Download Simplify each expression. 11. x ⋅ x ⋅ x SOLUTION: ANSWER: x 12

ANSWER: Study Guide and Review - Chapter 7
6 4
36x y
Simplify each expression.
3
11. x ⋅ x ⋅ x
5
3 3 2
15. [(2r t) ]
SOLUTION: SOLUTION: ANSWER: x
9
ANSWER: 18 6
64r t
2 5
12. (2xy)( −3x y )
SOLUTION: 3
16. (−2u )(5u)
SOLUTION: ANSWER: ANSWER: 3 6
−6x y
−10u
4
4
5 2
13. (−4ab )(−5a b )
2 3
3 3
17. (2x ) (x )
SOLUTION: SOLUTION: ANSWER: 6 6
20a b
3 2 2
14. (6x y )
ANSWER: SOLUTION: 8x
3 3
18. ANSWER: 15
(2x )
SOLUTION: 6 4
36x y
3 3 2
15. [(2r t) ]
SOLUTION: ANSWER: 4x
9
eSolutions Manual - Powered by Cognero
Page 1
2
19. GEOMETRY Use the formula V = πr h to find the
volume of the cylinder.
ANSWER: ANSWER: Study Guide and Review - Chapter 7
15
8x
45πx
Simplify each expression. Assume that no
denominator equals zero.
3 3
18. 4
(2x )
20. SOLUTION: SOLUTION: ANSWER: 4x
9
2
19. GEOMETRY Use the formula V = πr h to find the
volume of the cylinder.
SOLUTION: ANSWER: 21. SOLUTION: ANSWER: 45πx
ANSWER: 4
Simplify each expression. Assume that no
denominator equals zero.
20. 22. SOLUTION: SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero
ANSWER: 4y
−3 0 6
23. a b c
Page 2
ANSWER: ANSWER: Study Guide and Review - Chapter 7
25. 22. SOLUTION: SOLUTION: ANSWER: 4y
ANSWER: −3 0 6
x
23. a b c
6
SOLUTION: 26. SOLUTION: ANSWER: 24. SOLUTION: ANSWER: 1
27. ANSWER: SOLUTION: 25. SOLUTION: ANSWER: eSolutions Manual - Powered by Cognero
3
2 Page
4
28. GEOMETRY The area of a rectangle is 25x y
square feet. The width of the rectangle is 5xy feet.
What is the length of the rectangle?
ANSWER: ANSWER: 3
Study Guide and Review - Chapter 7
2 4
28. GEOMETRY The area of a rectangle is 25x y
square feet. The width of the rectangle is 5xy feet.
What is the length of the rectangle?
31. SOLUTION: SOLUTION: ANSWER: 5
32. SOLUTION: 3
The length of the rectangle is 5xy ft.
ANSWER: 3
5xy ft
ANSWER: Simplify.
29. SOLUTION: 33. SOLUTION: ANSWER: 7
30. ANSWER: 64
SOLUTION: 34. ANSWER: 3
SOLUTION: 31. SOLUTION: ANSWER: 4
eSolutions Manual - Powered by Cognero
35. Page 4
ANSWER: Study
Guide and Review - Chapter 7
64
ANSWER: Solve each equation.
34. x
37. 6 = 7776
SOLUTION: SOLUTION: Therefore, the solution is 5.
ANSWER: 4
35. ANSWER: 5
4x – 1
SOLUTION: 38. 4
= 32
SOLUTION: ANSWER: 2401
Therefore, the solution is .
36. SOLUTION: ANSWER: Express each number in scientific notation.
39. 2,300,000
ANSWER: SOLUTION: 2,300,000 → 2.300000
The decimal point moved 6 places to the left, so n =
6.
6
2,300,000 = 2.3 × 10
Solve each equation.
x
37. 6 = 7776
SOLUTION: Therefore,
solution
is 5.
eSolutions
Manual -the
Powered
by Cognero
ANSWER: 5
ANSWER: 6
2.3 × 10
40. 0.0000543
SOLUTION: 0.0000543 → 5.43
The decimal point moved 5 places to the right, so n =
–5.
−5
0.0000543 = 5.43 × 10
ANSWER: −5
Page 5
In scientific notation, the ratio of Earth’s diameter to
6
2,300,000 = 2.3 × 10
−2
Jupiter’s diameter is about 9.1 × 10 .
ANSWER: Study
Guide6 and Review - Chapter 7
2.3 × 10
40. 0.0000543
SOLUTION: 0.0000543 → 5.43
The decimal point moved 5 places to the right, so n =
–5.
−5
0.0000543 = 5.43 × 10
ANSWER: 5.43 × 10
−5
41. ASTRONOMY Earth has a diameter of about
8000 miles. Jupiter has a diameter of about 88,000
miles. Write in scientific notation the ratio of Earth’s
diameter to Jupiter’s diameter.
ANSWER: −2
about 9.1 × 10
Graph each function. Find the y-intercept, and
state the domain and range.
x
42. y = 2
SOLUTION: Complete a table of values for –2 < x < 2. Connect
the points on the graph with a smooth curve. x
x
y
2
2
–1
2
0
2
1
2
2
2
SOLUTION: 3
Earth: 8000 = 8.0 × 10
4
Jupiter: 88,000 = 8.8 × 10
In scientific notation, the ratio of Earth’s diameter to
−2
Jupiter’s diameter is about 9.1 × 10 .
ANSWER: −2
about 9.1 × 10
Graph each function. Find the y-intercept, and
state the domain and range.
–2
–2
–1
0
1
1
2
2
4
The graph crosses the y-axis at 1. The domain is all
real numbers, and the range is all real numbers
greater than 0.
ANSWER: 1; D = all real numbers;
R = {y| y > 0}
x
42. y = 2
SOLUTION: Complete a table of values for –2 < x < 2. Connect
the points on the graph with a smooth curve. x
x
y
2
–2
–2
2
–1
2
0
2
1
2
–1
x
43. y = 3 + 1
0
1
1
2
2 - Powered by22Cognero
eSolutions Manual
4
SOLUTION: Complete a table of values for –2 < x < 2. Connect
the points on the graph with a smooth curve. Page 6
x
x
y
3 +1
–2
–2
3
+1
Study Guide and Review - Chapter 7
x
x
43. y = 3 + 1
44. y = 4 + 2
SOLUTION: Complete a table of values for –2 < x < 2. Connect
the points on the graph with a smooth curve. x
x
y
3 +1
–2
+1
–2
4
–1
+1
–1
4
0
4 +2
1
4 +2
2
4 +2
–2
3
–1
3
0
3 +1
1
2
SOLUTION: Complete a table of values for –2 < x < 2. Connect
the points on the graph with a smooth curve. x
x
y
4 +2
0
2
1
4
2
10
3 +1
3 +1
The graph crosses the y-axis at 2. The domain is all
real numbers, and the range is all real numbers
greater than 1.
ANSWER: 2; D = all real numbers;
R = {y| y >1}
–2
–1
+2
+2
0
3
1
6
2
18
The graph crosses the y-axis at 3. The domain is all
real numbers, and the range is all real numbers
greater than 2.
ANSWER: 3; D = all real numbers;
R = {y| y > 2}
x
44. y = 4 + 2
x
SOLUTION: Complete a table of values for –2 < x < 2. Connect
the points on the graph with a smooth curve. x
x
y
4 +2
–2
–2
eSolutions Manual - Powered4by Cognero
+2
–1
–1
4
+2
45. y = 2 − 3
SOLUTION: Complete a table of values for –2 < x < 2.
Connect the points on the graph with a smooth
curve. x
x
2 –3
–2
2
–2
–3
y
Page 7
Study Guide and Review - Chapter 7
x
45. y = 2 − 3
SOLUTION: Complete a table of values for –2 < x < 2.
Connect the points on the graph with a smooth
curve. x
x
2 –3
–2
2
–1
2
0
2 –3
1
2 –3
2
2 –3
–2
–3
–1
–3
y
0
–2
1
–1
2
1
46. BIOLOGY The population of bacteria in a petri
dish increases according to the model p = 550(2.7)
0.008t
, where t is the number of hours and t = 0
corresponds to 1:00 P.M. Use this model to estimate
the number of bacteria in the dish at 5:00 P.M.
SOLUTION: If t = 0 corresponds to 1:00 P.M, then t = 4
represents 5:00 P.M.
There will be about 568 bacteria in the dish at 5:00
P.M.
ANSWER: about 568
47. Find the final value of $2500 invested at an interest
rate of 2% compounded monthly for 10 years.
SOLUTION: Use the equation for compound interest, with P =
2500, r = 0.02, n = 12, and t = 10.
The graph crosses the y-axis at –2. The domain is all
real numbers, and the range is all real numbers
greater than –3.
ANSWER: −2; D = all real numbers;
R = {y| y > −3}
The final value of the investment is about $3053.00.
ANSWER: $3053.00
46. BIOLOGY The population of bacteria in a petri
dish increases according to the model p = 550(2.7)
0.008t
, where t is the number of hours and t = 0
corresponds to 1:00 P.M. Use this model to estimate
the number of bacteria in the dish at 5:00 P.M.
48. COMPUTERS Zita’s computer is depreciating at a
rate of 3% per year. She bought the computer for
$1200.
a. Write an equation to represent this situation.
b. What will the computer’s value be after 5 years?
SOLUTION: a. Use the equation for exponential decay, with a =
1200 and r = 0.03.
eSolutions
Manual - Powered by Cognero
SOLUTION: If t = 0 corresponds to 1:00 P.M, then t = 4
represents 5:00 P.M.
Page 8
The equation that represents the depreciation of
t
The final value of the investment is about $3053.00.
ANSWER: Study
Guide and Review - Chapter 7
$3053.00
48. COMPUTERS Zita’s computer is depreciating at a
rate of 3% per year. She bought the computer for
$1200.
a. Write an equation to represent this situation.
b. What will the computer’s value be after 5 years?
SOLUTION: a. Use the equation for exponential decay, with a =
1200 and r = 0.03.
The equation that represents the depreciation of
t
Zita’s computer is y = 1200(1 − 0.03) .
b. Substitute 5 for t and solve.
–1.
ANSWER: −1, 1, −1
50. 3, 9, 27 ...
SOLUTION: Calculate the common ratio.
The common ratio is 3. Multiply each term by the
common ratio to find the next three terms.
27 × 3 = 81
81 × 3 = 243
243 × 3 = 729
The next three terms of the sequence are 81, 243,
and 729.
ANSWER: 81, 243, 729
51. 256, 128, 64, ...
After 5 years, Zita’s computer value is about
$1030.48.
SOLUTION: Calculate the common ratio.
ANSWER: t
a. 1200(1 − 0.03)
b. $1030.48
Find the next three terms in each geometric
sequence.
49. −1, 1, −1, 1, ...
SOLUTION: Calculate the common ratio.
The common ratio is –1. Multiply each term by the
common ratio to find the next three terms.
1 × –1 = –1
–1 × –1 = 1
1 × –1 = –1
The next three terms of the sequence are –1, 1, and
–1.
ANSWER: −1, 1, −1
The common ratio is
. Multiply each term by the
common ratio to find the next three terms.
64 × = 32
32 × = 16
16 × = 8
The next three terms of the sequence are 32, 16, and
8.
ANSWER: 32, 16, 8
Write the equation for the nth term of each
geometric sequence.
52. −1, 1, −1, 1, ...
SOLUTION: The first term of the sequence is –1. So, a 1 = –1.
Calculate the common ratio.
50. 3, 9, 27 ...
SOLUTION: Calculate
common
ratio.
eSolutions
Manualthe
- Powered
by Cognero
The common ratio is –1. So, r = –1.
Page 9
The next three terms of the sequence are 32, 16, and
8.
ANSWER: Study
Guide and Review - Chapter 7
32, 16, 8
Write the equation for the nth term of each
geometric sequence.
52. −1, 1, −1, 1, ...
SOLUTION: The first term of the sequence is –1. So, a 1 = –1.
Calculate the common ratio.
The common ratio is –1. So, r = –1.
ANSWER: n−1
a n = 3(3)
54. 256, 128, 64, ...
SOLUTION: The first term of the sequence is 256. So, a 1 = 256.
Calculate the common ratio.
The common ratio is
. So, r =
.
ANSWER: ANSWER: n−1
a n = −1(−1)
53. 3, 9, 27, ...
SOLUTION: The first term of the sequence is 3. So, a 1 = 3.
Calculate the common ratio.
The common ratio is 3. So, r = 3.
ANSWER: n−1
a n = 3(3)
54. 256, 128, 64, ...
SOLUTION: The first term of the sequence is 256. So, a 1 = 256.
Calculate the common ratio.
The common ratio is
. So, r =
eSolutions Manual - Powered by Cognero
ANSWER: .
Page 10