 464, 472
Geology, 80, 81, 410, 802
Geology Link, 81, 410, 802
Geometric models
of powers, 26
of special products, 501, 503
Geometric patterns, S58
Geometric probability, 890
Geometric sequences, 766–768
as functions, 767
finding the nth term of, 767
Geometry, see also Applications
acute angles, S56
acute triangles, S59
angle(s), S56
acute, S56
central, 681
classifying, S56
complementary, S57
corresponding, 121
naming, S56
obtuse, S56
right, S56
straight, S56
supplementary, S57
using a protractor to measure, S56
vertical, S57
annulus, 537
area
of a circle, Z4
of composite figures, 83
in the coordinate plane, 309
estimating, S61
of a parallelogram, S61
of a rectangle, Z4, 83, S61
of a square, Z4, 83, S61
surface, see Surface area
of a trapezoid, S61
of a triangle, Z4, 83, S61
base
of a cone, S64
of a cylinder, S64
of a polyhedron, S64
center of dilation, S70
central angles, 681
changing dimensions, 53, 123, 779
circle(s), Z3, S62
area of, Z4, S62
center of a, S62
circumference of, Z3, S62
diameter of, S62
radius of, S62
complementary angles, S57
composite figures, 83
areas of, 83
cones, 874, S64
surface area of, 500, S67
volume of, 500, S66
congruence, S59
congruence statements, S59
Connecting Algebra to, 52–53, 83,
209, 309, 500, 642–643, 779, 874
coordinate plane, Z7, 54
area in the, 309
distance in the, 642–643, 802
reflections in the, S69
rotations in the, S69
transformations in the, S69
translations in the, S69
corresponding angles, 121, S63
corresponding sides, 121, S63
cosine, 908
cube(s)
surface area of, S67
volume of, 779, S66
cylinders, 874, S64
surface area of, 500, S67
volume of, 500, S66
diameter, S62
dilations, S70
dimensions, changing, 53, 123, 779
drawing three-dimensional figures,
S65
edges of a polyhedron, S64
equilateral triangles, S59
faces of a polyhedron, S64
formulas, Z3–Z4
foundation plan, 875
fractals, 770, 865
geometric models
of powers, 26
of special products, 501, 503
geometric patterns, S58
geometric probability, 890
half-plane, 414
Heron’s formula, 810
indirect measurement, 122
isosceles trapezoids, S59
isosceles triangles, S59
kites, S59
nets, 874, S67
using to estimate surface area, S67
obtuse angles, S56
obtuse triangles, S59
parallel lines, S56
slopes of, 349–352
parallelograms, S59
area, S61
perimeter, Z3, 52–53, S60
estimating, S60
of polygons, 52
of a rectangle, Z3, S60
of a square, Z3, S60
perpendicular lines, S56
slopes of, 349–352
pi, Z3, S62
plane(s), S56
Cartesian, 58
coordinate, Z7, 54
naming, S56
polygons, 52–53, S58
regular, S58
polyhedrons, S64
bases, S64
edges, S64
vertices, S64
prisms, 874, S64
surface area of, 500, S67
volume of, 500, 779, S66
pyramids, 874, S64
surface area of, 500, S67
volume of, 500, 779, S66
Pythagorean Theorem, 641, 643, 807,
S68
quadrilaterals, S63
classifying, S63
radius, S62
rays, S56
naming, S56
rectangle(s), S59
area of, Z4, 83, S61
perimeter of, Z3, S60
reflections, 359, S69
in the coordinate plane, S69
of linear functions, 359
regular polygons, S58
rhombus, S59
right angles, S56
right triangles, S59
rotations, 358, S69
in the coordinate plane, S69
of linear functions, 358
scale, 116
scale drawing, 116
scale factor, 123
of a dilation, S70
scale model, 116
scalene triangles, S59
sectors, 680
similar figures, 121
sine, 908
square(s), Z3, S59
area of, Z4, 83, S61
perimeter of, Z3, S60
straight angles, S56
supplementary angles, S57
surface area, 500, S67
of a cone, S67
of a cube, S67
of a cylinder, S67
of a prism, S67
of a pyramid, S67
using nets to estimate, S67
surface-area-to-volume ratio, 869
symmetry, S63
tangent, 908
transformations, 357, S69
in the coordinate plane, S69
of linear functions, 357–360
of quadratic functions, 613–616
translations, 357, S69
in the coordinate plane, S69
of the graph of the square-root
function, 799
trapezoids, S59
area of, S59
triangle(s), Z3, S59
acute, S63
area of, Z4, 83, S61
classifying, S63
equilateral, S63
isosceles, S63
obtuse, S63
right, S63
scalene, S63
Triangle Inequality, 209
trigonometric ratios, 908–909
vertex
of a cone, S64
of a polyhedron, S64
vertical angles, S57
volume, 500, S66
estimating, S66
of a cone, 500, S66
of a cube, 779, S66
of a cylinder, 500, S66
of a prism, 500, 779, S66
of a pyramid, 500, 779, S66
Geometry Link, 770
Get Organized, see Graphic organizers
go.hrw.com, see Online Resources
Graph(s)
bar, 676–677, 678
circle, 676–677, 680
comparing, of quadratic functions, 615
connecting to function rules and
tables, 259
continuous, 231
discrete, 231
double-bar, 679
double-line, 680
of exponential functions, 775
finding slope from, 321
finding zeros of quadratic functions
from, 599
identifying linear functions by, 296
line, 679–682
misleading, 702–703
reading and interpreting, 675
of square-root functions, translations
of, 799
using, to factor polynomials, 555
using technology to make, 700–701
Graphic Organizers
Graphic Organizers are found in
every lesson. Some examples: 8,
17, 22, 28, 35
Graphics, reading and interpreting, 675
Graphing
data to choose a model, 789–790
functions, 252–256
inequalities, 168–170
linear functions, 298, 348
linear inequalities, 415
quadratic functions, 606–609
using a table of values, 591
radical functions, 804
rational functions, 873
using asymptotes, 860
relationships, 230–232
solving equations by, 91
solving systems of linear equations by,
383–385
solving quadratic equations by,
622–624, 656
Graphing Calculator, 12, 91, 259, 270,
348, 356, 358, 359, 384, 387, 427,
555, 597, 605, 612, 614, 615, 616,
617, 619, 623, 624, 625, 626, 627,
628, 629, 638, 646, 650, 653, 656,
719, 739, 775, 777, 787, 801, 802,
829, 865, 898
Greatest common factor (GCF),
Z21–Z22, 525–526
factoring by, 531–534
using, to write fractions in simplest
form, Z24
using prime factorization to find, Z21
Gridded Response, 45, 68–69, 71, 98,
105, 126, 143, 161, 193, 225, 251, 289,
306, 325, 331, 340, 355, 377, 387, 437,
439, 451, 519, 564, 581, 583, 605, 619,
671, 759, 803, 845, 857, 872, 919
Fill in Answer Grids Correctly, 68–69
Griffith-Joyner, Florence, 119
Grouping, factoring by, 533–534
Grouping symbols, 40, 41
Index
S155
Growth
exponential, see Exponential growth
modeling, 780
Guess and test, S42
H
Half-life, 783
Half-plane, 414
Hamm, Paul, 44
Handball team, 498
Health, 177, 178, 240, 322, 455
Health Link, 178
Helpful Hint, 8, 16, 21, 40, 41, 46, 47,
92, 94, 100, 115, 122, 123, 128, 134,
138, 139, 174, 194, 196, 202, 205, 212,
231, 238, 246, 252, 253, 262, 305, 336,
341, 343, 351, 352, 383, 384, 390, 391,
398, 399, 415, 467, 470, 494, 495, 525,
534, 542, 559, 567, 591, 599, 607, 615,
623, 631, 632, 637, 646, 653, 655, 688,
695, 714, 738, 739, 766, 772, 781, 783,
791, 798, 800, 806, 811, 816, 818, 825,
852, 894, 895, 902, 908
Heron of Alexandria, 810
Heron’s formula, 810
Hiking, 748
Histograms, 688
frequency and, 687–689
History, 97, 707, 741
History Link, 97, 707, 741
Hobbies, 124, 362, 419, 649, 657
Hobbies Link, 362
Home Economics, 856
Homework Help Online
Homework Help Online is available
for every lesson. Refer to the
go.hrw.com box at the beginning of
each exercise set. Some examples:
9, 17, 23, 29, 35
Horizontal lines, 351, 859
Hot-air balloons, 20
Hot Tip!, 67, 69, 71, 157, 159, 161, 221,
223, 225, 285, 287, 289, 373, 375,
377, 435, 437, 439, 515, 517, 519,
579, 581, 583, 667, 669, 671, 755,
757, 759, 841, 843, 845, 915, 917, 919
Hurricanes, 827
Huygens, Christian, 640
Hypothesis, S76
I
Identifying asymptotes, 859
Identities
equations as, 101
inequalities as, 196
Identity properties for addition
and multiplication, S78
S156
Index
Inclusive events, 734
probabilities of, 734
Inconsistent systems, 406
Independent events, 726–730
probability of, 727
Independent systems, 407
Independent variables, 246–250
Index, 832
Indirect measurement, 122
Inductive reasoning, S77
Inequalities
absolute-value, see Absolute-value
inequalities
compound, 202
defined, 168
graphing, 168–170, 169
linear, see Linear inequalities
properties of, 174, 180, 181
solutions of, 168
solving
absolute-value, 212–214
by addition, 174–177
compound, 202–205
by division, 180–182
multi-step, 188–190
by multiplication, 180–182
by subtraction, 174–177
two-step, 188–190
with variables on both sides, 194–197
writing, 168–170
Input, 55, 245
Input-output table, 55–56
Integer(s), 34
Integer exponents, 446–448
and powers of ten, 452–453
in scientific notation, 453–454
using patterns to investigate, 446
Intercepts, using, 303–305, 606–608
Interest, 133
compound, 782
simple, 133
Interpreting
graphics, 675
scatter plots and trend lines, 270
Interquartile range (IQR), 695
Intersection, 203
of sets, S78
Inverse operations, 77, 84, 92, 100,
107, 148, 174, S51
for powers, 832
Inverse variation, 851–854, 876
modeling, 850
Product Rule for, 853
Inverses
additive, 15, S78
multiplicative, 21, S78
IQR, see Interquartile range
Irrational numbers, 34
estimating, 33
Ishtar Gate, 506
Isolating variables, 77
Isosceles trapezoids, S59
Isosceles triangles, S59
K
Kangaroos, 626
Key words, 230
King, Martin Luther, Jr., 97
Kites, 198
Kites (geometric shape), S59
Know-It Note
Know-It Notes are found throughout
this book. Some examples: 15, 20,
21, 40, 46
Koopa (turtle), 136
L
Ladder diagram, 524
Landscaping, 387
Landscaping Link, 387
Law Enforcement, 801
LCD, see Least common denominator
LCM, see Least common multiple
Leading coefficients of
polynomials, 477
Leaning Tower of Pisa, 610
Least common denominator (LCD),
Z28
adding rational expressions by using,
887
solving rational equations by using,
900–901
subtracting rational expressions by
using, 887
Least common multiple (LCM),
Z21–Z22, 886–887
using, to find least common
denominator, Z28
using prime factorization to find,
Z28
Light-year, 455
Like denominators
addition of fractions with, Z30
addition of rational expressions with,
885
subtraction of fractions with, Z30
subtraction of rational expressions
with, 886
Like radicals, 811
combining, 811
Like terms, 47
Likely, equally, 720
Lincoln, Abraham, 97
Line(s), S56
horizontal, 351, 859
median-fit, 270, 271
naming, S56
parallel, see Parallel lines
perpendicular, see Perpendicular lines
slope of a, 311–313
trend, see Trend lines
vertical, 349, 859
Line graphs, 679–682
Line plots, S71
Linear equation(s)
defined, 298
point-slope form of, 342
slope-intercept form of, 335, 342
solving, by using a spreadsheet, 382
standard form of, 298
systems of, see Systems of linear
equations
Linear function(s)
defined, 296
families of, 356, 862
general form of, 791
graphing, 298, 348
identifying, 296–299
by graphs, 296
by lists of ordered pairs, 297
by tables, 297
by using ordered pairs, 297
reflections of, 359
rotations of, 358
transformations of, 357–360
vertical translations of, 357
Linear inequalities
defined, 414
graphing, 415
solutions of, 414
solving, 414–417
systems of, 421
solutions of, 421
solving, 421–423, 427
Linear models, 789–792
Link
Animals, 184
Art, 30, 545
Astronomy, 10, 330
Automobiles, 691
Biology, 105, 307, 450, 626, 871
Chemistry, 207, 456
Diving, 24
Ecology, 267
Electricity, 820
Engineering, 604
Geology, 81, 410, 802
Geometry, 770
Health, 178
History, 97, 707, 741
Hobbies, 362
Landscaping, 387
Math History, 58, 402, 506, 570, 810
Meteorology, 827
Military, 425
Music, 528
Number Theory, 276
Physics, 640
Recreation, 198
School, 731
Science, 346
Solar Energy, 898
Sports, 44, 119, 234, 498
Statistics, 88
Technology, 136, 749, 777
Transportation, 250, 480
Travel, 315, 610, 890
Winter Sports, 856
Lists of ordered pairs
identifying exponential functions by,
773, 790
identifying linear functions by, 297,
790
identifying quadratic functions by, 590,
790
Literal equations, 108
Logic, 707
Long division, 894
dividing polynomials by binomials,
894–895
Lookout Mountain Incline Railway,
315
M
Magnification, 906
Make a Conjecture, 318, 319, 612,
628, 644, 804, 850, 873
Make a model, S41
Make an organized list, S49
Make a Prediction, 145, 356
Make a table, S45
Manufacturing, 118, 150, 447
Mapping diagrams, 236
Marine Biology, 596
Markup, 139
Mars lander, 330
Math History, 251, 506, 570, 810
Math History Link, 58, 402, 506, 570,
810
Math Symbols, 229
Matrices, 746–747
Maximum values
for a box-and-whisker plot, 695
of parabolas, 592
Mean, 694, S72
Measure of central tendency, 694,
S72
Measurement(s), 122, 301, 345, 456,
562, 770, S53
absolute error and, S55
accuracy in, S54
comparing, S53
converting between systems of, S53
customary system of, S53
indirect, 122
metric system of, S53
precision in, S54
relative error and, S55
significant digits and, S54
tolerance intervals and, S55
Mechanics, 855, 857
Median, 694, S72
Median-fit line, 270–271
Medicine, 449, 481
Mental Math, 22, 46, 47, 134, 159,
565, S52
Meteorology, 10, 17, 110, 206, 207, 827
Meteorology Link, 827
Middleton Place Gardens, 387
Midpoint formula, S68
Military, 425
Military Link, 425
Minimum values
for a box-and-whisker plot, 695
of parabolas, 592
Misleading graphs and statistics,
702–703
Mode, 694, S72
Model(s)
choosing
graphing data for, 789–790
using patterns for, 790
exponential, 789–792
geometric
of powers, 26
of special products, 501, 503
linear, 789–792
quadratic, 789–792
rectangle, for multiplying polynomials,
494
Modeling
addition and subtraction of real
numbers, 14
completing the square, 644
equations with variables on both sides,
99
factoring, 530
factorization of trinomials, 538–539
growth and decay, 780
inverse variation, 850
one-step equations, 76
polynomial addition and subtraction,
482–483
polynomial division, 892
polynomial multiplication, 490–491
systems of linear equations, 389
variable relationships, 244
Money, 394
Monomials, 476
degrees of, 476
Moore’s law, 777
Multi-Step, 11, 57, 59, 126, 131, 137,
142, 143, 239, 240, 275, 346, 367,
386, 395, 401, 410, 418, 425, 451,
466, 498, 506, 528, 529, 563, 597,
609, 617, 634, 640, 649, 650, 658,
770, 777, 787, 793, 802, 803, 809,
815, 828, 856, 863, 890, 898, 904
Multi-step equations, solving, 92–95
Multi-step inequalities, solving,
188–190
Multi-Step Test Prep, 38, 60, 112,
146, 186, 210, 260, 278, 332, 364,
412, 428, 474, 508, 556, 572, 620,
660, 710, 744, 796, 830, 876, 906
Multi-Step Test Prep questions are
also found in every exercise set.
Some examples are: 10, 18, 24,
30, 36
Index
S157
Multiple Choice, 70–71, 158–159,
160–161, 288–289, 376–377, 437,
438–439, 516, 517, 518–519, 581,
582–583, 670–671, 757, 758–759,
842–843, 844–845, 916–917,
918–919
Choose Combinations of Answers,
916–917
Eliminate Answer Choices, 158–159
None of the Above or All of the Above,
842–843
Recognize Distracters, 374–375
Multiple representations, 15, 20,
21, 26, 27, 46, 47, 76, 79, 86, 99, 101,
115, 148, 169, 174, 180, 181, 196,
202, 203, 204, 212, 213, 236, 244,
259, 295, 320, 349, 351, 389, 446,
452, 460, 462, 463, 467, 469, 470,
482, 483, 490, 491, 501, 503, 530,
538, 539, 541, 558, 560, 592, 600,
601, 613, 628, 629, 630, 636, 642,
644, 645, 708, 709, 738, 739, 746,
798, 806, 822, 833, 851, 859, 893
Multiplication
of decimals, Z14–Z16
of fractions, Z32–Z33
of polynomials, 492–496
modeling, 490–491
rectangle model for, 494
vertical method for, 495
by powers of ten, 453
properties of, 46
of radical expressions, 816–818
of rational expressions, 878–881
of real numbers, 20–22
scalar, 747
of signed numbers, 20
solving equations by, 84–87
solving inequalities by, 180–182
of square-root expressions, containing
two terms, 817
by zero, 21
Multiplication properties of
exponents, 460–463
Multiplication Property of Equality,
86
Multiplication Property of
Inequality, 180, 181
Multiplicative inverses, 21
Music, 206, 496, 528, 853
Music Link, 528
Mutually exclusive events, 734
probabilities of, 734
N
Natural numbers, 34
Navigation, 909
Negative correlation, 263
Negative exponents, 446
Negative integer exponents, 452
S158
Index
Negative Power of a Quotient
Property, 470
Negative slope, 312
Nets, 874, S67
using to estimate surface area,
S67
Nightingale, Florence, 707
No correlation, 263
None of the Above, 842–843
Normal curve, S74
Normal distribution, S74
Notation, scientific, see Scientific
notation
Null set, see Empty set
Number families, S51
Number Sense, 528, 529
Number Theory, 37, 276, 634,
640
Connecting Algebra to, 404–405,
565
Number Theory Link, 276
Numbers
compatible, Z10, 46
composite, Z17–Z18
irrational, see Irrational numbers
natural, 34
prime, Z17–Z18, 524
random, see Random numbers
rational, 34
real, see Real numbers
signed, see Signed numbers
whole, 34
Numerical expressions, 6
Nutrition, 87, 88, 130, 142, 240
Parent Resources Online
Parent Resources Online are
available for every lesson. Refer
to the go.hrw.com box at the
beginning of each exercise set.
Some examples: 9, 17, 23,
29, 35
State Test Practice Online, 70, 160,
224, 288, 376, 438, 518, 582, 670,
758, 844, 918
Operations
inverse, see Inverse operations
order of, 40–42
Opposite binomials, 534, 868
Opposite coefficients, 397
Opposites, 15
factoring with, 534
Orangutans, 184
Order of operations, 40–42
Order rational numbers, S50
Ordered pairs, Z7, 54, 236
graphing, Z7
identifying exponential functions by
using, 590, 790
identifying linear functions by using,
297, 790
identifying quadratic functions by
using, 773, 790
Organizing data, 678–682
Origin, Z7, 54
Outcome, 713
Outlier, 695
Output, 55, 245
Overestimate, Z10
O
P
Obtuse angles, S56
Obtuse triangles, S59
Oceanography, 256
Ocelots, 267
Odds, 722
converting between probabilities and,
722
Online Resources
Career Resources Online, 106, 200,
347, 388, 547, 743
Chapter Project Online, 2, 72, 164,
226, 292, 378, 442, 520, 586, 672,
762, 846
Homework Help Online
Homework Help Online is available
for every lesson. Refer to the
go.hrw.com box at the
beginning of each exercise
set. Some examples: 9, 17, 23,
29, 35
Lab Resources Online, 12, 76, 99, 144,
259, 270, 382, 389, 482, 555, 612,
628, 700
Paella, 326
Parabola
axis of symmetry of a, 600
exploring, 598
finding
by using the formula, 601
by using zeros, 600
defined, 591
identifying the direction of a,
592
vertex of a, 592
finding the, 601
vertical translations of a, 615
width of a, 613
Parallel lines, S56
slopes of, 349–352
Parallelograms, S59
area of, S61
Parent functions, 357
linear, 862
quadratic, 612, 613, 862
rational, 862
square-root, 862
Parent Resources Online
Parent Resources Online are available
for every lesson. Refer to the
go.hrw.com box at the beginning of
each exercise set. Some examples:
9, 17, 23, 29, 35
Parentheses, 40
Pascal, Blaise, 570
Pascal’s Triangle, 570
Patterns
geometric, S58
looking for, 767
using
to choose a model, 790
to find properties of exponents,
458–459
to investigate integer exponents,
446
to investigate powers of ten, 452
Pearl, Nancy, 362
Pendulum clocks, 640
Pente, 37
Percent(s), 125, 127–129
applications of, 133–135
defined, 127
greater than 100%, 127
less than 1%, 127
writing as decimals, Z27
writing decimals as, Z27
Percent change, 138
Percent decrease, 138–140
Percent increase, 138–140
Percent proportion, 127
Perfect-square trinomials, 501,
558
Perfect squares, 32
Perimeter, Z3, 52–53, S60
estimating, S60
of polygons, 52
of a rectangle, Z3, S60
of a square, Z3, S60
Period, of a pendulum, 820
Permutations
combinations and, 736–739
defined, 737
Perpendicular lines, S56
slopes of, 349–352
Personal Finance, 307, 788
Pet Care, 795
pH, 472
Photography, 487, 497
Physical Science, 302, 465, 769
Physics, 478, 535, 553, 569, 616, 618,
634, 640, 655, 776, 820, 827, 854
Physics Link, 640
Pi, Z3, S62
Pimlico Race Course, 234
Place value, S50
Plane(s), S56
Cartesian, 58
coordinate, Z7, 54
naming, S56
Point-slope form of linear
equations, 341–344
Polygons, 52–53, S58
regular, S58
Polyhedrons, S64
bases of, S64
edges of, S64
vertices of, S64
Polynomial(s), 476–478, 589
addition of, 484–486
modeling, 482–483
cubic, 477
degrees of, 476
division of, see Division of polynomials
factoring
methods for, 568
using graphs for, 555
leading coefficients of, 477
multiplication of, see Multiplication of
polynomials
quadratic, 477
in standard form, 896
standard form of, 477
subtraction of, 484–486
modeling, 482–483
unfactorable, 567
Population, 120, 708–709
explore changes in, 144–145
Population density, 472
Positive correlation, 263
Positive integer exponents, 452
Positive Power of a Quotient
Property, 469
Positive slope, 312
Power(s), Z20, 26
exponents and, 26–28
geometric models of, 26
inverse operations for, 832
Negative, of a Quotient Property, 470
Positive, of a Quotient Property, 469
of a Power Property, 462
of a Product Property, 463
of ten, 452–453
multiplication by, 453
using patterns to investigate, 452
Power Property, Power of a, 462
Power Property of Equality, 822
Powers Property
Product of, 460
Quotient of, 467, 878
Precision, S54
Prediction, 715
Preparing for your final exam, 849
Prime factorization, Z19–Z20, 524
writing with exponents, Z20
Prime numbers, Z17–Z18, 524
Principal, 133
Prisms, 874, S64
surface area of, 500, S67
volume of, 500, 779, S66
Probability, 713, 744, 881, 882
converting between odds and, 722
of dependent events, 729
experimental, see Experimental
probability
geometric, 890
of inclusive events, 734
of independent events, 727
of mutually exclusive events, 734
theoretical, see Theoretical probability
Problem Solving on Location
Illinois, 162–163
Michigan, 290–291
New Jersey, 440–441
Ohio, 920–921
Pennsylvania, 760–761
South Carolina, 584–585
Problem-Solving Applications, 28,
33, 94, 175–176, 255, 343–344, 385,
503–504, 559–560, 607–608,
647–648, 729, 791–792, 901–902
Problem-Solving Plan, xx–xxi
Problem-Solving Strategies, S40–S49
Draw a diagram, S40
Find a pattern, S44
Guess and test, S42
Make a model, S41
Make an organized list, S49
Make a table, S45
Solve a simpler problem, S46
Use logical reasoning, S47
Use a Venn diagram, S48
Work backward, S43
Product of Powers Property, 460
Product Property
Power of a, 462
of Square Roots, 806
Zero, 866
Product Rule for Inverse Variation,
853
Products, special, see Special products
Properties
of addition, 46
of Equality, 79, 86
of Inequality, 174, 180, 181
of multiplication, 46
of zero, 21
Proportion(s), 114
applications of, 121–123
percent, 127
rates, ratios and, 114–117
Pyramids, 874, S64
surface area of, 500, S67
volume of, 500, 779, S66
Pythagorean Theorem, 641, 643, 807,
S68
Q
Quadrants, 54
Quadratic equations
defined, 622
discriminant of, 654
Index
S159
related function of, 622
roots of, 628–629, see also Solving
solving, 660
by completing the square, 646, 656
by factoring, 630–633, 656
by graphing, 622–624, 656
by using the Quadratic Formula,
652–657
by using square roots, 636–639, 656
standard form of, 622
Quadratic Formula
discriminant and, 652–657
using the
for estimating solutions, 653–654
solving quadratic equations by,
652–657
Quadratic functions, 620
characteristics of, 599–603
comparing graphs of, 615
defined, 590
domain of, 593
families of, 612, 862
general form of, 791
graphing, 606–609
using a table of values, 591
identifying, 590–593
range of, 593
transformations of, 613–616
zeros of, finding, from graphs, 599
Quadratic models, 789–792
Quadratic parent functions, 612,
613, 862
Quadratic polynomials, 477
Quadrilaterals, S63
classifying, S63
Quality Control, 715
Quartiles, 695
Question type, any
read the problem for understanding,
436–437
spatial reasoning, 756–757
translate words to math, 580–581
use a diagram, 516–517
Quotient of Powers Property, 467,
878
Quotient Property
Negative Power of a, 470
Positive Power of a, 469
of Square Roots, 806
R
Radical equations, 822–826
Radical expressions, 805–808
addition of, 811–813
division of, 816–818
multiplication of, 816–818
subtraction of, 811–813
Radical functions
graphing, 804
Radical symbol, 32
Radicals, like, see Like radicals
S160
Index
Radicand, 805
Radius, S62
Random numbers, 719
using, 719
Random samples, 703, 708–709, S73
Range, 82, 236, 237, 238, 239, 240, 241,
242, 248, 249, 250, 251, 256, 260,
261, 694, 857
of absolute-value functions, 366–367
interquartile (IQR), 695
of linear functions, 299
of quadratic functions, 593
reasonable, 248, 249, 250, 251, 255,
261, 283, 284, 299, 304, 360, 597,
853, 856, 861, 863
Rate of change
defined, 310
slope and, 310–313
Rates, 114
ratios, proportions and, 114–117
Ratio(s), 114
common, 766
equivalent, 114
rates, proportions and, 114–117
surface-area-to-volume, 869
trigonometric, 908–909
Rational equations, 906
defined, 900
solving, 900–903
by using cross products, 900
by using the lowest common
denominator, 900–901
Rational exponents, 832–834
Rational expressions
addition of, 885–888
with like denominators, 885
with unlike denominators, 887
defined, 866
division of, 878–881
multiplication of, 878–881
simplifying, 866–869
subtraction of, 885–888
with like denominators, 886
with unlike denominators, 887
Rational functions, 858–862
defined, 858
families of, 862
graphing, 873
using asymptotes, 860
Rational numbers, 34
comparing and ordering, S50
Rationalizing denominators,
817
using conjugates, 821
Rays, S56
naming, S56
Reading
graphics, 675
the problem, 445
Reading and Writing Math, 5, 75,
167, 229, 295, 381, 445, 523, 589,
675, 765, 849, see also Reading
Strategies; Study Strategies; Writing
Strategies
Reading Math, 32, 34, 54, 114, 121,
170, 247, 272, 320, 408, 446, 453,
454, 561, 680, 721, 722, 782, 854
Reading Strategies
Read a Lesson for Understanding, 523
Read and Interpret Graphics, 675
Read and Interpret Math Symbols, 229
Read and Understand the Problem, 445
Use Your Book for Success, 5
Ready to Go On?, 39, 61, 113, 147,
187, 211, 261, 279, 333, 365, 413,
429, 475, 509, 557, 573, 621, 661,
711, 745, 797, 831, 877, 907, see also
Assessment
Real Estate, 125
Real numbers, 34
addition of, 14–17
defined, 14
division of, 20–22
multiplication of, 20–22
square roots and, 32–35
subtraction of, 14–17
Reasonable answer, 33, 36, 79, 80,
81, 82, 88, 89, 95, 97, 104, 117, 118,
120, 122, 124, 128, 131, 136, 138,
139, 142, 143, 159, 170, 176, 182,
231, 255, 344, 385, 386, 416, 423,
616, 623, 638, 648, 656, 772, 781,
783, 798
Reasonable domain, 248, 249, 250,
251, 255, 261, 283, 284, 299, 304,
360, 597, 853, 856, 861, 863
Reasonable range, 248, 249, 250, 251,
255, 261, 283, 284, 299, 304, 360,
597, 853, 856, 861, 863
Reasonableness, 33, 35, 79, 80, 81,
82, 88, 89, 95, 97, 104, 115, 117, 118,
120, 122, 124, 128, 131, 136, 138,
139, 142, 143, 159, 250, 251, 255,
261, 265, 623, 638, 798
Reasoning
explaining your, in extended responses,
668–669
spatial, 756–757
Reciprocals, 21
Recognizing distracters, 374–375
Recreation, 22, 87, 151, 198, 234, 240,
276, 317, 394, 425, 808, 888
Recreation Link, 198
Rectangle(s), S59
area of, Z4, 83, S61
perimeter of, Z3, S60
Rectangle model for multiplying
polynomials, 494
Recycling, 8
Reflections, 359, S69
in the coordinate plane, S69
of linear functions, 359
Regular polygons, S58
Related quadratic equations, 622
Relations, 236
functions and, 236–238
Relationships
graphing, 230–232
variable, model, 244
Relative error, S55
Remember!, 42, 108, 149, 188, 203,
298, 299, 334, 335, 350, 357, 398,
406, 421, 446, 461, 476, 477, 484,
492, 504, 524, 540, 549, 607, 613,
638, 647, 652, 678, 737, 767, 790,
812, 817, 833, 851, 853, 861, 866,
869, 878, 879, 881, 887, 896
Remembering formulas, 765
Remodeling, 545
Repeating decimals, Z25, 34
Replacement set, 8
Representations
multiple, see Multiple representations
of solid figures, 874
Rhombus, S59
Right angles, S56
Right triangles, S59
Rise, 311
Roots
exploring, 628–629
of quadratic equations, 628–629
Rotations, 358, S69
in the coordinate plane, S69
of linear functions, 358
Rounding, Z9–Z11
Run, 311
S
Sales tax, 134
Sample space, 713
Samples, 708–709, S73
biased, 709, S73
random, 703, 708–709, S73
Sampling, bias and, 708–709, S73
Sandia Peak Tramway, 304
Scalar multiplication, 747
Scale, 116
Scale drawing, 116
Scale factor, 123
of a dilation, S70
Scale model, 116
Scalene triangles, S59
Scatter plots, 262
interpreting, 270
trend lines and, 262–265
School, 81, 197, 362, 386, 419, 731
School Link, 731
Science, 118, 346, 464, 532, 784
Science Link, 346
Scientific notation, 453–454
Seabiscuit, 234
Second coordinates, 236
Second differences, 590
Sectors, 680
Selected Answers, S79–S106
Sequences
arithmetic, see Arithmetic sequences
geometric, see Geometric sequences
Set-builder notation, 168
Sets, S78
Sheppard, Alfred, 118
Shipping, 275
Short Response, 25, 71, 82, 90, 137,
161, 185, 200, 222–223, 225, 235,
269, 289, 340, 377, 403, 426, 437,
439, 451, 481, 516, 517, 519, 546,
571, 580, 581, 583, 597, 611, 651,
671, 686, 718, 742, 757, 759, 787,
845, 865, 884, 919
Understand Short Response Scores,
222–223
Signed numbers
division of, 20
multiplication of, 20
Significant digits, S54
Silicon chips, 777
Similar figures, 121
Simple events, 737
Simple interest, 133
Simple random sample, 708–709
Simplest form
of a fraction, Z23
of a square-root expression, 805
Simplifying
exponential expressions, 460
expressions, 46–49
fractions, Z23
rational expressions, 866–869
Simulations, 712
Sine, 908
Skills Bank, S40–S78
Slope formula, 320–323
Slope-intercept form of linear
equations, 334–337
Slope(s), 311, 313
comparing, 313
finding
from equations, 322
from graphs, 321
from tables, 321
negative, 312
of parallel lines, 349–352
of perpendicular lines, 349–352
positive, 312
rate of change and, 310–313
undefined, 312
zero, 312
Snowshoes, 856
Solar cars, 691
Solar Energy, 898
Solar Energy Link, 898
Solar-powered aircraft, 898
Solid figures, representing, 874
Solution(s)
approximating, 91, 637–638
of equations, 77
estimating, using the Quadratic
Formula for, 653–654
extraneous, 824–825, 902
of inequalities, 168
of linear inequalities, 414
of systems of linear equations, 383
of systems of linear inequalities, 421
Solution set, 77, 148
empty set as, 102
Solve a simpler problem, S46
Solving
classic problems, 404–405
linear equations by using a
spreadsheet, 382
rational equations, 900–901
special systems, 406–409
systems of linear equations, 383–401
systems of linear inequalities, 427
Space Shuttle, 150
Spatial reasoning, 756–757
Special products
of binomials, 501–505
factoring, 558–561
geometric models of, 501, 503
Special systems, solving, 406–409
Split stem-and-leaf plot, 693
Sports, 42, 44, 50, 104, 107, 110, 119,
151, 170, 176, 178, 207, 234, 306,
410, 471, 498, 509, 596, 625, 632,
658, 690, 696, 697, 698, 716, 717,
768, 769, 776, 807
Sports Link, 44, 119, 234, 498
Spreadsheet 13, 382, 700–701
Square(s)
perfect, 32
two, difference of, 503, 560
Square(s) (geometric figure), Z3, S59
area of, Z4, 83, S61
perimeter of, Z3, S60
Square, completing the, see Completing
the square
Square root(s), 32
Product Property of, 806
Quotient Property of, 806
real numbers and, 32–35
solving quadratic equations by using,
636–639, 656
Square-root expressions, see also
Radical expressions
multiplication of, containing two
terms, 817
simplest form of, 805
Square-root functions, 798–800
domain of, 799
families of, 862
graphs of, translations of, 799
Square-Root Property, 636
Standard deviation, S74
Standard form, 454
of linear equations, 298
of polynomials, 477
polynomials in, 896
of quadratic equations, 622
Index
S161
Standardized Test Prep, 70–71,
160–161, 224–225, 288–289,
376–377, 438–439, 518–519,
582–583, 670–671, 758–759,
844–845, 918–919, see also
Assessment
Statistics, 82, 88, 455, 775
misleading, 702–703
Statistics Link, 88
Stem-and-leaf plot, 687
back-to-back, 687
Step functions, S75
Stonehenge II, 118
Straight angles, S56
Stratified random sample, 708–709
Student to Student, 47, 76, 169, 238,
304, 392, 462, 551, 656, 727, 792, 868
Study Guide: Preview, 4, 74, 166, 228,
294, 380, 444, 522, 588, 674, 764,
848, see also Assessment
Study Guide: Review, 62–65, 152–155,
216–219, 280–283, 368–371,
430–433, 510–513, 574–577,
662–665, 750–753, 836–839, 910–913,
see also Assessment
Study Strategies
Learn Vocabulary, 589
Prepare for Your Final Exam, 849
Remember Formulas, 765
Use Multiple Representations, 295
Use Your Notes Effectively, 167
Use Your Own Words, 75
Subset, S78
Substitution
solving systems of linear equations by,
390–393
Subtraction
of decimals, Z12–Z13
of fractions, Z30–Z31
with like denominators, Z30
with unlike denominators, Z30–Z31
of polynomials, 484–486
modeling, 482–483
of radical expressions, 811–813
of rational expressions, 885–888
with like denominators, 886
with unlike denominators, 887
of real numbers, 14–17, 15
solving equations by, 77–79
solving inequalities by, 174–177
Subtraction Property of Equality,
79, 86
Subtraction Property of Inequality,
174
Supplementary angles, S57
Surface area, 500, S67
of a cone, S67
of a cube, S67
of a cylinder, S67
of a prism, S67
of a pyramid, S67
using nets to estimate, S67
Surface-area-to-volume ratio, 869
S162
Index
Symmetric Property of Equality,
185
Symmetry, S63
axis of, see Axis of symmetry
line of, S63
Systematic random sample, 708–709
Systems of linear equations
consistent, 406
classification of, 407
dependent, 407
identifying solutions of, 383
inconsistent, 406
independent, 407
modeling, 389
solving
by elimination, 397–401
by graphing, 383–385
by substitution, 390–393
System of linear inequalities,
421–423
T
Tables
connecting to function rules and
graphs, 259
creating, to evaluate expressions,
12–13
finding slope from, 321
frequency, 688
identifying linear functions by, 297
of values, graphing quadratic functions
using, 591
Tangent, 908
Technology, 29, 136, 457, 514, 526,
742, 749, 777
using, to make graphs, 700–701
Technology Lab
Connect Function Rules, Tables, and
Graphs, 259
Create a Table to Evaluate Expressions,
12–13
Explore Roots, Zeros, and x-intercepts,
628–629
Families of Linear Functions, 356
The Family of Quadratic Functions,
612
Graph Linear Functions, 348
Graph Radical Functions, 804
Graph Rational Functions, 873
Interpret Scatter Plots and Trend Lines,
270
Solve Equations by Graphing, 91
Solve Linear Equations by Using a
Spreadsheet, 382
Solve Systems of Linear Inequalities,
427
Use a Graph to Factor Polynomials,
555
Use Random Numbers, 719
Use Technology to Make Graphs,
700–701
Technology Link, 136, 749, 777
Telephone numbers, 741
Temperature, 151
Ten, powers of, see Powers of ten
Terminating decimals, Z25, 34
Terms, 47, 272, 476, 817
Test Prep
Test Prep questions are found in every
exercise set. Some examples: 11, 19,
25, 31, 37; see also Assessment
Test Tackler, see also Assessment
Any Question Type
Read the Problem for
Understanding, 436–437
Spatial Reasoning, 756–757
Translate Words to Math, 580–581
Use a Diagram, 516–517
Extended Response
Explain Your Reasoning, 668–669
Understand the Scores, 286–287
Gridded Response
Fill in Answer Grids Correctly, 68–69
Multiple Choice
Choose Combinations of Answers,
916–917
Eliminate Answer Choices, 158–159
None of the Above or All of the
Above, 842–843
Recognize Distracters, 374–375
Short Response
Understand Short Response Scores,
222–223
Theoretical probability, 720–723
Third quartile values, 695
Tip (amount of money), 134
Tolerance intervals, S55
Tolkowsky, Marcel, 861
Transcontinental railroad, 890
Transformations, 357, S69
in the coordinate plane, S69
of linear functions, 357–360
of quadratic functions, 613–616
Transitive Property of Equality, 185
Translations, 357, S69
in the coordinate plane, S69
of the graph of the square-root
function, 799
Transportation, 96, 118, 177, 207, 250,
257, 267, 300, 301, 331, 480, 827
Transportation Link, 250, 480
Trapezoids, S59
area of, S59
Travel, 18, 36, 90, 104, 183, 274, 275,
304, 315, 610, 855, 889, 890, 904
Travel Link, 315, 610, 890
Tree diagram, Z5, 736
Trend lines, 265
interpreting, 270
scatter plots and, 262–265
Trial, 713
Triangle(s), Z3, S59, S63
acute, S63
area of, Z4, 83, S61
classifying, S63
equilateral, S63
isosceles, S63
obtuse, S63
right, S63
scalene, S63
Triangle Inequality, 209
Triathlon, 46
Trigonometric ratios, 908–909
Trinomials, 477
factoring, 540–554
modeling factorization of, 538–539
perfect-square, 501, 558
Truth Tables, 201
Tsunamis, 802
Two-step equations, solving,
92–95
Two-step inequalities, solving,
188–190
U
Undefined slope, 312
Underestimate, Z10
Understanding
the problem, 445
read a lesson for, 523
read the problem for, 436–437
Unfactorable polynomials, 567
Union, 204
of sets, S78
Unit rate, 114
Unlike denominators
addition of fractions with, Z30
addition of rational expressions with,
887
subtraction of fractions with, Z31
subtraction of rational expressions
with, 887
Use logical reasoning, S47
Use a Venn diagram, S48
V
Values, excluded, 848, 858
Van Dyk, Ernst, 107
Variable(s), 6
on both sides
modeling equations with, 99
solving equations with, 100–103
solving inequalities with, 194–197
dependent, 246, 247, 248, 249, 250
expressions and, 6–8
independent, 246–250
solving for, 107–109
Variable relationships, model, 244
Variation
constant of, 326, 851
direct, see Direct variation
inverse, see Inverse variation
Vertex
of absolute-value graphs, 366
of a cone, S64
of a parabola, 592
of a polyhedron, S64
axis of symmetry through, 598
finding the, 601
Vertical angles, S57
Vertical line(s), 768, 859
Vertical-line test, 243
Vertical method for multiplication
of polynomials, 495
Vertical translations
of linear functions, 357
of a parabola, 615
Vocabulary, 9, 17, 23, 29, 35, 43, 49,
57, 80, 103, 109, 117, 124, 130, 135,
141, 171, 206, 233, 239, 249, 266,
275, 300, 306, 314, 329, 353, 361,
386, 409, 418, 424, 455, 479, 505,
527, 594, 603, 625, 649, 657, 683,
690, 697, 704, 716, 723, 730, 740,
769, 776, 785, 801, 808, 813, 826,
855, 863, 870, 903
learning, 589
Vocabulary Connections, 4, 74, 166,
228, 294, 380, 444, 522, 588, 674,
764, 848
Volume, 500, S66
estimating, S66
of a cone, 500, S66
of a cube, 779, S66
of a cylinder, 500, S66
of a prism, 500, 779, S66
of a pyramid, 500, 779, S66
Voluntary response sample, 709
Vomit Comet, 798
W
Wadlow, Robert P., 88
Wages, 301, 329
War Admiral, 234
Waterfalls, 625
Weather, 23, 690, 691, 697
What if...?, 16, 18, 22, 28, 30, 33, 55,
79, 86, 90, 98, 104, 131, 176, 268,
276, 299, 331, 344, 360, 362, 388,
400, 410, 416, 478, 532, 560, 624,
632, 655, 881, 888
Whole numbers, 34
Width of a parabola, 613
Wildlife Refuge, 267
Wind turbines, 820
Winter Sports, 856
Winter Sports Link, 856
Work backward, S43
Write About It
Write About It questions are found in
every exercise set. Some examples:
9, 19, 24, 29, 31
Writing Math, 6, 33, 55, 77, 102, 148,
168, 237, 254, 334, 393, 452, 468,
485, 531, 687, 696, 767, 859
Writing Strategies, Write a Convincing
Argument/Explanation, 381
X
x-axis, Z7, 54
x-coordinate, 54
x-intercept, 303
exploring, 628–629
x-values, 236
Y
y-axis, Z7, 54
y-coordinate, 54
y-intercept, 303
y-values, 236
Yosemite Falls, 625
Z
Zero(s)
divided by a number, 21
division by, 21
exploring, 628–629
finding the axis of symmetry of a
parabola by using, 600
of a function, 599
properties of, 21
of quadratic functions, finding, from
graphs, 599
Zero exponent, 446
Zero Product Property, 630, 866
Zero slope, 312
Index
S163
Credits
Abbreviations used: (t) top, (c) center, (b) bottom, (l) left,
(r) right, (bkgd) background
Staff
Bruce Albrecht, Lorraine Cooper, Marc Cooper, Jennifer Craycraft, Martize Cross,
Nina Degollado, Lydia Doty, Sam Dudgeon, Kelli R. Flanagan, Mary Fraser, Stephanie
Friedman, Jeff Galvez, Pam Garner, José Garza, Diannia Green, Tom Hamilton, Tracie
Harris, Liz Huckestein, Jevara Jackson, Kadonna Knape, Cathy Kuhles, Jill M. Lawson,
Peter Leighton, Christine MacInnis, Jessika Maier, Jeff Mapua, Jonathan Martindill,
Stacey Murray, Susan Mussey, Kim Nguyen, Matthew Osment, Sara Phelps, Manda
Reid, Patrick Ricci, Michael Rinella, Michelle Rumpf-Dike, Beth Sample, Annette
Saunders, Katie Seawell, Kay Selke, Robyn Setzen, Patricia Sinnott, Victoria Smith,
Jeannie Taylor, Karen Vigil, April Warn, Ken Whiteside, Sherri Whitmarsh, Aimee F.
Wiley, David Wynn
Photo
All images HRW Photo unless otherwise noted.
Master Icons—teens, authors (all), Sam Dudgeon/HRW.
Cover/Title page: Richard Cummins/Lonely Planet Images
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814 (bl), Brand X Pictures; 816 (tr), ON-PAGE CREDIT; 820 (tl), ©Bob Daemmrich/The
Image Works; 820 (bl), Brand X Pictures; 827 (bl), AP Photo/NOAA; 828 (bl), Brand
X Pictures; 830 (cr), Walker/PictureQuest; 830 (tl), Brand X Pictures; 830 (bc), AP
Photo/Anna Branthwaite.
Chapter Twelve: Page 846–847 (bkgd), Victoria Smith/HRW; 849 Sam Dudgeon/
HRW; 851 (tr), © RubberBall/Alamy; 853 (tl), MedioImages/Alamy; 856 (tl), AP
Photo/Robert F. Bukaty; 856 (bl), PhotoDisc/Getty Images; 858 (tr), Steve Hamblin/
Alamy; 861 (tl), Courtesy of Texas Highways Magazine; 864 (bl), PhotoDisc/Getty
Images; 866 (tr), Gerald C. Kelley/Photo Researchers, Inc.; 868 (bl), © Paul Barton/
CORBIS; 869 (tl), © SuperStock; 871 (cl), AP Photo/Lou Krasky; 871 (bl), PhotoDisc/
Getty Images; 876 (tl), PhotoDisc/Getty Images; 876 (br), AP Photo/Tyler Morning
Telegraph, Tom Worner; 876 (sky), PhotoDisc/Getty Images; 878 (tr), © Stock
Connection Distribution / Alamy; 885 (tr), Philippe Blondel/Photo Researchers, Inc.;
890 (tl), Courtesy Texas Parks & Wildlife Department; 893 (tc), AP Photo/Dolores
Ochoa; 893 (tr), © Nigel Francis/Robert Harding/Alamy Photos; 898 (cl), AP Photo/
NASA, Nick Galante, PMRF; 900 (tr), © Tom Stewart/CORBIS; 904 (br), ON-PAGE
CREDIT; 906 (b), © Dynamic Graphics Group/i2i/Alamy; 906 (movie screen), © Ralph
Nelson/Imagine Entertainment/ZUMA/CORBIS; 920 (br), AP Photo/Tim Johnson; 920
(tr), Focus on Sport/Getty Images; 920 (cr), Sam Dudgeon/HRW; 921 (tc), Stefano
Rellandini/Reuters/Corbis; 921 (br), JOEL SAGET/AFP/Getty Images.
Student Handbook: S2 (tl), PhotoDisc/Getty Images; S3 (br), Sam Dudgeon/HRW
Chapter Ten: Page 672–673 (bkgd), Austin American-Statesman, Jay Janner; 678
(tr), Victoria Smith/HRW; 680 (all), Sam Dudgeon/HRW; 681 (cl), Leigh Beisch/Getty
Images; 687 (tr), © Tom Stewart/CORBIS; 691 (cl), © Reuters/CORBIS; 694 (tr), AP
Photo/Jerry Laizure; 696 (tr), Victoria Smith/HRW; 698 (cr), © Michael Prince/CORBIS;
707 (tl), © Bettmann/CORBIS; 710 (cr), Stuart Franklin/Getty Images; 710 (bl), Stuart
Franklin/Getty Images; 712 (tr), Sam Dudgeon/HRW; 713 (tl), Sam Dudgeon/HRW;
713 (tc), United States Mint image; 713 (tr), Sam Dudgeon/HRW; 713 (c), United
States Mint image; 713 (c), United States Mint image; 713 (bc, br), Sam Dudgeon/
HRW; 716 (tl, tc), Sam Dudgeon/HRW; 716 (penny), PhotoDisc/Getty Images; 716
(dime), PhotoDisc/Getty Images; 716 (nickel), PhotoDisc/Getty Images; 716 (bl),
PhotoDisc/Getty Images; 716 (bc), Sam Dudgeon/HRW; 716 (br), Victoria Smith/HRW;
717 (bl), Sam Dudgeon/HRW; 718 (cr), © European Communities; 720 (tr), © Warren
Faidley/Weatherstock; 721 (bl), Tom Stewart/CORBIS; 722 (cr), Victoria Smith/HRW;
724 (bl), Sam Dudgeon/HRW; 727 (tl), David Young-Wolff/Alamy; 728 (tl), Peter
Van Steen/HRW; 728 (bl, bc), Victoria Smith/HRW; 729 (tr), Victoria Smith/HRW; 730
(cr), Sam Dudgeon/HRW; 731 (bl), © Jose Luis Pelaez, Inc./CORBIS; 732 (tl), Sam
Dudgeon/HRW; 735 (all), Sam Dudgeon/HRW; 736 (all), Sam Dudgeon/HRW; 741 (cr),
Sam Dudgeon/HRW; 741 (cl), © Underwood & Underwood/CORBIS; 742 (tl), Sam
Dudgeon/HRW; 743 (tr), Foodcollection.com/Alamy; 743 (bl), © Comstock Images;
744 (tl), Sam Dudgeon/HRW; 744 (b), © Handout/Hasbro/Ray Stubblebine/Reuters/
CORBIS; 749 (cl), Courtesy of Blue Sky Studios/ZUMA Press; 760 (tr), Victora Smith/
HRW; 761 (tr), Courtesy of Gulf Coast Bird Observatory.
Chapter Eleven: Page 762–763 (bkgd), © Merlin D. Tuttle/Bat Conservation
International; 766 (tr), Randy Lincks/Masterfile; 770 (cl), Gregory Sams/Photo
Researchers, Inc.; 777 (tl), Lucidio Studio, Inc./Alamy; 781 (tr), © 1989 Carmen Lomas
Garza, Collection of Paula Maciel Benecke & Norbert Benecke, Aptos CA, photo
Credits
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