SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
Chapters 1 - 12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines
2 2 2 2 2 1–1
Chapter 2: Matrices
2 2–1
Chapter 3: Linear Programming, A Geometric Approach
2 2 2 2 2 3–1
Chapter 4: The Simplex Method
2 2 2 4–1
Chapter 5: Sets and Counting
2 2 2 5–1
Chapter 6: Probability
2 6–1
Chapter 7: Probability and Statistics
2 2 2 7–1
Chapter 8: Markov Processes
2 2 8–1
Chapter 9: The Theory of Games
2 2 2 2 9–1
Chapter 10: The Mathematics of Finance
2 2 2 2 10–1
Chapter 11: Logic
2 11–1
Chapter 12: Difference Equations and Mathematical Models
2 2 2 2 2 12–1
, Chapter 1 2
Exercises21.1 5
6.2 Left21,2down2
2
1. Right22,2up23 y
y
(2,23)
x
x
( )
–1,2 –2522
7.2 Left220,2up240
2. Left21,2up24 y
y
(–20,240)
(–1,24)
x
x
8.2 Right225,2up230
3.2 Down22 y
y
(25,230)
x
x
(0,2–2)
9. Point2Q2is222units2to2the2left2and222units2up2or
4. Right22
y (—2,22).
10. Point2P2is232units2to2the2right2and222units2down2or
(3,—2).
x
(2,20) 12
11. —2(1)2+2 (3)2=2—22+12=2—1so2 yes2 the2 point2 is
3
on2the2line.
5. Left22,2up21 12
y 12. —2(2)2+2 (6)2=2—12is2 false,2 so2 no2 the2 point2 is2 not
3
on2the2line
(–2,21)
x
Copyright2©220232Pearson2Education,2Inc. 1-1
, Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
12 24.2 02=25
13 —2x2+2 y2 =2—12 Substitute2 the2 x2 and2 y no2solution
3
. x-
coordinates2of2the2point2into2the2equation:
f 12 ıh2 f h intercept:2none2
' ,23 →2—2 ' 1 ı +212(3)2=2—12→2—1+12=2—12 is When2x2=20,2y2=252
y' ı '2 ı
y-intercept:2(0,25)
2222 J y22J 3
a2false2statement.2So2no2the2point2is2not2on2t 25.2When2y2=20,2x2=272
he2line. x-
f 1h f1 h intercept:2(7,20)202
14 —2 ' ı + ' ı (—1)2=2—12 is2true2so2yes2the2point2is =27
.
no2solution
'y3 ıJ222'y3 ıJ y-intercept:2none
on2the2line. 26.2 02=2–8x
15.2 m2=25,2b2=28 x2=20
x-intercept:2(0,20)
16.2 m2=2–22and2b2=2–6 y2=2–8(0)
y2=20
17.2 y2=20x2+23;2m2=20,2b2=23 y-intercept:2(0,20)
22 22 12
y2=2 x2+20;2 m2=2 ,2 b2=20 27 02=2 x2–21
18 3
3 3 .
. x2=23
19.2 14x2+272y2=221 x-intercept:2(3,20)
12
72y2=2—14x2+221 y2 =2 (0)2–21
3
y2 =2—2x2+23
y2=2–1
y-intercept:2(0,2–1)
20 x2—2y2 =23 y
. —y2 =2—x2+23
y2 =2x2—23
(3,20)
21.222 3x2=25 x
5 (0,2–1)
x2=2
3
1 2
28. When2x2=20,2y2=20.
22 – x2+ y2 =210
. 2 3 When2x2=21,2y2=22.
22 12 y
y2 =2 x2+10
3 2
32
y2 =2 x2+15 (1,22)
4 x
(0,20)
23. 02=2—4x2+28
4x2 =28
x2=22
x-intercept:2(2,20)
y2=2–4(0)2+28
y2=28
y-intercept:2(0,28)
1-2 Copyright2©220232Pearson2Education,2Inc.
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
Chapters 1 - 12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines
2 2 2 2 2 1–1
Chapter 2: Matrices
2 2–1
Chapter 3: Linear Programming, A Geometric Approach
2 2 2 2 2 3–1
Chapter 4: The Simplex Method
2 2 2 4–1
Chapter 5: Sets and Counting
2 2 2 5–1
Chapter 6: Probability
2 6–1
Chapter 7: Probability and Statistics
2 2 2 7–1
Chapter 8: Markov Processes
2 2 8–1
Chapter 9: The Theory of Games
2 2 2 2 9–1
Chapter 10: The Mathematics of Finance
2 2 2 2 10–1
Chapter 11: Logic
2 11–1
Chapter 12: Difference Equations and Mathematical Models
2 2 2 2 2 12–1
, Chapter 1 2
Exercises21.1 5
6.2 Left21,2down2
2
1. Right22,2up23 y
y
(2,23)
x
x
( )
–1,2 –2522
7.2 Left220,2up240
2. Left21,2up24 y
y
(–20,240)
(–1,24)
x
x
8.2 Right225,2up230
3.2 Down22 y
y
(25,230)
x
x
(0,2–2)
9. Point2Q2is222units2to2the2left2and222units2up2or
4. Right22
y (—2,22).
10. Point2P2is232units2to2the2right2and222units2down2or
(3,—2).
x
(2,20) 12
11. —2(1)2+2 (3)2=2—22+12=2—1so2 yes2 the2 point2 is
3
on2the2line.
5. Left22,2up21 12
y 12. —2(2)2+2 (6)2=2—12is2 false,2 so2 no2 the2 point2 is2 not
3
on2the2line
(–2,21)
x
Copyright2©220232Pearson2Education,2Inc. 1-1
, Chapter21:2Linear2Equations2and2Straight2Lines ISM:2Finite2Math
12 24.2 02=25
13 —2x2+2 y2 =2—12 Substitute2 the2 x2 and2 y no2solution
3
. x-
coordinates2of2the2point2into2the2equation:
f 12 ıh2 f h intercept:2none2
' ,23 →2—2 ' 1 ı +212(3)2=2—12→2—1+12=2—12 is When2x2=20,2y2=252
y' ı '2 ı
y-intercept:2(0,25)
2222 J y22J 3
a2false2statement.2So2no2the2point2is2not2on2t 25.2When2y2=20,2x2=272
he2line. x-
f 1h f1 h intercept:2(7,20)202
14 —2 ' ı + ' ı (—1)2=2—12 is2true2so2yes2the2point2is =27
.
no2solution
'y3 ıJ222'y3 ıJ y-intercept:2none
on2the2line. 26.2 02=2–8x
15.2 m2=25,2b2=28 x2=20
x-intercept:2(0,20)
16.2 m2=2–22and2b2=2–6 y2=2–8(0)
y2=20
17.2 y2=20x2+23;2m2=20,2b2=23 y-intercept:2(0,20)
22 22 12
y2=2 x2+20;2 m2=2 ,2 b2=20 27 02=2 x2–21
18 3
3 3 .
. x2=23
19.2 14x2+272y2=221 x-intercept:2(3,20)
12
72y2=2—14x2+221 y2 =2 (0)2–21
3
y2 =2—2x2+23
y2=2–1
y-intercept:2(0,2–1)
20 x2—2y2 =23 y
. —y2 =2—x2+23
y2 =2x2—23
(3,20)
21.222 3x2=25 x
5 (0,2–1)
x2=2
3
1 2
28. When2x2=20,2y2=20.
22 – x2+ y2 =210
. 2 3 When2x2=21,2y2=22.
22 12 y
y2 =2 x2+10
3 2
32
y2 =2 x2+15 (1,22)
4 x
(0,20)
23. 02=2—4x2+28
4x2 =28
x2=22
x-intercept:2(2,20)
y2=2–4(0)2+28
y2=28
y-intercept:2(0,28)
1-2 Copyright2©220232Pearson2Education,2Inc.
