Download State whether each sentence is true or false . If false , replace the

solving
= x + 5, you would have 2x + 4 = x
+ 10x + 25. The statement is true.
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.
2. The expressions
and
are equivalent.
10. The range of the function
is .
SOLUTION: The range of the function
the statement is false.
is {y|y ≥ 0}. So, SOLUTION: ANSWER: false;
false;
ANSWER: Graph each function. Compare to the parent
graph. State the domain and range.
false;
12. y =
4. In the expression −5
2
, the radicand is 2.
SOLUTION: The expression under the radical sign is called the
radicand. In the expression
, the radicand is 2.
The statement is true.
ANSWER: true
+ 2
SOLUTION: Make a table.
x
0
0.5
y
2
≈ 2.7
1
3
2
≈ 3.4
3
≈ 3.7
4
4
Plot the points on a coordinate system and draw a
smooth curve that connects then.
6. The cosine of an angle is found by dividing the
measure of the side opposite to the angle by the
hypotenuse.
SOLUTION: The sine of an angle is found by dividing the measure
of the side opposite of the angle by the hypotenuse.
So, the statement is false. The cosine of an angle is
found by dividing the measure of the side adjacent
to the angle by the hypotenuse.
ANSWER: false; adjacent
8. After the first step in solving
= x + 5, you
2
would have 2x + 4 = x + 10x + 25.
SOLUTION: To solve
= x + 5, you first need to square
each side of the equation. After the first step in
2
solving
= x + 5, you would have 2x + 4 = x
+ 10x + 25. The statement is true.
The value 2 is being added to the parent function
, so the graph is translated up 2 units from
the parent graph
. Another way to identify
the translation is to note that the y-values in the table
are 2 greater than the corresponding y-values for the
parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ 2}.
ANSWER: translated up 2; D = {x|x ≥ 0}, R = {y|y ≥ 2}
ANSWER: true
10. The range of the function
is .
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SOLUTION: The range of the function
the statement is false.
Page 1
is {y|y ≥ 0}. So, the statement is false.
ANSWER: Study Guide and Review - Chapter 10
false;
Graph each function. Compare to the parent
graph. State the domain and range.
12. y =
− 6
SOLUTION: x
0
0.5
y
–6
≈ –
5.3
+ 2
SOLUTION: Make a table.
x
0
0.5
y
2
≈ 2.7
14. y =
1
3
2
≈ 3.4
3
≈ 3.7
1
–5
2
≈ –
4.6
3
≈ –
4.3
4
–4
4
4
Plot the points on a coordinate system and draw a
smooth curve that connects then.
The value 6 is being subtracted from the parent
function
, so the graph is translated down 6
The value 2 is being added to the parent function
, so the graph is translated up 2 units from
the parent graph
. Another way to identify
the translation is to note that the y-values in the table
are 2 greater than the corresponding y-values for the
parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ 2}.
units from the parent graph
. Another way to
identify the translation is to note that the y-values in
the table are 6 less than the corresponding y-values
for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ –6}.
ANSWER: translated down 6; D = {x|x ≥ 0}, R = {y|y ≥ –6}
ANSWER: translated up 2; D = {x|x ≥ 0}, R = {y|y ≥ 2}
16. y =
+ 5
SOLUTION: x
0
0.5
y
5
≈ 5.7
14. y =
1
6
2
≈ 6.4
3
≈ 6.7
4
7
− 6
SOLUTION: x
0
0.5
y
–6
≈ –
5.3
1
–5
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2
≈ –
4.6
3
≈ –
4.3
4
–4
The value 5 is being added to the parent function
Page 2
, so the graph is translated up 5 units from
the parent graph
. Another way to identify
ANSWER: Study Guide and Review - Chapter 10
16. y =
+ 5
SOLUTION: x
0
0.5
y
5
≈ 5.7
20. SOLUTION: 1
6
2
≈ 6.4
3
≈ 6.7
4
7
ANSWER: 22. SOLUTION: The value 5 is being added to the parent function
, so the graph is translated up 5 units from
the parent graph
. Another way to identify
the translation is to note that the y-values in the table
are 5 greater than the corresponding y-values for the
parent function. The domain is {x|x ≥ 0} and the range is {y|y ≥ 5}.
ANSWER: ANSWER: translated up 5; D = {x|x ≥ 0}, R = {y|y ≥ 5}
24. SOLUTION: Simplify.
18. SOLUTION: ANSWER: ANSWER: 26. SOLUTION: 20. eSolutions Manual - Powered by Cognero
SOLUTION: Page 3
0.15 = 9, 2.15 hours is equal to 2 hours and 9
minutes.
ANSWER: ANSWER: about 2.15 hours or 2 hours and 9 minutes
Study Guide and Review - Chapter 10
Simplify each expression.
26. 30. SOLUTION: SOLUTION: ANSWER: 32. SOLUTION: ANSWER: −6 − 3
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?
34. SOLUTION: SOLUTION: Substitution 10 for d. ANSWER: The storm will last about 2.15 hours. To convert 2.15
hours to hours and minutes, multiply the number of
minutes in an hour by the decimal part. Because 60 • 0.15 = 9, 2.15 hours is equal to 2 hours and 9
minutes.
ANSWER: about 2.15 hours or 2 hours and 9 minutes
Simplify each expression.
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.
SOLUTION: Substitute 32 for g and 984 for d. 30. SOLUTION: eSolutions
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Page 4
ANSWER: −41
ANSWER: Study Guide and Review - Chapter 10
36. MOTION The velocity of a dropped object when it
40. 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.
SOLUTION: SOLUTION: Substitute 32 for g and 984 for d. Check:
The speed of the penny when it hits the ground is
about 250.95 feet per second.
ANSWER: ANSWER: about 250.95 ft/s
Solve each equation. Check your solution.
42. 38. SOLUTION: SOLUTION: Check:
Check:
Because 10 does not satisfy the original equation, 5 is
the only solution.
ANSWER: −41
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40. SOLUTION: ANSWER: 5
Determine whether each set of measures can
be lengths of the sides of a right triangle. Page 5
44. 6, 8, 10
SOLUTION: Because 10 does not satisfy the original equation, 5 is
the only solution.
ANSWER: Study
Guide and Review - Chapter 10
5
2
2
ANSWER: no
Determine whether each set of measures can
be lengths of the sides of a right triangle.
44. 6, 8, 10
SOLUTION: Since the measure of the longest side is 10, let c =
2
10, a = 6, and b = 8. Then determine whether c =
2
2
a +b .
48. 2, 3, 4
SOLUTION: Since the measure of the longest side is 4, let c = 4, a
2
2
2
2
No, because c ≠ a + b , a triangle with side lengths
2, 3, and 4 is not a right triangle.
2
Yes, because c = a + b , a triangle with side
lengths 6, 8, and 10 is a right triangle.
ANSWER: no
ANSWER: yes
50. 5, 12, 13
46. 12, 16, 21
SOLUTION: Since the measure of the longest side is 21, let c =
2
21, a = 12, and b = 16. Then determine whether c =
2
2
= 2, and b = 3. Then determine whether c = a +
2
b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths
12, 16, and 21 is not a right triangle.
SOLUTION: Since the measure of the longest side is 13, let c =
2
13, a = 5, and b = 12. Then determine whether c =
2
2
a +b .
2
a +b .
2
2
2
Yes, because c = a + b , a triangle with side
lengths 5, 12, and 13 is a right triangle.
2
2
2
No, because c ≠ a + b , a triangle with side lengths
12, 16, and 21 is not a right triangle.
ANSWER: no
ANSWER: yes
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?
48. 2, 3, 4
SOLUTION: Since the measure of the longest side is 4, let c = 4, a
2
2
= 2, and b = 3. Then determine whether c = a +
2
b .
SOLUTION: Use the Pythagorean Theorem, substituting 10 for a
and 15 for b.
2
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No, because c ≠ a + b , a triangle with side lengths
2, 3, and 4 is not a right triangle.
Page 6
The ladder is approximately 18.0 feet long.
ANSWER: 2
2
2
Yes, because c = a + b , a triangle with side
lengths 5, 12, and 13 is a right triangle.
ANSWER: Study
Guide and Review - Chapter 10
yes
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?
SOLUTION: Use the Pythagorean Theorem, substituting 10 for a
and 15 for b.
The ladder is approximately 18.0 feet long.
ANSWER: 18.0 ft
Find the values of the three trigonometric
ratios for angle A .
54. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero
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