SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1:
d Linear Equations and Straight Lines
d d d d 1–1
Chapter 2:
d Matrices 2–1
Chapter 3:
d Linear Programming, A Geometric Approach
d d d d 3–1
Chapter 4:
d The Simplex Method
d d 4–1
Chapter 5:
d Sets and Counting
d d 5–1
Chapter 6:
d Probability 6–1
Chapter 7:
d Probability and Statistics
d d 7–1
Chapter 8:
d Markov Processesd 8–1
Chapter 9:
d The Theory of Games
d d d 9–1
Chapter 10: The Mathematics of Finance
d d d d 10–1
Chapter 11: Logic
d 11–1
Chapter 12: Difference Equations and Mathematical Models
d d d d d 12–1
, Chapter 1 d
Exercisesd1.1 5
6.d Leftd1,ddownd
2
1. Rightd2,dupd3 y
y
(2,d3)
x
x
(–1, – 52)
d d
d
7.d Leftd20,dupd40
2. Leftd1,dupd4 y
y
(–20,d40)
(–1,d4)
x
x
8.d Rightd25,dupd30
3.d Downd2 y
y
(25,d30)
x
x
(0,d–2)
9. PointdQdisd2dunitsdtodthedleftdandd2dunitsdupdor
4. Rightd2
y (—2,d2).
10. PointdPdisd3dunitsdtodthedrightdandd2dunitsddowndor
(3,—2).
x
(2,d0) 1d
11. —2(1)d+d (3)d=d—2d+1d=d—1sod yesd thed pointd is
3
ondthedline.
5. Leftd2,dupd1 1d
y 12. —2(2)d+d (6)d=d—1disd false,d sod nod thed pointd isd not
3
ondthedline
(–2,d1)
x
Copyrightd©d2023dPearsondEducation,dInc. 1-1
, Chapterd1:dLineardEquationsdanddStraightdLines ISM:dFinitedMath
1d 24.d 0d=d5
13. —2xd+d yd =d—1d Substituted thed xd andd y nodsolution
3 x-
coordinatesdofdthedpointdintodthedequation: intercept:dnonedWh
f 1d ıhd f h
' ,d3 →d—2 ' 1 ı +d1d(3)d=d—1d→d—1+1d=d—1d is endxd=d0,dyd=d5dy-
y' ı 'd ı intercept:d(0,d5)
2ddd J yd2J 3
adfalsedstatement.dSodnodthedpointdisdnotdondthedline. 25.dWhendyd=d0,dxd=d7dx-
f 1 h f1h intercept:d(7,d0)d0d=
—2 ' ı + ' ı(—1)d=d—1d isdtruedsodyesdthedpointdis d7
14. nodsolution
'y3 ıJddd'y3 ıJ y-intercept:dnone
ondthedline. 26.d 0d=d–8x
15.d md=d5,dbd=d8 xd=d0
x-intercept:d(0,d0)
16.d md=d–2danddbd=d–6 yd=d–8(0)
yd=d0
17.d yd=d0xd+d3;dmd=d0,dbd=d3 y-intercept:d(0,d0)
2d 2d 1d
18. yd=d xd+d0;d md=d ,d bd=d0 27. 0d=d xd–d1
3 3 3
xd=d3
19.d 14xd+d7dyd=d21 x-intercept:d(3,d0)
1d
7dyd=d—14xd+d21 yd =d (0)d–d1
3
yd =d—2xd+d3 yd=d–1
y-intercept:d(0,d–1)
20. xd—dyd =d3 y
—yd=d—xd+d3
yd=dxd—d3
(3,d0)
21.ddd 3xd=d5 x
5 (0,d–1)
xd=d
3
1 2 28. Whendxd=d0,dyd=d0.
22. – xd+ yd =d10
2 3 Whendxd=d1,dyd=d2.
2d 1d y
yd=d xd+10
3 2
3d
yd =d xd+15 (1,d2)
4 x
(0,d0)
23. 0d=d—4xd+d8
4xd =d8
xd=d2
x-intercept:d(2,d0)
yd=d–4(0)d+d8
yd=d8
y-intercept:d(0,d8)
1-2 Copyrightd©d2023dPearsondEducation,dInc.
Finite Mathematics & Its Applications
13th Edition by Goldstein Chapters 1 - 12
, Contents
Chapter 1:
d Linear Equations and Straight Lines
d d d d 1–1
Chapter 2:
d Matrices 2–1
Chapter 3:
d Linear Programming, A Geometric Approach
d d d d 3–1
Chapter 4:
d The Simplex Method
d d 4–1
Chapter 5:
d Sets and Counting
d d 5–1
Chapter 6:
d Probability 6–1
Chapter 7:
d Probability and Statistics
d d 7–1
Chapter 8:
d Markov Processesd 8–1
Chapter 9:
d The Theory of Games
d d d 9–1
Chapter 10: The Mathematics of Finance
d d d d 10–1
Chapter 11: Logic
d 11–1
Chapter 12: Difference Equations and Mathematical Models
d d d d d 12–1
, Chapter 1 d
Exercisesd1.1 5
6.d Leftd1,ddownd
2
1. Rightd2,dupd3 y
y
(2,d3)
x
x
(–1, – 52)
d d
d
7.d Leftd20,dupd40
2. Leftd1,dupd4 y
y
(–20,d40)
(–1,d4)
x
x
8.d Rightd25,dupd30
3.d Downd2 y
y
(25,d30)
x
x
(0,d–2)
9. PointdQdisd2dunitsdtodthedleftdandd2dunitsdupdor
4. Rightd2
y (—2,d2).
10. PointdPdisd3dunitsdtodthedrightdandd2dunitsddowndor
(3,—2).
x
(2,d0) 1d
11. —2(1)d+d (3)d=d—2d+1d=d—1sod yesd thed pointd is
3
ondthedline.
5. Leftd2,dupd1 1d
y 12. —2(2)d+d (6)d=d—1disd false,d sod nod thed pointd isd not
3
ondthedline
(–2,d1)
x
Copyrightd©d2023dPearsondEducation,dInc. 1-1
, Chapterd1:dLineardEquationsdanddStraightdLines ISM:dFinitedMath
1d 24.d 0d=d5
13. —2xd+d yd =d—1d Substituted thed xd andd y nodsolution
3 x-
coordinatesdofdthedpointdintodthedequation: intercept:dnonedWh
f 1d ıhd f h
' ,d3 →d—2 ' 1 ı +d1d(3)d=d—1d→d—1+1d=d—1d is endxd=d0,dyd=d5dy-
y' ı 'd ı intercept:d(0,d5)
2ddd J yd2J 3
adfalsedstatement.dSodnodthedpointdisdnotdondthedline. 25.dWhendyd=d0,dxd=d7dx-
f 1 h f1h intercept:d(7,d0)d0d=
—2 ' ı + ' ı(—1)d=d—1d isdtruedsodyesdthedpointdis d7
14. nodsolution
'y3 ıJddd'y3 ıJ y-intercept:dnone
ondthedline. 26.d 0d=d–8x
15.d md=d5,dbd=d8 xd=d0
x-intercept:d(0,d0)
16.d md=d–2danddbd=d–6 yd=d–8(0)
yd=d0
17.d yd=d0xd+d3;dmd=d0,dbd=d3 y-intercept:d(0,d0)
2d 2d 1d
18. yd=d xd+d0;d md=d ,d bd=d0 27. 0d=d xd–d1
3 3 3
xd=d3
19.d 14xd+d7dyd=d21 x-intercept:d(3,d0)
1d
7dyd=d—14xd+d21 yd =d (0)d–d1
3
yd =d—2xd+d3 yd=d–1
y-intercept:d(0,d–1)
20. xd—dyd =d3 y
—yd=d—xd+d3
yd=dxd—d3
(3,d0)
21.ddd 3xd=d5 x
5 (0,d–1)
xd=d
3
1 2 28. Whendxd=d0,dyd=d0.
22. – xd+ yd =d10
2 3 Whendxd=d1,dyd=d2.
2d 1d y
yd=d xd+10
3 2
3d
yd =d xd+15 (1,d2)
4 x
(0,d0)
23. 0d=d—4xd+d8
4xd =d8
xd=d2
x-intercept:d(2,d0)
yd=d–4(0)d+d8
yd=d8
y-intercept:d(0,d8)
1-2 Copyrightd©d2023dPearsondEducation,dInc.
