8. After the first step in solving
= x + 5, you
2
would have 2x + 4 = x + 10x + 25.
ANSWER: true
Study Guide and Review - Chapter 10
State whether each sentence is true or false . If
false , replace the underlined word, phrase,
expression, or number to make a true
sentence.
1. A triangle with sides having measures of 3, 4, and 6
is a right triangle.
ANSWER: false; sample answer 3, 4, and 5
2. The expressions
and
9. The converse of the Pythagorean Theorem is true.
ANSWER: true
10. The range of the function
is .
ANSWER: false;
are equivalent.
ANSWER: Graph each function. Compare to the parent
graph. State the domain and range.
11. y =
false;
– 3
ANSWER: translated down 3; D = {x|x ≥ 0}, R = {y|y ≥ –3}
3. The expressions 2 +
and are conjugates.
ANSWER: true
4. In the expression −5
, the radicand is 2.
ANSWER: true
5. The shortest side of a right triangle is the hypotenuse.
ANSWER: false; longest
12. y =
+ 2
ANSWER: translated up 2; D = {x|x ≥ 0}, R = {y|y ≥ 2}
6. The cosine of an angle is found by dividing the
measure of the side opposite to the angle by the
hypotenuse.
ANSWER: false; adjacent
7. The domain of the function
is .
ANSWER: false;
8. After the first step in solving
= x + 5, you
2
would have 2x + 4 = x + 10x + 25.
13. y = −5
ANSWER: stretched vertically and reflected across the x-axis;
D = {x|x ≥ 0}, R = {y|y ≤ 0}
ANSWER: true
9. The converse of the Pythagorean Theorem is true.
ANSWER: true
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10. The range of the function
Page 1
is .
Study Guide and Review - Chapter 10
13. y = −5
16. y =
ANSWER: stretched vertically and reflected across the x-axis;
D = {x|x ≥ 0}, R = {y|y ≤ 0}
14. y =
− 6
ANSWER: translated down 6; D = {x|x ≥ 0}, R = {y|y ≥ –6}
+ 5
ANSWER: translated up 5; D = {x|x ≥ 0}, R = {y|y ≥ 5}
17. GEOMETRY The function s =
can be used to
find the length of a side of a square given its area.
Use this function to determine the length of a side of
a square with an area of 90 square inches. Round to
the nearest tenth if necessary.
ANSWER: 9.5 in.
Simplify.
18. ANSWER: 15. y =
19. ANSWER: translated right 1; D = {x|x ≥ 1}, R = {y|y ≥ 0}
ANSWER: 20. ANSWER: 21. ANSWER: 36
16. y =
+ 5
ANSWER: translated up 5; D = {x|x ≥ 0}, R = {y|y ≥ 5}
22. ANSWER: eSolutions Manual - Powered by Cognero
Page 2
23. and d is the diameter of the storm in miles. A storm
is 10 miles in diameter. How long will it last?
21. ANSWER: about 2.15 hours or 2 hours and 9 minutes
ANSWER: Study
Guide and Review - Chapter 10
36
Simplify each expression.
22. 29. ANSWER: ANSWER: 23. 30. ANSWER: ANSWER: 24. 31. ANSWER: ANSWER: 32. ANSWER: 25. ANSWER: 33. ANSWER: 26. 34. ANSWER: ANSWER: −6 − 3
35. 27. ANSWER: ANSWER: 36. MOTION The velocity of a dropped object when it
hits the ground can be found using
, where
v is the velocity in feet per second, g is the
acceleration due to gravity, and d is the distance in
feet the object drops. Find the speed of a penny
when it hits the ground, after being dropped from 984
feet. Use 32 feet per second squared for g.
28. WEATHER To estimate how long a thunderstorm
will last, use
, where t is the time in hours
and d is the diameter of the storm in miles. A storm
is 10 miles in diameter. How long will it last?
ANSWER: about 250.95 ft/s
ANSWER: about 2.15 hours or 2 hours and 9 minutes
Solve each equation. Check your solution.
Simplify each expression.
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29. ANSWER: 37. Page 3
ANSWER: no solution
when it hits the ground, after being dropped from 984
feet. Use 32 feet per second squared for g.
be lengths of the sides of a right triangle.
44. 6, 8, 10
ANSWER: yes
ANSWER: Study
Guide and Review - Chapter 10
about 250.95 ft/s
Solve each equation. Check your solution.
45. 3, 4, 5
37. ANSWER: yes
ANSWER: no solution
46. 12, 16, 21
ANSWER: no
38. ANSWER: −41
47. 10, 12, 15
ANSWER: no
39. ANSWER: 32
48. 2, 3, 4
ANSWER: 49. 7, 24, 25
ANSWER: no
40. ANSWER: yes
50. 5, 12, 13
41. ANSWER: yes
ANSWER: 12
51. 15, 19, 23
42. ANSWER: no
ANSWER: 5
43. FREE FALL Assuming no air resistance, the time t
in seconds that it takes an object to fall h feet can be
determined by
52. LADDER A ladder is leaning on a building. The
base of the ladder is 10 feet from the building, and
the ladder reaches up 15 feet on the building. How
long is the ladder?
. If a skydiver jumps from an
ANSWER: 18.0 ft
airplane and free falls for 10 seconds before opening
the parachute, how many feet does she fall?
Find the values of the three trigonometric
ratios for angle A .
ANSWER: 1600 ft
Determine whether each set of measures can
be lengths of the sides of a right triangle.
44. 6, 8, 10
ANSWER: yes
53. ANSWER: 45. 3, 4, 5
ANSWER: yes
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46. 12, 16, 21
Page 4
ANSWER: Study Guide and Review - Chapter 10
54. ANSWER: 55. RAMPS How long is the ramp?
ANSWER: 6 ft
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