SOLUTION MANUAL
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
Chapters 1 - 12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Programming, A Geometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Counting 5–1
Chapter 6: Probability 6–1
Chapter 7: Probability and Statistics 7–1
Chapter 8: Markov Processes 8–1
Chapter 9: The Theory of Games 9–1
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Logic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
, Chapter 1
Exercises 1.1 5
6. Left 1, down
2
1. Right 2, up 3 y
y
(2, 3)
x
x
( )
–1, – 52
7. Left 20, up 40
2. Left 1, up 4 y
y
(–20, 40)
(–1, 4)
x
x
8. Right 25, up 30
3. Down 2 y
y
(25, 30)
x
x
(0, –2)
9. Point aQ ais a2 aunits ato athe aleft aand a2 aunits aup aor
4. Right 2
y (—2, a2).
10. Point aP ais a3 aunits ato athe aright aand a2 aunits adown aor
(3,—2).
x
(2, 0) 1a
11. —2(1) a+ a (3) a= a—2 a+1 a= a—1so a yes a the a point a is
3
on athe
aline.
5. Left a2, aup
a1 12. 1a
y
—2(2) a+ a (6) a= a—1 ais a false, a so a no a the a point a is a not
3
on athe
aline
(–2, 1)
x
Copyright © 2023 Pearson Education, Inc. 1-1
, Chapter 1: Linear Equations and Straight Lines ISM: Finite Math
1a 24. a 0 a= a5
13 —2x a+ a y a = a—1 a Substitute a the a x a and a y no asolution
3
. x-intercept:
coordinates aof athe apoint ainto athe aequation:
f 1 a hıa f h anone aWhen ax
' ,a3 → a—2 ' 1 ı + a1 a(3)a=a—1 a→ a—1+1 a=a—1 a is a= a0, ay a= a5ay-
y' ı ' ı
intercept: a(0, a5)
2 a a aJ ya2J 3
a afalse astatement. aSo ano athe apoint ais 25. aWhen ay a= a0, ax
anot aon athealine. a= a7 ax-intercept:
a(7, a0)a0 a= a7
f 1h f1 h
14 —2 ' ı + ' ı (—1) a=a—1 a is atrue aso ayes athe no asolution
.
apoint ais
'y3 ıJ a a a'y3 ıJ y-intercept: anone
on athe aline. 26. a 0 a= a–8x
15. a m a= a5, ab x a= a0
a= a8
x-intercept: a(0, a0)
y a= a–8(0)
16. a m a= a–2 aand ab a= a–6 y a= a0
y-intercept: a(0, a0)
17. a y a= a0x a+ a3; am a=
a0, ab a= a3
2a 2a 1a
y a= a x a+a0; a m a= a , 27 0 a= a x a – a1
18 3
. .
a b a= a0 x a= a3
3 3
19. a 14x a+a7 ay a= x-intercept: a(3, a0)
1a
a21 y a = a (0) a– a1
3
7 ay a = a—14x a+
y a= a–1
a21
y a = a—2x a+a3
y-intercept: a(0, a–1)
20 x a— ay a = a3 y
. —y a = a—x a+a3
y a = ax a—a3
(3, 0)
21. a a a 3x a= x
a5 (0, –1)
5
x a= a
3
28. When ax a= a0, ay a= a0.
1 2
22 – x a+ y a = a10 4
. 2 3
2a 1a
y a= a x
a+10
3 2
3a
y a= a x
a+15
1-2 Copyright © 2023 Pearson Education, Inc.
Finite Mathematics & Its Applications
13th Edition by Larry J. Goldstein,
Chapters 1 - 12, Complete
, Contents
Chapter 1: Linear Equations and Straight Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Programming, A Geometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Counting 5–1
Chapter 6: Probability 6–1
Chapter 7: Probability and Statistics 7–1
Chapter 8: Markov Processes 8–1
Chapter 9: The Theory of Games 9–1
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Logic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
, Chapter 1
Exercises 1.1 5
6. Left 1, down
2
1. Right 2, up 3 y
y
(2, 3)
x
x
( )
–1, – 52
7. Left 20, up 40
2. Left 1, up 4 y
y
(–20, 40)
(–1, 4)
x
x
8. Right 25, up 30
3. Down 2 y
y
(25, 30)
x
x
(0, –2)
9. Point aQ ais a2 aunits ato athe aleft aand a2 aunits aup aor
4. Right 2
y (—2, a2).
10. Point aP ais a3 aunits ato athe aright aand a2 aunits adown aor
(3,—2).
x
(2, 0) 1a
11. —2(1) a+ a (3) a= a—2 a+1 a= a—1so a yes a the a point a is
3
on athe
aline.
5. Left a2, aup
a1 12. 1a
y
—2(2) a+ a (6) a= a—1 ais a false, a so a no a the a point a is a not
3
on athe
aline
(–2, 1)
x
Copyright © 2023 Pearson Education, Inc. 1-1
, Chapter 1: Linear Equations and Straight Lines ISM: Finite Math
1a 24. a 0 a= a5
13 —2x a+ a y a = a—1 a Substitute a the a x a and a y no asolution
3
. x-intercept:
coordinates aof athe apoint ainto athe aequation:
f 1 a hıa f h anone aWhen ax
' ,a3 → a—2 ' 1 ı + a1 a(3)a=a—1 a→ a—1+1 a=a—1 a is a= a0, ay a= a5ay-
y' ı ' ı
intercept: a(0, a5)
2 a a aJ ya2J 3
a afalse astatement. aSo ano athe apoint ais 25. aWhen ay a= a0, ax
anot aon athealine. a= a7 ax-intercept:
a(7, a0)a0 a= a7
f 1h f1 h
14 —2 ' ı + ' ı (—1) a=a—1 a is atrue aso ayes athe no asolution
.
apoint ais
'y3 ıJ a a a'y3 ıJ y-intercept: anone
on athe aline. 26. a 0 a= a–8x
15. a m a= a5, ab x a= a0
a= a8
x-intercept: a(0, a0)
y a= a–8(0)
16. a m a= a–2 aand ab a= a–6 y a= a0
y-intercept: a(0, a0)
17. a y a= a0x a+ a3; am a=
a0, ab a= a3
2a 2a 1a
y a= a x a+a0; a m a= a , 27 0 a= a x a – a1
18 3
. .
a b a= a0 x a= a3
3 3
19. a 14x a+a7 ay a= x-intercept: a(3, a0)
1a
a21 y a = a (0) a– a1
3
7 ay a = a—14x a+
y a= a–1
a21
y a = a—2x a+a3
y-intercept: a(0, a–1)
20 x a— ay a = a3 y
. —y a = a—x a+a3
y a = ax a—a3
(3, 0)
21. a a a 3x a= x
a5 (0, –1)
5
x a= a
3
28. When ax a= a0, ay a= a0.
1 2
22 – x a+ y a = a10 4
. 2 3
2a 1a
y a= a x
a+10
3 2
3a
y a= a x
a+15
1-2 Copyright © 2023 Pearson Education, Inc.
