Extra Practice
Chapter 1
29. Sample answer: You know the
temperature in Quito in degrees
Celsius and the temperature in
Miami in degrees Fahrenheit. You
need to find out which one is
greater.
32. Input
2
4
6
8
Output
33.
7.5
10
12.5
y
15
Evaluate the expression.
4.4
7 5
1.1 1. k 1 9 when k 5 7 16 2. 21 2 x when x 5 318 3. 3.5 1 t when t 5 0.9 4. y 2 }3 when y 5 }
}
12 24
8
2 8
}
7. z when z 5 }
3 27
m
5. } when m 5 9.6 2.4 6. 1.5t when t 5 2.3
4
3.45
1.2 9. 25 2 7 1 8 26
3
3 27
13. } 10
2
3
4
8. p when p 5 0.2
0.0016
10. 67 2 3 p 4 55
11. 82 4 4 1 12 28
12. 9 1 6 4 3 11
1
14. }
(7 2 5.5)2 0.75
15. 3 1 4(3 1 24) 111
16. }[27 2 (2 1 5)]2 240
3
3
5
1.3 Translate the verbal phrase into an expression.
3
17. } of a number m }3 m
x
18. the quotient of a number x and 7 }
19. the difference of a number y and 3 y 2 3
20. 6 more than 3 times a number n 3n 1 6
4
4
7
1.3 Write an expression for the situation.
21. Number of minutes left in a 45 minute class after m minutes have gone by 45 2 m
1
1
34.
x
y
c
22. Number of meters in c centimeters }
100
1.4 Write an equation or an inequality.
23. The product of 12 and the difference of a number r and 4 is 72. 12 p (r 2 4) 5 72
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24. The difference of a number q and 18 is greater than 10 and less than 15. 10 < q 2 18 < 15
1.4 Solve the equation using mental math.
25. d 2 13 5 25 38
1
x
21
35.
26. 12z 5 96 8
k
28. } 5 12 72
27. 23 2 m 5 7 16
6
1.5 29. For the following, identify what you know and what you need to find out.
You do not need to solve the problem. 29. See margin.
y
One day the temperature in Quito, Ecuador, was 208C. The temperature
in Miami, Florida was 758F. Which temperature was higher?
n1an-01ep-02-t
1.6 30. Identify the number of significant digits in the measurements
(a) 25.03 m and (b) 1.620 ft. a. 4 b. 3
1.7 31. Identify the domain and range of the function.
Input
3
4
5
6
Output
9
11
13
15
domain: 3, 4, 5, 6; range: 9, 11, 13, 15
10
10
36.
x
y
1.7 32. The domain of the function y 5 1.25x 1 5 is 2, 4, 6, and 8. Make a table for
n1an-01ep-03-t
1
x
22
the function. Identify the range of the function.
See margin for table; range: 7.5, 10, 12.5, 15.
1.8 Graph the function.
33–36. See margin.
33. y 5 x 1 2; domain: 0, 1, 2, and 3
34. y 5 3x 2 3; domain: 1, 2, 3, and 4
35. y 5 1.5x; domain: 0, 20, 40, and 60
1
36. y 5 }
x 1 2; domain: 0, 4, 8, and 12
4
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Extra Practice
Chapter 2
2.1 Evaluate the expression.
}
}
3. Î 6400 80
}
1. -Ï 36 -6
2. ±Ï 400 ±20
}
4. ±Ï 144
±12
2.1 Approximate the square root to the nearest integer.
}
}
}
12
5. Ï 135
}
7. -Ï 160 -13
6. -Ï 75 -9
8. Ï 250 -16
Solve the equation. Check your solution.
2.2 9. x 1 4 5 20 16
13. 7h 5 63 9
10. 8 5 m 2 13 21
11. t 1 2 5 210 212
14. 24t 5 244 11
15. } 5 13 52
2.3 17. 4x 1 3 5 27 6
y
23
b
4
16. } 5 8 224
18. 6m 2 4 5 14 3
t
4
19. 50 5 7y 2 6 8
x
7
20. } 2 3 5 9 48
2.4 23. 6x 1 3x 1 8 5 35 3
26. 7m 1 3(m 1 2) 5 224 23
2.5 29. 8x 2 4 5 3x 1 6 2
21. } 1 3 5 22 235
22. 6p 2 2p 5 28 7
24. 12w 2 5 2 3w 5 40 5
25. 4d 2 3 2 2d 5 215 26
27. 5x 2 3(x 2 5) 5 13 21
3
28. }(2y 2 8) 5 6 8
30. 10 2 2x 5 3x 2 20 6
31. 5 2 5x 5 14 2 8x 3
4
1
2
32. 3(2y 2 5) 5 4y 2 7 4
12. z 2 8 5 27 1
3
4
34. 3x 2 3 5 }(2x 1 12) 8
33. 9 1 4y 5 2(3 2 y) 2}
2.6 Solve the proportion. Check your solution.
7
x
35. } 5 } 56
2
16
m
6
36. } 5 } 2
9
z
48
37. } 5 } 16
4
27
30
t
38. } 5 } 6
12
50
10
2.6 Write the sentence as a proportion. Then solve the proportion.
5
7
15
9
x
3 12
y
6
42. 6 is to 18 as y is to 3. }
5 }; 1
18 3
39. 5 is to 7 as 15 is to x. } 5 }
x ; 21
40. 9 is to 3 as x is to 12. } 5 }; 36
g 16
41. g is to 9 as 16 is to 12. }
5 }; 12
9
12
2.7 Solve the proportion. Check your solution.
6
12
43. }
5}
14
x
7
2x 1 6
x
7
2
47. } 5 } 4
6x
4
18
12
7
x 1 13
4
45. } 5 }
8
44. } 5 } 1
3b
5b 2 7
8
11
8
2x 1 12
48. } 5 } 8
12
y15
10
8
46. }
y 5 } 20
6
x18
4.8 2 2x
8
0.4 1 x
10
49. } 5 } 22 50. } 5 } 1.6
2.8 Solve the literal equation for x. Then use the solution to solve the specific
equation.
c
c1b
51. ax 2 b 5 c; 6x 2 5 5 25 x 5 }
a ;5
52. a(b 2 x) 5 c; 2(8 2 x) 5 26 x 5 b 2 }
a ; 11
2.8 Write the equation so that y is a function of x.
53. 5x 1 y 5 10
y 5 25x 1 10
54. 8x 2 2y 5 16
55. 7x 1 3y 5 6 2 5x
y 5 4x 2 8
y 5 24x 1 2
56. 21 5 6x 1 7y
y 5 2 }6 x 1 3
7
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Extra Practice
Chapter 3
1–12. See Additional Answers.
1. K(24, 22)
2. L(5, 0)
3. M(3, 21)
4. N(22, 2)
Quadrant III
Quadrant IV
Quadrant II
on the x2axis
5. P(0, 4)
6. Q(23.5, 5)
7. R(2.5, 6)
8. S(21, 21.5)
Quadrant II
Quadrant I
Quadrant III
on the y-axis
3.1 Graph the function with the given domain. Then identify the range of
the function. 9, 10. See margin for art.
y
13.
3.1 Plot the point in a coordinate plane. Describe the location of the point. 1–8. See margin for art.
1
x
21
1
10. y 5 }
x 2 3; domain: 24, 22, 0, 2, 4
9. y 5 22x 1 2; domain: 22, 21, 0, 1, 2
2
range: 22, 0, 2, 4, 6
3.2 Graph the equation. 11–18. See margin.
14.
y
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range: 25, 24, 23, 22, 21
11. y 2 x 5 3
12. y 1 3x 5 5
13. y 2 4x 5 10
14. y 5 4
15. 2x 2 y 5 0
16. 3x 1 y 5 0
17. 3x 1 2y 5 26
18. x 5 0.5
3.3 Find the x‑intercept and the y‑intercept of the graph of the equation. 19–22. See margin.
1
19. 2x 2 y 5 12
20. 25x 2 2y 5 20
3
4
21. 24x 1 1.5y 5 4
22. y 5 }x 2 15
x
21
3.3 Graph the equation. Label the points where the line crosses the axes. 23–26. See margin.
y
15.
23. y 5 3x 2 6
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1
7
29. (25, 3) and (28, 10) 2}3
31. (22, 5) and (22, 10) no slope 32. (6, 24) and (4, 24) 0
1
3
3.5 Identify the slope and y‑intercept of the line with the given equation. 33–36. See margin.
33. y 5 7x 1 8
y
34. y 5 10x 2 6
35. y 5 3 2 4x
36. y 5 x
3.5 Rewrite the equation in slope‑intercept form. Then identify the slope and
the y‑intercept of the line. 37–40. See margin.
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3
37. 2x 1 y 5 8
x
21
y
38. 10x 2 y 5 20
39. 5x 1 2y 5 10
40. 22x 2 y 5 3
43. 2x 1 y 5 1
44. 22x 1 3y 5 29
3.6 Graph the equation. 41–44. See margin.
41. y 5 2x 2 4
17.
26. 0.3x 2 y 5 6
2
28. (23, 0) and (2, 25) 21
30. (9, 4) and (0, 1) }
x
16.
3
3.4 Find the slope of the line that passes through the points.
27. (4, 2) and (6, 8) 3
21
2
1
25. }
x1}
y 5 10
24. 4x 1 5y 5 220
3
42. y 5 2}
x11
4
3.6 Graph the direct variation equation. 45–52. See margin.
n1an-04ep-16-t
1
1
x
45. y 5 2x
46. y 5 2x
47. y 5 4x
48. 5x 1 y 5 0
49. x 2 2y 5 0
50. 3x 1 y 5 0
51. 2y 5 9x
52. y 2 }x 5 0
5
4
3.7 Find the value of x so that the function has the given value.
53. f(x) 5 27x 2 3; 217 2
18.
y
56. m(x) 5 x 2 2
57. t(x) 5 x 1 4
58. z(x) 5 6x
59. h(x) 5 22x
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x
19. x-int: 6, y-int: 212
20. x-int: 24, y-int: 210
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55. t(x) 5 3x 1 1; 211 24
3.7 Graph the function. Compare the graph with the graph of f(x) 5 x. 56–59. See margin.
2
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21
16
5
54. g(x) 5 5x 2 4; 12 }
21. x-int: 21, y-int: }8
3
22. x-int: 20, y-int: 215
23–26. See Additional Answers.
33. slope: 7, y-intercept: 8
34. slope: 10, y-intercept: 26
35. slope: 24, y-intercept: 3
36. slope: 1, y-intercept: 0
37. y 5 22x 1 8; slope: 22,
y-intercept: 8
38. y 5 10x 2 20; slope: 10,
y-intercept: 220
39. y 5 2 }5 x 1 5; slope: 2 }5,
2
2
y-intercept: 5
40. y 5 22x 2 3; slope: 22,
y-intercept: 23
41–52, 56–59. See Additional
Answers.
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Extra Practice
Chapter 4
13.
4.1 Write an equation of the line with the given slope and y‑intercept.
y
3
x
21
14.
2. slope: 22
3. slope: 5
y‑intercept: 6
y 5 3x 1 6
4. slope: 21
y‑intercept: 23
y 5 2x 2 3
y‑intercept: 4
y 5 22x 1 4
1
5. slope: }
y‑intercept: 21
y 5 5x 2 1
7
6. slope: 2}
10
2
y‑intercept: 25
y‑intercept: 8
7
y 5 }1x 2 5
y 5 2} x 1 8
10
2
4.2 Write an equation of the line that passes through the given point and has
the given slope m.
y
2
8. (21, 5); m 5 24
9. (26, 3); m 5 }
3
y 5 2x 1 2
y 5 24x 1 1
y 5 }2 x 1 7
3
4.2 Write an equation of the line that passes through the given points.
7. (3, 8); m 5 2
1
x
22
1
12. 2, }
, (6, 3)
1
10. (2, 4), (5, 13)
11. (1, 22), (22, 13)
y 5 3x 2 2
y 5 25x 1 3
4.3 Graph the equation. 13–15. See margin.
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15.
1. slope: 3
y
13. y 2 3 5 23(x 1 4)
3
2
y 5 }2 x 2 1
3
2
15. y 2 6 5 }
(x 2 3)
14. y 1 5 5 22(x 2 1)
3
4.3 Write an equation in point‑slope form of the line that passes through the
given points. 16–18. See margin.
n1an-05ep-02-t
16. (24, 2), (22, 16)
1
x
23
17. (3, 9), (27, 4)
18. (10, 22), (12, 26)
4.4 Write an equation in standard form of the line that passes through the given
point and has the given slope m or that passes through the two given points.
16–18. Sample answers are given.
16. y 2 2 5 7(x 1 4)
17. y 2 9 5 }1 (x 2 3)
2
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-t
19. (2, 7), m 5 24
20. (5, 11), m 5 3
21. (1, 22), (22, 4)
2x 1 y 5 0
4x 1 y 5 15
3x 2 y 5 4 2 }5x 1 70
6
4.5 Write an equation of the line that passes through
the given point and is
parallel to the given line.
18. y 1 2 5 22(x 2 10)
28. y
22. (5, 4), y 5 3x 1 5
y 5 3x 2 11
60
50
40
30
20
10
0
29.
30.
y 5 25x 2 22
perpendicular to the given line.
line of fit
0 1 2 3 4 5 6 x
y
7
6
31.
3
5
5
y 5 2}x 1 14
3
25. (212, 22), y 5 3x 1 2
26. (15, 211), y 5 }x 2 8
1
y 5 2 }x 2 6
3
27. (7, 26), 4x 1 6y 5 7
33
y 5 }3x 2}
2
2
4.6 Make a scatter plot of the data in the table. Draw a line of fit. Write an
equation of the line. 28, 29. See margin for art.
28.
4.7
29.
x
1
2
3
3.5
4
4.5
5
y
20
35
40
55
60
45
60
x
10
20
30
40
50
60
y
55
45
45
40
35
20
Sample answer: y 5 10x 1 10
Sample answer: y 5 2 }5x 1 70
Make a scatter plot of the data. Find the equation of the best‑fitting line.6
Approximate the value of y for x 5 7. 30–31. See margin for art.
30.
line of fit
n1an-05ep-05-t
x
0
2
4
6
8
y
0.5
3
4
5.5
7
y 5 0.78x 1 0.9; 6.36
2
1
0
24. (8, 23), y 5 }x 1 5
4.5 Write an equation of the line that passes through the given point and is
y
70
60
line of fit
50
40
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30
20
10
0
0 10 20 30 40 50 60 70 x
5
4
3
3
4
3
y 5 }x 2 9
4
23. (23, 27), y 5 25x 2 2
31.
EP5
x
0
1
y
5
8
3
6
8
12
15
14
y 5 1.1x 1 6.7; 14.4
0 2 4 6 8 10 12 x
y
18
15
12
9
6
3
0
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line of fit
0 1 2 3 4 5 6 7 8 x
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Extra Practice
Chapter 5
1–9. See Additional Answers.
10.
Solve the inequality. Graph your solution. 1–24. See margin for art.
27
26
25
2
24
9. 28.5 ≤ t 2 10
t ≥ 1.5
25.5
12.
26
24
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22
5.2 13. 3p ≤ 27
0
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5
4
4
14.
24
15.
2
16.
215
17.
0
6
8
10
23
22
21
4
6
8
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z ≤ }2
210
25
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1
1
2
y > 210
19. 0.3z ≤ 2.4
20. 25 > 22.5s
22. 0.09d < 21.8
23. } > 215
25. 3x 1 5 ≥ 20
10
s > 210
y
0.3
24. 21.8t < 9
y > 24.5
t > 25
z<3
29. 8(m 1 2) < 4(5 1 2m)
all real numbers
32. 6(25 1 3p) ≥ 3(6p 2 10)
3
27. 8(t 1 4) > 28
t > 25
30. 6d 2 4 2 3d ≥ 14
d≥6
5
6
2
33. }(12z 2 24) > }
(25z 2 25)
5
all real numbers
no solution
y<6
5.4 Solve the inequality. Graph your solution. 34–42. See margin for art.
34. 2 ≤ y 2 4 < 7
35. 227 < 9x < 27
6 ≤ y < 11
5
37. 15 < }(18a 2 9) ≤ 30
9
2 < a ≤ 3}1
2
18.
r < 24 or r ≥ 22
42. 2n 2 1 > 1 or 2n 1 8 > n 1 8
22
t ≥ 4 or t < 28
m > 22 or m < 25
19.
2<z<5
39. 3r 1 7 < 25 or 32 ≤ 7r 1 46
1
41. 9t 2 20 ≥ 4t or 4 < }
t
40. 24m < 8 or 2m 2 2 < 212
212
26
0
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36. 2 < 6z 2 10 < 20
23 < x < 3
38. 2v > 12 or v 1 2 < 6
v > 6 or v < 4
2
218
z≤8
26. 6z 2 5 < 13
x≥5
28. 7 2 8n ≤ 4n 2 17
n≥2
2
31. }
y 1 28 > 20 1 2y
0
112
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x≥6
18. 23 ≥ }
y
22
5.3 Solve the inequality, if possible. Graph your solution. 25–33. See margin for art.
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n1an-06ep-14-t
15
3
m ≤ 4.61
y < 25.5
d < 220
3
12
5
16. } < 5
n ≤ 26
2
21. 4.8z ≤ 3.2
13.
8
4
8
x
15. } ≥ 2
3
n
2
m ≤ }3
6
4. m 1 3 < 2
x≤7
m < 21
7
3
7
2
1
1
7. 1 } > 6 } 1 z z < 24 } 8. 3 }
≥ 1}
1 k k ≤ 2}
12. 1.48 2 m ≥ 23.13
t < 22
17. 26m ≥ 29
3. 4 ≥ x 2 3
11. 26.9 > 21.4 1 y
14. 213t > 26
p≤9
4.61
3
x ≤ 23
3
5
6. 2} 1 n < 23}
4
8
n < 26}3
8
10. r 1 4 < 20.7
r < 24.7
y>5
1 n ≤ 2}1
5. 2 1 n ≤ 4}
2
11.
28
2. 5 1 x ≤ 2
5.1 1. y 2 2 > 3
24.7
n < 22 or n > 0
5.5 Solve the equation, if possible.
4
20.
215
21.
6
8
10
n1an-06ep-18-t
210
25
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43. x 5 8
44. y 5 210
45. m 1 6 5 5
68
no solution
211, 21
47. t 2 7 5 21
48. 6z 2 4 5 36
49. 46s 1 11 5 252
214, 28
22, 10
no solution
51. 5r 1 10 5 15
52. 23s 1 4 5 14
53. 247v 1 2 5 32
21, 1
23}2 , 1
no solution
3
5.6 Solve the inequality. Graph your solution. 55–66. See margin for art.
12
0
2
3
24
n1an-06ep-20-t
0
22
2
4
55. x ≤ 3
22.
240
23.
230
220
23 ≤ x ≤ 3
59. x 1 2 > 6
x < 28 or x > 4
63. 3p 2 3 ≤ 12
210
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24.5
28
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26
24
22
25.
2
26.
1
27.
26
28.
0
24
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22
0
4
6
8
2
3
4
24
22
0
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2
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13
10
23, 4
50. r 1 3 2 16 5 24
215, 9
6
3}3, 6
5
2
58. q < }
5
57. s > 1.2

5w 2 4 2 4 5 8
54. 12 }
2
2}5 < q < }2
s < 21.2 or s > 1.2
5
61. 8 2 m < 3
62. 4n 2 1 ≥ 7 3
n ≤ 2} or n ≥ 2
5 < m < 11
2
2 c 1 2 < 64
65. 25a 2 1 1 3 ≤ 11 66. 4}

3
2 }3 ≤ a ≤ 1
227 < c < 21
5
69. 4x 1 y > 3
70. x ≤ 25
71. 3(x 2 8) ≤ 6y
72. 2x 2 y ≥ 22
73. y > 8
74. 2(x 2 1) ≥ 1 2 y
75. x 2 8 ≤ y 1 2
76. 2x ≥ 22y
77. 3(y 2 8) > x 2 9
78. 2(2x 2 1) ≥ 4 1 y
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29.
n1an-06ep-26-t
1
y ≤ 25 or y ≥ 5
60. y 1 3 ≤ 5
28 ≤ y ≤ 2
64. 3q 1 2 2 3 ≥ 8
21 ≤ p ≤ 7
q ≤ 2} or q ≥ 3
3
5.7 Graph the inequality.
67–78. See margin.
67. y ≥ x 1 5
68. y < x 2 1
0
24.
26
56. y ≥ 5
46. 4z 2 2 5 14
2
24
31.
22
0
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2
4
30.
3
5
6
7
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33.
2
4
6
8
10
32.
8
24
n1an-06ep-30-t
22
0
n1an-06ep-31-t
2
4
24
22
0
2
4
34–42, 55–78. See Additional
Answers.
3/18/11 10:39:01 PM
n1an-06ep-33-t
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EP6
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Extra Practice
Chapter 6
25.
6.1 Solve the linear system by graphing. Check your solution.
y
2
26.
3. x 2 y 5 4
4. 4x 2 y 5 10
5. 3x 2 2y 5 25
16
2
1
6. }
x1}
y5}
y 5 24x 2 2 (22, 6)
4x 1 3y 5 218 (23, 22)
x 1 y 5 22 (1, 23)
3
3
2
5
3
8
(6, 4)
2}x 1 y 5 }
5
6.2 Solve the linear system using substitution.
y
7. y 5 2x 1 6
22y 2 2x 5 8
8. y 5 3x 1 5
10. 2x 2 y 5 0
x
3
1
x 1 y 5 21 2}2, }1
2
x 5 y 2 3 (23, 0)
2
n1an-ep07-01-t
26
2. y 5 3x 1 12
x 5 4 (4, 6)
x
22
2x 1 y 5 23
1. y 5 x 2 1
y 5 2x 1 5 (3, 2)
y 5 22x 1 5
9. x 5 2y 2 5
2
2x 2 y 5 11 (9, 7)
3
1
12. }
x1}
y55
11. 1.5x 2 2.5y 5 22
x 1 3y 5 256 (28, 216)
4
1
x 2 }y 5 6 (7, 2)
2
2
x 2 y 5 10 (3, 27)
2y 2 4x 5 10
Solve the linear system using elimination.
27.
6.3 13. x 1 2y 5 2
y
2x 1 3y 5 13 (24, 3)
10x 1 5y 5 215
16. 5x 1 4y 5 6
n1an-ep07-02-t
1
x
7
5x 1 7y 5 29 (26, 3)
34.
21. 8x 2 3y 5 61
3
2
2x 1 6y 5 11 1 10, 2} 2
2
5x 1 2y 5 249 (29, 22)
7y 5 4x 2 79 1 }9, 210 2
4
2x 2 5y 5 223 (11, 9)
24. 15x 2 8y 5 6
14 9
25x 2 12y 5 16 1 }
, }2
5 2
6.5 Graph the linear system. Then use the graph to tell whether the linear
21
n1an-ep07-03-t
y 5 22
system has one solution, no solution, or infinitely many solutions. 25–27. See margin for art.
x
25. 2x 1 y 5 23
26. 2y 2 4x 5 10
y 5 22x 1 5
22y 2 2x 5 8
no solution
one solution
6.5 Solve the linear system using substitution or elimination.
y 5 25
2
30. 5x 1 5y 5 232
31. 4x 1 6y 5 11
32. 3y 2 3x 5 12
33. x 1 2y 5 230
y 5 3x 2 12 (20, 48)
y 5 x 2 4 no solution
34. y ≥ 25
35. x ≥ 23
x 2 y > 24
38. x > 3
y 2 4x < 8
x > 21
39. x 1 y > 3
x<5
y > 22
y≤0
1
n1an-ep07-05-t
22
36. y < 22x 2 3
y<1
37. x 1 4y ≥ 28
y
y5x14
x2y>5
x 1 2y ≤ 8
x 2 5y > 10
x
EP7
y 5 22x 2 3
38.
y
39.
y
y
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1
n1an-ep07-06-t
1
x
21
1
1
1
1
y5}
x 1 15 (230, 0)
2
y ≤ 22
36.
3x 1 3y 5 14 no solution
6.6 Graph the system of inequalities. 34–39. See margin.
x
21
y 5 22x 2 3
infinitely many solutions
29. 2y 2 3x 5 36
2
y 5 2}
x 1 7 no solution
3
n1an-ep07-04-t
27. 10x 1 5y 5 215
28. y 2 3x 5 5
x 5 y 2 5 (0, 5)
y
37.
20. 5x 1 2y 5 219
23. 5x 2 2y 5 53
6x 1 4y 5 31 1 }5, 4 2
1
35.
18. 4x 2 3y 5 39
10x 2 7y 5 216 (23, 22)
22. 4x 2 3y 5 22
y
17. 10y 2 3x 5 241
3x 2 5y 5 16 (23, 25)
6.4 19. x 1 y 5 23
y 5 22x 2 3
15. 3x 1 2y 5 231
x 2 4y 5 240 (12, 13)
7x 1 4y 5 14 1 4, 2}2 2
1
14. 3x 2 4y 5 216
x
x
n1an-ep07-08-t
EP7
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Extra Practice
Chapter 7
41.
y
Simplify the expression. In exercises involving numerical bases only, write
your answer using exponents.
7.1 1. 53 p 54 57
5. [(24)3]2 (24)
2
87 5
8
7.2 13. }
2
y
8
43.
1 4y3 2
5 3
x
21. }
y
64y
27
1
29. }
y
x
8
1
33. y210 }
10
7.4 41. y 5 3x
q
1 2
3 4 2
5x y
23. }
2
25x 2y 6
4
6a4b5
ab
3
1 a2abb 2
24. } p }
2 2
}
2x y
}
8
48b
1
16
27. 70 1
28. 425 p 43 }
1
30. (322)3 }
1
31. }
32
25
32. }
64
26
824
8
2
10c5
35. 10b23c 5 }
3
6
e
36. (2d 5e22)23 }
15
b
(2e)24g5
3
(22z)
39. }
296z 5
25
g8
8d
40. }
}9
5 23
16e
eg
3
1
53. y 5 4 p }
x
y
44. y 5 5 p 2x
1
3
46. y 5 2} p 5x
47. y 5 25 p 2x
48. y 5 2} p 4x
50. y 5 (0.2)x
51. y 5 3 p (0.2)x
1
52. y 5 2 p }
1
1
54. y 5 }
p }
132
x
x
1 94 2
43. y 5 }
1
2
7.5 49. y 5 1 }1 2
x
1
55. y 5 22 p }
132
2
x
132
x
3
56. y 5 2}
p 1
4 }
132
x
132
7.5 Tell whether the table represents an exponential function. If so, write a rule
for the function.
x
57.
n1an-ep08-05-t
x
21
y
5
​}​
2
0
5
1
59.
x
n1an-ep08-06-t
2
10
exponential; y 5 5 p 2
y
21
4x18
y
20. }4
26. (25)23 2}
42. y 5 1.25x
1
45. y 5 }
p 2x
1
2
1 6x3y 2
p
}7
Graph the function. 41–60. See margin.
x
x
47.
648u 10
z
}
8
81c
1
t5
38. }
}3
25 3
6t u 6u
3
21
2
1
34. (3c)24 }
4
y
y5
y
1
3
10
9 2
7.3 Simplify the expression. Write your answer using only positive exponents.
2
46.
4 4
729
x24
y
x
n1an-ep08-04-t
21
p
1
10 5
16. 1012 p }
7
2}5
7
7
1q2
19. }
12. (24s 2)3(2s 3)6 24096s 24
25
3
5
1 23 2
1
125
37. }
}4
25
45.
15. 2}
2
22. }
2
1
81
23
122
y
n1an-ep08-03-t
21
6
p 42 5
4
14. 4}
3
3u
1 u 2 p 1}
z 2
1
p}
}
6
25. 324 }
n1an-ep08-02-t
21
11. (3d2)3 p 2d2 54d 8
t
9
8. n2 p n 4 p n 5 n11
10. (22x)3 28x 3
1
18. }
p t 13 t 4
9
75
4. (28)2 216
7
7.3 Evaluate the expression.
2
44.
4
172
n1an-ep08-01-t
21
7. m 5 p m2 m
4
1
17. 79 p }
2
3. (22)3 p (22)6 (22) 9
6. (8 p 4)5 8 5 p 4 5
9. (y 3)5 y 15
x
21
42.
2. 6 p 67 6 8
6
20
58.
3
40
x
21
0
1
2
3
y
80
40
20
10
5
x
exponential; y 5 40 p 1 }1 2
x
x
21
0
1
2
3
y
1
0
1
4
9
60.
2
x
21
0
1
y
48
36
27
2
3
1
4
3
16
20​​​}​ 15​​​}​​
x
exponential; y 5 36 p 1 }3 2
not exponential
4
EP8
48.
1
y
21
n1an-ep08-07-t
x
49.
50.
y
51.
y
y
CS10_A1_MESE618203_C07EP.indd 8
3/19/11 12:39:13 AM
1
21
1
x
21
3
x
21
x
52–56. See Additional Answers.
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Extra Practice
Chapter 8
Find the sum or difference.
8.1 1. (6x 2 21 7) 1 (x 2 2 9)
2. (8y 2 223y 2 10) 1 (211y 2 1 2y 2 7)
23y 2 y 2 17
7x 2 2
3. (10m22 2 7m 1 2) 2 (3m2 2 2m 1 5)
7m 2 5m 2 3
5. (6b 3 1 12b 2 2 b) 2 (15b 2 1 7b 2 8)
6b3 2 3b 2 2 8b 1 8
Find the product.
8.2
7. 5x 4(2x 3 2 3x 2 1 5x 2 1)
10x 7 2 15x 6 1 25x 5 2 5x4
10. (2x 2 2 5x 1 6)(3x 2 2)
6x 3 2 19x 2 1 28x 2 12
8.3 13. (x2 1 10)2
x 1 20x 1 100
16. (3x 2 4y)(3x 1 4y)
9x 2 2 16y 2
8.4 Solve the equation.
4. (2t 3 2
3t 2 21 5t) 2 (6t 3 1 3t 2 2 5t)
3
24t 2 6t 1 10t
6. (r 2 2 8 1 4r 3 1 5r) 2 (7r 3 2 3r 2 1 5)
23r 3 1 4r 2 1 5r 2 13
8. (x 2 1 4x 1 2)(x 1 7)
9. (2x 1 3)(4x 1 2)
x 3 1 11x 2 1 30x 1 14
8x 2 1 16x 1 6
11. (3x 2 7)(x 1 5)
12. (9t 2 2)(2t 2 3)
14. (m 1 8)(m 2 8)
15. (4x 2 2)(4x 1 2)
17. (6 2 3t)(6 1 3t)
18. (211x 2 4y)2
19. (m 1 8)(m 2 2) 5 0 28, 2
20. (2y 2 6)(y 1 3) 5 0 63
21. (5y 2 3)(2y 2 4) 5 0 }, 2
22. 3b 2 1 9b 5 0 23, 0
23. 212m2 2 3m 5 0 2}4 , 0
3x 2 1 8x 2 35
18t 2 2 31t 1 6
2
16x 2 2 4
m 2 64
36 2 9t 2
121x 2 1 88xy 1 16y 2
1
3
5
24. 14k 2 5 28k 0, 2
8.5 Factor the trinomial.
25. y 2 1 7y 1 12 (y 1 3)(y 1 4)
26. x 2 2 12x 1 35 (x 2 7)(x 2 5) 27. x 2 1 5x 2 36 (x 2 4)(x 1 9)
28. q 2 1 3q 2 40
29. m2 2 29m 1 100
(q 2 5)(q 1 8)
8.5 Solve the equation.
30. y 2 1 14y 2 72
(m 2 25)(m 2 4)
31. m2 2 7m 1 10 5 0 2, 5
2
(y 2 4)(y 1 18)
32. p 2 2 7p 5 18 22, 9
33. z 2 2 13z 1 24 5 212 4, 9
2
34. n 1 8 5 6n 2, 4
35. r 2 15r 5 28r 2 10 2, 5
8.6 Factor the trinomial.
(3k 2 4)(k 2 2)
2(x 2 3)(x 2 2)
36. c 2 2 8 5 213c 1 6 214, 1
37. 2x 2 1 5x 2 6
38. 3k 2 2 10k 1 8
39. 4k 2 2 12k 1 5 (2k 2 1)(2k 2 5)
40. 6t 2 2 5t 2 6 (2t 2 3)(3t 1 2)
41. 23s 2 2 7s 2 2
42. 2v 2 2 5v 1 3 (2v 2 3)(v 2 1)
2(3s 1 1)(s 1 2)
8.6 Solve the equation.
2
3
43. 23x 2 1 14x 2 8 5 0 }, 4
4
3
46. 3p 2 2 28 5 17p 2}, 7
3 3
2 4
44. 8t 2 1 6t 5 9 2}, }
1
45. 2x 2 1 3x 2 2 5 0 22, }
1
47. 16m2 2 1 5 215m 21, }
48. t(6t 2 7) 5 3 2}, }
50. 9y 2 2 49 (3y 2 7)(3y 1 7)
51. 12y 2 2 27 3(2y 2 3)(2y 1 3)
53. 4x 2 2 12x 1 9 (2x 2 3) 2
54. 27x 2 2 36x 1 12 3(3x 2 2) 2
16
1 3
3 2
2
8.7 Factor the polynomial.
49. y 2 2 36 (y 1 6)(y 2 6)
52. x 2 2 8x 1 16 (x 2 4) 2
55. g 2 1 10g 1 25 (g 1 5)
2
56. 9b 2 1 24b 1 16 (3b 1 4)
8.8 Factor the polynomial completely.
(3z 2 1)(z 2 5)
2
2
57. 4w 2 1 28w 1 49 (2w 1 7)
(5m 2 3)(m 2 4)
58. 2x 2 1 8x 1 6 2(x 1 1)(x 1 3) 59. 3z 2 2 16z 1 5
60. 5m2 2 23m 1 12
61. 3y 3 1215y 2 1 2y 1 10
63. 98m 3 2 18m
(3y 1 2)(y 1 5)
64. 8h2k 2 32k
8k(h 2 2)(h 1 2)
62. 30z 3 2 14z 2 2 8z
2z(5z 2 4)(3z 1 1)
65. 2h 3 2 3h2 2 18h 1 27
(h 1 3)(h 2 3)(2h 2 3)
EP9
2m(7m 2 3)(7m 1 3)
66. 212z 3 1 12z 2 2 3z
23z(2z 2 1) 2
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Extra Practice
Chapter 9
9.1 Graph the function. Compare the graph with the graph of y 5 x 2. 1–8. See margin.
1–7. See Additional Answers.
8.
y
2
x
21
2
1. y 5 4x 2
2. y 5 25x 2
1 2
3. y 5 }
x
4. y 5 2}
x2
5
5. y 5 x 2 1 3
6. y 5 x 2 2 2
7. y 5 3x 2 1 4
8. y 5 24x 2 2 3
2
9.2 Graph the function. Label the vertex and axis of symmetry. 9–14. See margin.
9. y 5 x 2 1 4x 1 4
12. y 5 3x 2 1 12x 1 8
The graph is a vertical stretch by a
factor of 4, a reflection in the
x-axis, and a vertical translation of
3 units down of y 5 x 2 .
y
9.
13. y 5 22x 2 1 6
14. y 5 }x 2 2 3x
15. x 2 1 3x 2 10 5 0 25, 2
18. 2x 2 1 3x 2 20 5 0 24, }5
2
16. x 2 1 14 5 9x 2, 7
17. 2x 2 1 3x 5 218 23, 6
19. 2x 2 1 x 5 6 22, }3
1 2
20. }
x 2 x 5 12 24, 6
2
2
if necessary.
1
x
21. 2x 2 2 20 5 78 67
22. 3y 2 1 16 5 4 no solution
23. 16y 2 2 6 5 3 6 0.75
24. 48 2 x 2 5 252 610
25. 5m2 2 5 5 10 61.73
26. 2 2 5t 2 5 4 no solution
9.5 Solve the equation by completing the square. Round the solutions to the
x 5 22
10.
nearest hundredth, if necessary.
y
27. x 2 1 4x 2 21 5 0 27, 3
(21, 4)
28. g 2 2 10g 5 24 22, 12
29. 4m2 1 8m 2 7 5 0 22.66, 0.66
9.6 Use the quadratic formula to solve the equation. Round the solutions to the
n1an-ep10-09-t
nearest hundredth, if necessary.
1
x
22
30. h2 1 6h 2 72 5 0 212, 6
31. 3x 2 2 7x 1 2 5 0 0.33, 2
32. 2k 2 2 5k 1 2 5 0 0.5, 2
33. n2 1 1 5 5n 0.21, 4.79
34. 2z 1 4 5 3z 2 20.87, 1.54
35. 5x 2 2 4x 5 2 20.35, 1.15
9.7 Solve the system.
y
36. y 5 2 x 2 1 5x 2 4
2
3
37. y 5 }x 2 2 3x 2 1
y 5 2x 2 4 (0, –4) and (3, 2)
n1an-ep10-10-t
(, )
1
x5
12.
y 5 2x 2 1 (0, –1) and (3, –4)
y 5 2 4x 2 7 (–3, 5) and (–1, –3)
function, or a quadratic function. Then write an equation for the function. 39–42. See margin.
x
3
2
39.
y
41.
8
x 5 22
n1an-ep10-11-t
1
x
x
21
0
1
2
3
y
3
0
3
12
27
x
1
2
3
4
5
y
1
2
4
8
16
40.
42.
x
0
1
2
3
4
y
25
22
1
4
7
x
22
21
0
1
2
y
18
14
10
6
2
9.9 43. Linear Function 1 has equation 2x 2 5y 5 212. The graph of Linear
Function 2 contains (23, 23), (0, 2), (3, 7), and (6, 12). Which function is
increasing more rapidly? The slope of Linear Function 1 is }5, while the slope of Linear Function 2
2
5
EP10 is }. So Linear Function 1 is increasing more rapidly.
(22, 24)
(0, 6)
38. y 5 2 2x 2 1 4x 2 1
9.8 Tell whether the table of values represents a linear function, an exponential
3 1
2 2
21
13.
3
4
9.4 Solve the equation. Round the solutions to the nearest hundredth,
(22, 0) 21
11.
11. y 5 2x 2 2 6x 1 5
9.3 Solve the equation by graphing.
n1an-ep10-08-t
x 5 21
10. y 5 2x 2 2 2x 1 3
y
3
14.
x50
n1an-ep10-12-t
x 5 2 10
CS10_A1_MESE618203_C09EP.indd
1
21
39. quadratic function; y 5 3x 2
40. linear function; y 5 3x 2 5
41. exponential function;
y 5 0.5 p 2 x
42. linear function; y 5 24x 1 10
y
x
x
21
3/19/11 1:52:32 AM
22
(2, 23)
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Extra Practice
Chapter 10
Stem
6
7
8
9
10
9
–1
09
9
–9
10
0
90
9
–8
80
70
60
–6
9
4
2
0
–7
Frequency
1. population: parents or guardians
of high school students, sampling
method: systematic sample
2. Yes. Sample answer: The
sampling method might be biased
because only the parents or guardians of students are called and not
other spectators.
3. Potentially biased. Sample
answer: The question encourages
the listener to agree with the
researcher.
7. 6
10.1 In Exercises 1–3, use the following information.
1–3. See margin.
Some parents want to gather information about updating the sound system
in the high school auditorium. They obtain a list of high school students and
call the parents or guardians of every 20th student on the list. The question
they ask is “Don’t you think the sound system in the high school auditorium
needs updating?”
1. Identify the population and classify the sampling method.
2. Is the sampling method used likely to result in a biased sample? Explain.
3. Tell whether the question is potentially biased. Explain your answer.
10.2 4. The numbers of stories in ten of the world’s tallest buildings are given
below. Find the mean, median, mode(s), range, and mean absolute
deviation of the data. Round to the nearest hundredth, if necessary.
101, 88, 88, 108, 88, 88, 80, 69, 102, 78
mean: 89, median: 88, mode: 88, range: 39, mean absolute deviation: 8.8
10.3 In Exercises 5 and 6, use the given two-way table showing the side dish
chosen with the lunch plate and supper plate at a diner on one day.
Leaves
9
8
0 8 8 8 8
n1an-ep13-01-t
1 2 8
Key: 6⏐9 5 69
8.
Salad
Fries
Broccoli
Total
Lunch
26
47
9
82
Supper
42
29
34
105
Total
68
76
43
187
5. What was the most popular side at lunch? at dinner? overall? fries; salad; fries
60
72.5
85
69
80 88
n1an-ep13-02-t
97.5
110
6. About what percent of the total number of sides were salad or broccoli? about 59%
In Exercises 7 and 8, use the data in Exercise 4, above.
101 108
10.4
7. Make a histogram and a stem-and-leaf plot of the data. See margin.
10.5 8. Make a box-and-whisker plot of the data. Identify any outliers. See margin.
n1an-ep13-03-t
10.5 In Exercises 9 and 10, use the following information.
The box-and-whisker plot shows the maximum
elevations (in thousands of feet) in the top 13
U.S. states ranked by maximum elevation.
9. What is the median of the maximum
8
10
8.7
elevations in these states? 13,500 ft
12
14
12.7
13.5
16
14.4
18
20
22
20.3
10. What is the interquartile range of the maximum elevations in these
states?
1,700 ft
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Extra Practice
Chapter 11
11.1 In Exercises 1 and 2, use the following information. A bag contains 3 red,
3 blue, and 3 yellow marbles. You toss a coin and then draw a marble out of
the bag at random.
1. Find the number of possible outcomes in the sample space. Then list the
possible outcomes. 6 possible outcomes; heads, yellow; heads, red;
heads, blue; tails, yellow; tails, red; tails, blue
2. What is the probability that the coin shows tails and the marble is blue? }1
6
11.1 3. You toss a coin 3 times. What are the odds against the coin’s showing
heads twice and tails once? 5 : 3
11.2 4. In how many ways can you arrange the letters in the word SPRING? 720 ways
5. In how many ways can you arrange 3 of the letters in the word TULIP? 60 ways
11.2 Evaluate the expression.
6. 7! 5040
7. 8P 3 336
8.
P 720
9. 5P5 120
10 3
11.3 10. You can choose 3 books from a list of 5 books to read for English class.
How many combinations of 3 books are possible? 10 combinations
11. You are making a snack tray. You plan to choose 3 of 5 available types
of bread and 3 of 6 available types of cheese. How many different
combinations of bread and cheese are possible? 200
11.3 Evaluate the expression.
12. 6C2 15
13. 7C3 35
14.
C 210
10 4
15.
C
20 15
15,504
11.4 Events A and B are disjoint. Find P(A or B).
16. P(A) 5 0.4, P(B) 5 0.15 0.55
17. P(A) 5 0.3, P(B) 5 0.5 0.8
18. P(A) 5 0.7, P(B) 5 0.21 0.91
11.4 Find the indicated probability. State whether A and B are disjoint events.
19. P(A) 5 0.25
20. P(A) 5 0.52
21. P(A) 5 0.54
22.
P(B) 5 0.55
P(B) 5 0.15
P(B) 5 0.28
P(A or B) 5 ?
P(A or B) 5 0.67
P(A or B) 5 0.65
P(A and B) 5 0.2
P(A and B) 5 ?
P(A and B) 5 ?
0.6; not disjoint
0; disjoint
0.17; not disjoint
11.4 A card is randomly selected from a standard deck of 52 cards. Find the
probability of drawing the given card.
1
23. a jack and a club }
52
2
24. an ace or a 10 }
13
P(A) 5 0.5
P(B) 5 0.4
P(A or B) 5 ?
P(A and B) 5 0.3
0.6; not disjoint
4
25. a queen or a heart }
13
11.5 Events A and B are independent. Find the missing probability.
26. P(A) 5 0.8 0.2
P(B) 5 0.25
P(A and B) 5
? 0.125
P(B) 5 0.4
P(A and B) 5 0.05
27. P(A) 5
?
28. P(A) 5 0.9 0.3
P(B) 5 ?
P(A and B) 5 0.27
11.5 Events A and B are dependent. Find the missing probability.
29. P(A) 5 0.4 0.24
P(B | A) 5 0.6
P(A and B) 5
?
0.4
P(B | A) 5 0.75
P(A and B) 5 0.3
30. P(A) 5
?
31. P(A) 5 0.15 0.2
P(B | A) 5 ?
P(A and B) 5 0.03
EP12
CS10_A1_MESE618203_C11EP.indd 12
4/7/11 5:34:40 AM
EP12
CC13_A1_METE647067_C11EP.indd 12
6/4/11 3:52:40 PM