Solution Manual for Algebra for College Students, 8th Edition

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I NSTRUCTOR ’ S
S OLUTIONS M ANUAL
D ANIEL S. M ILLER
Niagara County Community College
A LGEBRA
FOR C OLLEGE S TUDENTS
EIGHTH EDITION
Robert Blitzer
Miami Dade College

TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
ALGEBRA FOR COLLEGE STUDENTS
Chapter 1: Algebra, Mathematical Models, and Problem Solving 1
Chapter 2: Functions and Linear Functions 67
Chapter 3: Systems of Linear Functions 131
Chapter 4: Inequalities and Problem Solving 251
Chapter 5: Polynomials, Polynomial Functions, and Factoring 331
Chapter 6: Rational Expressions, Functions, and Equations 423
Chapter 7: Radicals, Radical Functions, and Rational Exponents 587
Chapter 8: Quadratic Equations and Functions 677
Chapter 9: Exponential and Logarithmic Functions 839
Chapter 10: Conic Sections and Systems of Nonlinear Equations 943
Chapter 11: More on Polynomial and Rational Functions 1051
Chapter 12: Sequences, Induction, and Probability 1135

Chapter 1
Algebra, Mathematical Models, and Problem Solving
1
1.1 Check Points
1. a.

eight times a number five more
8 5 8 5x x  

b.

the quotient of a decreased bynumber and seven twice the number
2 2
7 7
x x
x x  

2.
replace with 10
23 0.12
23 0.12(10)
23 1.2
21.8
x
x
 
 


At age 10, the average neurotic level is 21.8.
3.
replace with 13
2
2
2
8 6( 3)
8 6(13 3)
8 6(10)
8 6(100)
8 600
608
x
x 
  
 
 
 


4. a. 2010 is 10 years after 2000.
replace with 10
2
2
46 541 17,650
46(10) 541(10) 17,650
46(100) 541(10) 17,650
4600 5410 17,650
27,660
x
D x x
D
  
  
  
  


The formula indicates that the mean student-loan
debt for college students who graduated in 2010
was $27,660.
b. The model value, $27,660, is more than the
actual data value, $26,682. Thus, the
mathematical model overestimates by $978.
5. a. true; Because the number 13 is an element of the
set of integers.
b. true; Because 6 is not an element of
{7, 8, 9, 10}, the statement is true.
6. a. 8 is less than 2; true
b. 7 is greater than 3; true
c. 1 is less than or equal to 4; false
d. 5 is greater than or equal to 5; true
e. 2 is greater than or equal to 14; true
7. a.  2 5x x 

Section 1.1 Algebraic Expressions, Real Numbers, and Interval Notation
3
48. false;
π is a real number.
49. –6 is less than –2; true
50. –7 is less than –3; true
51. 5 is greater than –7; true
52. 3 is greater than –8; true
53. 0 is less than –4; false. 0 is greater than –4.
54. 0 is less than –5; false. 0 is greater than –5.
55. –4 is less than or equal to 1; true
56. –5 is less than or equal to 1; true
57. –2 is less than or equal to –6; false. –2 is greater
than –6.
58. –3 is less than or equal to –7; false. –3 is greater
than –7.
59. –2 is less than or equal to –2; true
60. –3 is less than or equal to –3; true
61. –2 is greater than or equal to –2; true
62. –3 is greater than or equal to –3; true
63. 2 is less than or equal to 1
2
 ; false. 2 is greater
than 1
2
 .
64. 4 is less than or equal to 1
2
 ; false. 4 is greater
than 1
2
 .
65.  1 6x x 
66.  2 4x x  
67.  5 2x x  
68.  4 3x x  
69.  3 1x x  
70.  2 5x x  
71.  2x x 
72.  3x x 
73.  3x x  
74.  5x x  
75.  3x x 
76.  2x x 
77.  5.5x x 
78.  3.5x x 
79. true
80. true
81. false;    

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Section 1.3 Graphing Equations
13
1.3 Check Points
1.
2. Make a table:
2
2
2
2
2
2
2
2
1 ( , )
3 1 ( 3) 8 ( 3, 8)
2 1 ( 2) 3 ( 2, 3)
1 1 ( 1) 0 ( 1, 0)
0 1 (0) 1 (0,1)
1 1 (1) 0 (1, 0)
2 1 (2) 3 (2, 3)
3 1 (3) 8 (3, 8)
x y x x y
y
y
y
y
y
y
y
= −
− = − − = − − −
− = − − = − − −
− = − − = −
= − =
= − =
= − = − −
= − = − −
3. Make a table:
1 ( , )
4 4 1 3 3 ( 4,3)
3 3 1 2 2 ( 3, 2)
2 2 1 1 1 ( 2,1)
1 1 1 0 0 ( 1,0)
0 0 1 1 1 (0,1)
1 1 1 2 2 (1, 2)
2 2 1 3 3 (2,3)
x y x x y
y
y
y
y
y
y
y
 
       
       
       
     

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Chapter 1 Algebra, Mathematical Models, and Problem Solving
14
1.3 Exercise Set
1. – 10.
11. x  ,x y
−3  3,5
−2  2, 0
−1  1, 3 
0  0, 4
1  1, 3
2  2,0
3  3,5
12. x  ,x y
−3  3, 0
−2  2, 5 
−1  1, 8 
0  0, 9
1  1, 8
2  2, 5
3  3, 0
13. x  ,x y
−3  3, 5 
−2  2, 4 
−1  1, 3 
0  0, 2
1  1, 1
2  2,0
3  3,1

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Section 1.3 Graphing Equations
15
14. x  ,x y
−3  3, 1 
−2  2, 0
−1  1,1
0  0, 2
1  1,3
2  2, 4
3  3,5
15. x  ,x y
−3  3, 5 
−2  2, 3 
−1  1, 1 
0  0,1
1  1,3
2  2,5
3  3, 7
16. x  ,x y
−3  3, 10 
−2  2, 8 
−1  1, 6 
0  0, 4
1  1, 2
2  2,0
3  3, 2
17. x  ,x y
−3 3
3, 2
 
  
−2  2,1
−1 1
1, 2
 
  
0  0,0
1 1
1, 2
 
 

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Chapter 1 Algebra, Mathematical Models, and Problem Solving
16
18. x  ,x y
−3 7
3, 2
 
  
−2  2,3
−1 5
1, 2
 
  
0  0, 2
1 3
1, 2
 
  
2  2,1
3 1
3, 2
 
  
19. x  ,x y
−3  3, 4
−2  2,3
−1  1, 2
0  0,1
1  1, 2
2  2,3
3  3, 4
20. x  ,x y
−3  3, 2
−2  2,1
−1  1, 0
0  0, 1
1  1,0
2  2,1
3  3, 2
21. x  ,x y
−3  3, 6
−2  2, 4
−1  1, 2
0  0,0
1  1, 2
2  2, 4
3  3, 6

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Section 1.3 Graphing Equations
17
22. x  ,x y
−3  3, 6 
−2  2, 4 
−1  1, 2 
0  0,0
1  1, 2
2  2, 4
3  3, 6
23. ( , )
3 ( 3, 9)
2 ( 2, 4)
1 ( 1, 1)
0 (0,0)
1 (1, 1)
2 (2, 4)
3 (3, 9)
x x y
  
  
  



24. ( , )
9
3 ( 3, )
2
2 ( 2, 2)
1
1 ( 1, )
2
0 (0,0)
1
1 (1, )
2
2 (2, 2)
9
3 (3, )
2
x x y
  
  
  



25. ( , )
3 ( 3, 27)
2 ( 2, 8)
1 ( 1, 1)
0 (0,0)
1 (1,1)
2 (2,8)
3 (3, 27)
x x y
  
  
  

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Chapter 1 Algebra, Mathematical Models, and Problem Solving
18
26. x  ,x y
−3  3, 28 
−2  2, 9 
−1  1, 2 
0  0, 1
1  1,0
2  2,7
3  3, 26
27. [–5, 5, 1] by [–5, 5, 1]
This matches graph c.
28. [–10, 10, 2] by [– 4, 4, 2]
This matches graph d.
29. [–20, 80, 10] by [–30, 70, 10]
This matches graph b.
30. [–40, 40, 20] by [–1000, 1000, 100]
This matches graph a.
31. The equation that corresponds to 2Y in the table is
(c), 2 2y x  . We can tell because all of the
points ( 3,5) , ( 2, 4) , ( 1,3) , (0, 2) , (1,1) ,
(2,0) , and (3, 1) are on the line 2y x  , but all
are not on any of the others.
32. The equation that corresponds to 1Y in the table is
(b), 2
1y x . We can tell because all of the points
( 3,9) , ( 2, 4) , ( 1,1) , (0,0) , (1,1) , (2, 4) , and
(3,9) are on the graph 2
y x , but all are not on
any of the others.
33. No. It passes through the point (0, 2) .
34. Yes. It passes through the point (0,0) .
35. (2,0)
36. (0, 2)
37. The graphs of 1Y and 2Y intersect at the points
( 2, 4) and (1,1) .
38. The values of 1Y and 2Y are the same when
2x   and 1x  .
39. 2 4y x 
40. 4

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Section 1.3 Graphing Equations
19
41. 2
3y x 
42. 2 2y x 
43. ( , )
3 ( 3,5)
2 ( 2,5)
1 ( 1,5)
0 (0,5)
1 (1,5)
2 (2,5)
3 (3,5)
x x y
 
 
 
44. ( , )
3 ( 3, 1)
2 ( 2, 1)
1 ( 1, 1)
0 (0, 1)
1 (1, 1)
2 (2, 1)
3 (3, 1)
x x y
  
  
  




45.
 
 
( , )
1
2 2, 2
1 1, 1
1 1 , 2
2 2
1 1 , 3
3 3
1 1 ,3
3 3
1 1 , 2
2 2
1 1,1
1
2 2, 2
x x y
 
    
  
 
    
 
    
 
  
 
  
 
  

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Chapter 1 Algebra, Mathematical Models, and Problem Solving
20
46.
 
 
( , )
1
2 2, 2
1 1,1
1 1 , 2
2 2
1 1 ,3
3 3
1 1 , 3
3 3
1 1 , 2
2 2
1 1, 1
1
2 2, 2
x x y
 
   
 
 
   
 
   
 
  
 
  

 
  
47. The greatest percentage of the U.S. population that
used the internet was 84%, in 2013.
48. The least percentage of the U.S. population that
used the internet was 70%, in 2011.
49. The percentage of the U.S. population that used the
internet remained constant in 2009 and 2010 at
71%.
50. The percentage of the U.S. population that used the
internet increased most rapidly between 2011 and
2012. It increased by 9%.
51. The percentage of the U.S. population that used the
internet decreased most rapidly between 2008 and
2009. It decreased by 3%.
52. Between 2007 to 2013, the increase was 9%.
53. At age 8, women have the least number of
awakenings, averaging about 1 awakening per
night.
54. At age 65, men have the greatest number of
awakenings, averaging about 8 awakenings per
night.
55. The difference between the number of awakenings
for 25-year-old men and women is about 1.9.
56. The difference between the number of awakenings
for 18-year-old men and women is about 1.1.
57. graph a
58. graph d
59. graph b
60. graph c
61. graph b
62. graph a
63. graph c
64. graph b
65. – 72. Answers will vary.
73. makes sense
74. does not make sense; Explanations will vary.
Sample explanation: Most graphing utilities do not
display numbers on the axes.
75. makes sense

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