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

SOLUTION: In a right triangle, the side opposite the right angle is
the hypotenuse. This side is always the longest. So,
the statement is false. The longest side of a right
triangle is the hypotenuse.
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.
SOLUTION: 2
If a, b, and c are the sides of a right triangle, then c
2
2
2
= a + b , where c is the greatest number. Since 6
2
2
2
2
2
= 36 and 3 + 4 = 25, 6 ≠ 3 + 4 . Thus, a triangle
with sides having measures of 3, 4, and 6 is not a
2
2
right triangle. So, the statement is false. Since 3 + 4
2
= 25 and 5 = 25, a triangle with sides having
measures of 3, 4, and 5 would be a right triangle.
2. The expressions
and
are equivalent.
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.
7. The domain of the function
is .
SOLUTION: The domain of the function
the statement is false.
is {x|x ≥ 0}. So, 8. After the first step in solving
= x + 5, you
2
would have 2x + 4 = x + 10x + 25.
SOLUTION: SOLUTION: false;
To solve
= x + 5, you first need to square
each side of the equation. After the first step in
3. The expressions 2 +
and are conjugates.
SOLUTION: Binomials of the form
and are called conjugates. So, the binomials and are conjugates. The statement is
true.
4. In the expression −5
solving
= x + 5, you would have 2x + 4 = x
+ 10x + 25. The statement is true.
2
9. The converse of the Pythagorean Theorem is true.
SOLUTION: 2
2
2
If c ≠ a + b , then the triangle is not a right
triangle. So, the converse of the Pythagorean
Theorem is true. The statement is true.
, 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.
5. The shortest side of a right triangle is the hypotenuse.
SOLUTION: In a right triangle, the side opposite the right angle is
the hypotenuse. This side is always the longest. So,
the statement is false. The longest side of a right
triangle is the hypotenuse.
6. The cosine of an angle is found by dividing the
measure of the side opposite to the angle by the
hypotenuse.
SOLUTION: The Manual
sine of- an
anglebyisCognero
found by dividing the measure
eSolutions
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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
10. The range of the function
is .
SOLUTION: The range of the function
the statement is false.
is {y|y ≥ 0}. So, Graph each function. Compare to the parent
graph. State the domain and range.
11. y =
+ 3
SOLUTION: Make a table.
x
0
0.5
3
≈ 3.7
y
1
4
2
≈ 4.4
3
≈ 4.7
4
5
Page
Plot the points on a coordinate systems and draw
a1
smooth curve that connects them.
10. The range of the function
is .
SOLUTION: The
rangeand
of the
function
Study
Guide
Review
- Chapter is {y|y ≥ 0}. So, 10
the statement is false.
Graph each function. Compare to the parent
graph. State the domain and range.
11. y =
12. y =
+ 2
SOLUTION: Make a table.
x
0
0.5
y
2
≈ 2.7
+ 3
SOLUTION: Make a table.
x
0
0.5
3
≈ 3.7
y
the translation is to note that the y-values in the table
are 3 more than the corresponding y-values for the
parent function. The domain is {x | x ≥ 0} and the range is {y | y ≥ 3}.
1
4
2
≈ 4.4
3
≈ 4.7
4
5
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.
Plot the points on a coordinate systems and draw a
smooth curve that connects them.
The value 2 is being added to the parent function
, so the graph is translated up 2 units from
The value 3 is being added to the parent function
, so the graph is translated up 3 units from
the parent graph
. Another way to identify
the translation is to note that the y-values in the table
are 3 more than the corresponding y-values for the
parent function. The domain is {x | x ≥ 0} and the range is {y | y ≥ 3}.
12. y =
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}.
13. y = −5
SOLUTION: x
0
y
0
0.5
≈ –3.5
1
–5
2
≈ –7.1
+ 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.
The parent function
is multiplied by a value
less than 1, so the graph is a vertical stretch of
and a reflection across the x-axis. Another
way to identify the stretch is to notice that the yvalues in the table are –5 times the corresponding yvalues for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≤ 0}.
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Page 2
14. y =
− 6
SOLUTION: 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
Study
Guide
and Review
- Chapter
10
parent
function.
The domain
is {x|x ≥ 0} and the range is {y|y ≥ 2}.
13. y = −5
15. y =
SOLUTION: x
0
y
0
0.5
≈ –3.5
1
–5
2
≈ –7.1
The parent function
is multiplied by a value
less than 1, so the graph is a vertical stretch of
and a reflection across the x-axis. Another
way to identify the stretch is to notice that the yvalues in the table are –5 times the corresponding yvalues for the parent function. The domain is {x|x ≥ 0} and the range is {y|y ≤ 0}.
14. y =
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}.
− 6
SOLUTION: x
0
0.5
y
–6
≈ –
5.3
1
–5
2
≈ –
4.6
3
≈ –
4.3
4
–4
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}.
15. y =
2
1
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3
≈ 1.4
4
≈ 1.7
2
1
3
≈ 1.4
4
≈ 1.7
The value 1 is being subtracted from the square root
of the parent function
, so the graph is
translated 1 unit right from the parent graph
.
Another way to identify the translation is to note that
the x-values in the table are 1 more than the
corresponding x-values for the parent function. The
domain is {x|x ≥ 1}, and the range is {y|y ≥ 0}.
16. y =
The value 6 is being subtracted from the parent
function
, so the graph is translated down 6
SOLUTION: x
1
1.5
y
0
≈ 0.7
SOLUTION: x
1
1.5
y
0
≈ 0.7
+ 5
SOLUTION: x
0
0.5
y
5
≈ 5.7
1
6
2
≈ 6.4
3
≈ 6.7
4
7
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}.
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.
SOLUTION: Page 3
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
Study
Guide
and Review
- Chapter
10
parent
function.
The domain
is {x|x ≥ 0} and the range is {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.
22. SOLUTION: SOLUTION: 23. SOLUTION: The side length of the square is about 9.5 inches.
Simplify.
18. SOLUTION: 24. SOLUTION: 19. SOLUTION: 20. SOLUTION: 25. SOLUTION: 21. SOLUTION: 22. eSolutions Manual - Powered by Cognero
SOLUTION: Page 4
Study Guide and Review - Chapter 10
27. 25. SOLUTION: SOLUTION: 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?
SOLUTION: Substitution 10 for d. 26. SOLUTION: 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.
Simplify each expression.
29. SOLUTION: 27. SOLUTION: 30. SOLUTION: eSolutions Manual - Powered by Cognero
Page 5
SOLUTION: Study Guide and Review - Chapter 10
36. MOTION The velocity of a dropped object when it
30. 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. 31. SOLUTION: 32. SOLUTION: The speed of the penny when it hits the ground is
about 250.95 feet per second.
Solve each equation. Check your solution.
33. 37. SOLUTION: SOLUTION: 34. SOLUTION: Because the square root of a number cannot be
negative, there is no solution.
38. SOLUTION: 35. SOLUTION: 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
whenManual
it hits- Powered
the ground,
after being dropped from 984
eSolutions
by Cognero
feet. Use 32 feet per second squared for g.
SOLUTION: Check:
Page 6
Because the square root of a number cannot be
Study
Guide there
and Review
- Chapter 10
negative,
is no solution.
38. 40. SOLUTION: SOLUTION: Check:
Check:
41. SOLUTION: 39. SOLUTION: Check:
Check:
Because 5 does not satisfy the original equation, 12 is
the only solution.
40. SOLUTION: 42. SOLUTION: eSolutions Manual - Powered by Cognero
Check:
Page 7
Check:
Because
doesReview
not satisfy
the original
Study
Guide5and
- Chapter
10 equation, 12 is
the only solution.
The skydiver will fall 1600 feet before opening the
parachute.
Determine whether each set of measures can
be lengths of the sides of a right triangle.
44. 6, 8, 10
42. SOLUTION: 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 .
Check:
2
2
2
Yes, because c = a + b , a triangle with side
lengths 6, 8, and 10 is a right triangle.
45. 3, 4, 5
Because 10 does not satisfy the original equation, 5 is
the only solution.
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
SOLUTION: Since the measure of the longest side is 5, let c = 5, a
2
2
= 3, and b = 4. Then determine whether c = a +
2
b .
. If a skydiver jumps from an
airplane and free falls for 10 seconds before opening
the parachute, how many feet does she fall?
SOLUTION: Substitute 10 for t. 2
2
2
Yes, because c = a + b , a triangle with side
lengths 3, 4, and 5 is a right triangle.
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
a +b .
2
The skydiver will fall 1600 feet before opening the
parachute.
Determine whether each set of measures can
right triangle.
44. 6, 8, 10
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be lengths
of the sides
of a
SOLUTION: 2
2
No, because c ≠ a + b , a triangle with side lengths
12, 16, and 21 is not a right triangle.
47. 10, 12, 15
SOLUTION: Since the measure of the longest side is 15, let c Page
= 8
2
15, a = 10, and b = 12. Then determine whether c =
2
2
a +b .
2
2
2
No,
because
, a triangle
Study
Guide
andc Review
10with side lengths
≠ a + -bChapter
12, 16, and 21 is not a right triangle.
47. 10, 12, 15
2
a +b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths
10, 12, and 15 is not a right triangle.
48. 2, 3, 4
2
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
2
2
Yes, because c = a + b , a triangle with side
lengths 5, 12, and 13 is a right triangle.
51. 15, 19, 23
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 .
2
2
2
No, because c ≠ a + b , a triangle with side lengths
2, 3, and 4 is not a right triangle.
49. 7, 24, 25
SOLUTION: Since the measure of the longest side is 25, let c =
2
25, a = 7, and b = 24. Then determine whether c =
2
2
50. 5, 12, 13
SOLUTION: Since the measure of the longest side is 15, let c =
2
15, a = 10, and b = 12. Then determine whether c =
2
2
Yes, because c = a + b , a triangle with side
lengths 7, 24, and 25 is a right triangle.
2
a +b .
2
2
SOLUTION: Since the measure of the longest side is 23, let c =
2
23, a = 15, and b = 19. Then determine whether c =
2
2
a +b .
2
2
2
No, because c ≠ a + b , a triangle with side lengths
15, 19, and 23 is not a right triangle.
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.
2
Yes, because c = a + b , a triangle with side
lengths 7, 24, and 25 is a right triangle.
50. 5, 12, 13
The ladder is approximately 18.0 feet long.
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
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Find the values of the three trigonometric
ratios for angle A .
Page 9
Study Guide and Review - Chapter 10
The ladder is approximately 18.0 feet long.
Find the values of the three trigonometric
ratios for angle A .
55. RAMPS How long is the ramp?
53. SOLUTION: SOLUTION: You know the measure of the side opposite the angle
and the measure of the angle. Use the sine ratio.
The ramp is 6 feet long.
54. SOLUTION: 55. RAMPS How long is the ramp?
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SOLUTION: You know the measure of the side opposite the angle
Page 10