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 are equivalent.
ANSWER:
false;
3.The expressions 2 + and areconjugates.
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
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
would have 2x + 4 = x2 + 10x + 25.
ANSWER:
true
9.The converse of the Pythagorean Theorem is true.
ANSWER:
true
10.The range of the function is .
ANSWER:
false;
Graph each function. Compare to the parent
graph. State the domain and range.
11.y = – 3
ANSWER:
translated down 3; D = {x|x≥0},R={y|y≥–3}
12.y = +2
ANSWER:
translated up 2; D = {x|x≥0},R={y|y≥2}
13.y = −5
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}
15.y =
ANSWER:
translated right 1; D = {x|x≥1},R={y|y≥0}
16.y = +5
ANSWER:
translated up 5; D = {x|x≥0},R={y|y≥5}
17.GEOMETRY The function s = canbeusedto
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:
19.
ANSWER:
20.
ANSWER:
21.
ANSWER:
36
22.
ANSWER:
23.
ANSWER:
24.
ANSWER:
25.
ANSWER:
26.
ANSWER:
−6 − 3
27.
ANSWER:
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 2.15 hours or 2 hours and 9 minutes
Simplify each expression.
29.
ANSWER:
30.
ANSWER:
31.
ANSWER:
32.
ANSWER:
33.
ANSWER:
34.
ANSWER:
35.
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.
ANSWER:
about 250.95 ft/s
Solve each equation. Check your solution.
37.
ANSWER:
no solution
38.
ANSWER:
−41
39.
ANSWER:
32
40.
ANSWER:
41.
ANSWER:
12
42.
ANSWER:
5
43.FREEFALL Assuming no air resistance, the time t
in seconds that it takes an object to fall h feet can be
determined by . If a skydiver jumps from an
airplane and free falls for 10 seconds before opening
the parachute, how many feet does she fall?
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
45.3, 4, 5
ANSWER:
yes
46.12, 16, 21
ANSWER:
no
47.10, 12, 15
ANSWER:
no
48.2, 3, 4
ANSWER:
no
49.7, 24, 25
ANSWER:
yes
50.5, 12, 13
ANSWER:
yes
51.15, 19, 23
ANSWER:
no
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?
ANSWER:
18.0 ft
Find the values of the three trigonometric
ratios for angle A.
53.
ANSWER:
54.
ANSWER:
55.RAMPS How long is the ramp?
ANSWER:
6 ft
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 are equivalent.
ANSWER:
false;
3.The expressions 2 + and areconjugates.
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
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
would have 2x + 4 = x2 + 10x + 25.
ANSWER:
true
9.The converse of the Pythagorean Theorem is true.
ANSWER:
true
10.The range of the function is .
ANSWER:
false;
Graph each function. Compare to the parent
graph. State the domain and range.
11.y = – 3
ANSWER:
translated down 3; D = {x|x≥0},R={y|y≥–3}
12.y = +2
ANSWER:
translated up 2; D = {x|x≥0},R={y|y≥2}
13.y = −5
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}
15.y =
ANSWER:
translated right 1; D = {x|x≥1},R={y|y≥0}
16.y = +5
ANSWER:
translated up 5; D = {x|x≥0},R={y|y≥5}
17.GEOMETRY The function s = canbeusedto
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:
19.
ANSWER:
20.
ANSWER:
21.
ANSWER:
36
22.
ANSWER:
23.
ANSWER:
24.
ANSWER:
25.
ANSWER:
26.
ANSWER:
−6 − 3
27.
ANSWER:
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 2.15 hours or 2 hours and 9 minutes
Simplify each expression.
29.
ANSWER:
30.
ANSWER:
31.
ANSWER:
32.
ANSWER:
33.
ANSWER:
34.
ANSWER:
35.
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.
ANSWER:
about 250.95 ft/s
Solve each equation. Check your solution.
37.
ANSWER:
no solution
38.
ANSWER:
−41
39.
ANSWER:
32
40.
ANSWER:
41.
ANSWER:
12
42.
ANSWER:
5
43.FREEFALL Assuming no air resistance, the time t
in seconds that it takes an object to fall h feet can be
determined by . If a skydiver jumps from an
airplane and free falls for 10 seconds before opening
the parachute, how many feet does she fall?
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
45.3, 4, 5
ANSWER:
yes
46.12, 16, 21
ANSWER:
no
47.10, 12, 15
ANSWER:
no
48.2, 3, 4
ANSWER:
no
49.7, 24, 25
ANSWER:
yes
50.5, 12, 13
ANSWER:
yes
51.15, 19, 23
ANSWER:
no
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?
ANSWER:
18.0 ft
Find the values of the three trigonometric
ratios for angle A.
53.
ANSWER:
54.
ANSWER:
55.RAMPS How long is the ramp?
ANSWER:
6 ft
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Study Guide and Review - Chapter 10
