Test bank and solution manual of elementary and intermeidate albegra 4e (1)

CONTENTS Chapter 1 Foundations of Algebra...1 Chapter 2 Solving Linear Equations and Inequalities ...14 Chapter 3 Graphing Linear Equations and Inequalities...53 Chapter 4 Systems of Lin

Seminole State College of Florida

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ISBN-13: 978-0-321-92525-1

ISBN-10: 0-321-92525-4

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CONTENTS

Chapter 1 Foundations of Algebra 1

Chapter 2 Solving Linear Equations and Inequalities 14

Chapter 3 Graphing Linear Equations and Inequalities 53

Chapter 4 Systems of Linear Equations and Inequalities 80

Chapter 5 Polynomials 106

Chapter 6 Factoring 123

Chapter 7 Rational Expressions and Equations 142

Chapter 8 More on Inequalities, Absolute Value, and Functions 174

Chapter 9 Rational Exponents, Radicals, and Complex Numbers 182

Chapter 10 Quadratic Equations and Functions 204

Chapter 11 Exponential and Logarithmic Functions 238

Chapter 12 Conic Sections 255

12 Rational because 1 and 4 are integers

14 Rational because −12 is an integer and all

integers are rational numbers

20 Rational because 0.13 can be expressed as the

fraction 13

99, the ratio of two integers

22 False There are real numbers that are not rational

2 of the way between

5 and 6, so we divide the space between 5 and 6

into 2 equal divisions and place a dot on the 1st

mark to the right of 5

30 The number 2

5

− is located 2

5 of the way between

0 and −1, so we divide the space between 0 and

1

− into 5 equal divisions and place a dot on the

2nd mark to the left of 0

10between 7 and 8, so we divide the space between 7 and 8 into 10 equal divisions and place a dot on the 4th mark to the right of 7

34 First divide the number line between 7− and 8− into tenths The number 7.62− falls between 7.6

− and 7.7− on the number line Subdivide this section into hundredths and place a dot on the 2ndmark to the left of 7.6−

36 6 = because 6 is 6 units from 0 on a number 6line

38 − = because 88 8 − is 8 units from 0 on a number line

40 −4.5 =4.5 because 4.5− is 4.5 units from 0 on a number line

42 23 23

5 = 5 because 23

5 is

32

5 units from 0 on a number line

44 −67.8 =67.8 because 67.8− is 67.8 units from 0

56 3.5− < 3.1− because 3.5− is farther to the left

on a number line than 3.1−

6 is farther to the right on

a number line than 31

− is equal to 10.4, which is farther to the

right on a number line than 3.2

64 −0.59 = 0.59 because the absolute value of

9 is farther to the left on

a number line than the absolute value of 45

9, which is equal to 45

9

68 −10 > 8− because the absolute value of 10−

is 10, the absolute value of 8− is 8, and 10 is

farther to the right on a number line than 8

70 −5.36 < 5.76 because the absolute value of

5.36

− is 5.36, the absolute value of 5.76 is 5.76,

and 5.36 is farther to the left on a number line than

− is 7

11, and 9

11 is farther to the right on a number line than

44 Incorrect 2 is not a factor of the numerator

46 Incorrect The prime factorization of 108 should

be 2 2 3 3 3⋅ ⋅ ⋅ ⋅

48 If 130 of the 250 calories come from fat, the

fraction of calories in a serving that comes from

50 If 120 square feet of the 1830 square feet are used

as a home office, the fraction of her home that is

84 of her week sleeping

54 50 40 18 4+ + + =112 hours for the listed

activities The non-listed activities take

2 7

2 2 2 278

28 3 1 3 ( )1

45

2 3

2 737

3 16116

82 The LCD of 6 and 8 is 24

( ) ( ) ( ) ( )

20 360

86 ( )2

858 $5723

2 Base: 9; Exponent: 4; “nine to the fourth power”

4 Base: –8; Exponent: 2; “negative eight squared”

6 Base: 3; Exponent: 8; “additive inverse of three to

the eighth power”

= −

98 Distributive Property The parentheses were not simplified first

100 Commutative Property of Addition The addition was not performed from left to right

102 Mistake: Subtracted before multiplying

Correct: 19 6 10 8( ) 19 6 2

19 127

= − + ÷ − −

= − + +

= −

106 Since the instructor drops one quiz, the 4, there is

a total of 8 quizzes Add the quiz scores and

108 Assume that Lisa will not make lower than 68

and that score will be dropped Add the test

scores (268) and subtract from the lowest

possible points for an A (4 tests multiplied by a

score of 90 = 360 points) 360 – 268 = 92

110 Add the unemployment figures for each month

and divide by 12, the number of months in a

1 v

c

−

58 Mistake: Could be translated as 2(a− 7)

Correct: Seven less than two times a

60 Mistake: Could be translated as 4y+ 6

Correct: Four times the sum of y and six

62 Mistake: Could be translated as (m−3)(m+ 2)

Correct: m minus the product of three and the sum of m and two

64 The product of one-half the height and the sum of

a and b

66 The product ofπ, the radius squared, and the height

68 Twice the product of π, the radius, and the sum

of the radius and the height

70 The product of a and x squared added to the product of b and x added to c

Puzzle Problem

a) 1,n+ n+ 2b) 2,n+ n+ 4c) 2,n+ n+ 4

1 8 1 1

1 8 110

1 289

18 8

18 826

2 2

2 16 2 5

2222

3 3

48 246

3 10430215

24 a) Let a=1,b=0.5,c= −4,d = 6

1 6 0.5 4

6 28

z z z z

z z z

16 For 4

y y

3313

− −

− −

=+ −

18 a) We must find the perimeter of a rectangle

24 Begin by finding the area (in square feet) of the

room Let l = 15 ft and w = 14 ft

Now multiply the area (in square feet) of the

room by the cost per square foot

2

121

32 242

16 24

384 ft

A bh

A A A

=

=

=

=b) Now multiply the area by the cost per square foot: 384 $6.50( )=$2496

30 a) Begin by finding the area of the room in square feet if the island was not there and also find the area of the island in square feet Area of room:

( )

16.5 15247.5 sq ft

A lw A A

=

=

=Area of island:

( )

3.5 2

7 sq ft

A lw A A

=

=

=Subtract the area of the island from the area

of the room

247.5 7− =240.5 sq ft

b) Now divide the area you just found by the area of a single tile: 240.5 0.25÷ =962pieces of tile

c) Multiply the number of tiles by the price per tile: 962 $3.95( )=$3799.90

d) Multiply the area by $8 per square foot:

( )

240.5 $8 =$1924

32 Begin by finding the area of the CD including

the center and the area of the center

Find the radius of the CD: 53 2 23 1

238728

=

=Area of CD:

2 2

2

7288.26562525.97 in

A r A A A

πππ

2

780.7656252.41 in

A r A A A

πππ

the CD: 25.97−2.41=23.56≈23.6 in.2

34 Begin by finding the area (in square feet) of the

side of the house if the window was not there

and area (in square feet) of the window

To find the area of the side of the house, find the

area of the composite figure of a rectangle and

10 44.5 44.5 9.5

2

445 211.375656.375 ft

A lw bh

A A A

=Area of window:

( )

2

3 4.513.5 ft

A lw A A

=

=

=Subtract the area of the window from the area of

V V

V r V V

ππ

118.0625 63

113.5 in

V r h V

V V

πππ

of 8 hours and 45 minutes or 8.75 hours Also find the total distance traveled by subtracting the beginning odometer reading from the final odometer reading: 45,785.2 – 45,362.6 = 422.6 miles We are looking for an average driving rate, so use the formula r d

t

=

422.68.7548.3 mph

d r t r r

=

=

≈

44 Begin by converting 87 hours, 34 minutes and 47

46 Since the flight begins in EST and ends in CST,

you must add 1 hour to the difference between

arrival and departure: 2 hours and 40 minutes +

1 hour = 3 hours, 40 minutes or32 hr

3

2368.2 3

31350.06 miles

53929217.7 C

58589476.6 C

4.5 12763.407

To find the number of marbles that would fit inside the jar, divide the volume of the jar in cubic inches

by the volume of a marble

12 No, because the variable terms have exponents

greater than 1

14 Yes, because the variable term contains a single

variable and has an exponent of 1

16 Yes, because the variable terms contain a single

variable and have an exponent of 1

18 Solve the equation for a

9 989

= −Check:

0 3.43.4

b

b b

0 11.311.3

x x

x x

38 Solve the equation for z

t

t t

t t

50 Solve the equation for c

m

m m

+ =

=+

32

x

x x

− =−

=+

=Check: ( ( ) ) ( ( ) )

60 Solve the equation for x

0 2.72.7

x

x x

Because the linear equation is an identity, every

real number is a solution

64 Solve the equation for y

The expressions on each side of the equation

have the same variable term but different

constant terms, so the equation is a contradiction

and has no solution

66 Solve the equation for b

have the same variable term but different

constant terms, so the equation is a contradiction

and has no solution

68 Solve the equation for x

real number is a solution

70 Let x be the payment Kent must make

+ =

=+

=Kent must make a payment of $1912

72 Let x be the value on the fifth die

+ =

=+

=The fifth die should have a value of 5

74 Let x be amount of the third injection

110 110+ + =x 350

+ =

=+

=The third injection should be 130 cc

76 Let x be the missing side of the triangle

Remember that the perimeter is the sum of all of the sides

a b c P x

x x

x x

+ =

=+

=The length of the missing side is 6 cm

80 To find the total in sales, we must first multiply

the quantity sold by the price per unit

Blouses: 3 $25( )=$75

Slacks: 5 $30( )=$150

Shoes: 2 $85( )=$170

Let x be the amount that Tamika needs to sell to

make her goal Translate this situation into an

=+

=Tamika needs to sell $205 more No, Tamika

will probably not meet her goal because she still

has over one-third of her goal to go but only one

hour left to work

82 Let x represent the fraction of the respondents

who believed that the increase was due to men

and women equally Remember that the fractions

are parts of a whole, so set the sum of the

fractions equal to 1 whole

1

50 280

50 5022501125

25 of the respondents believed that the increase

was due to men and women equally

Puzzle Problem

Let x represent the fraction of the group that received

the medication but showed no discernible effect from it We are told that the participants who showed improvement 1

3

⎛ ⎞

⎜ ⎟ took the medication and that the

participants who experienced side effects 1

We can translate this into an equation

x x x x

x x

24 of the group that received the medication showed

no discernible effects from it

6 Solve the equation for t

56

? 4

512

3 6

3 32

x x

x

=

=

=Check: ( ) ?

x

=

=

=Check: ( ) ?

x

= −

= −

= −Check: ( ) ?

22 Solve the equation for y

n

=

=

=Check: ( )

c

=

=

=Check: ( ) ( ) ?

34 Solve the equation for r

r

=

=

=Check: ( ) ( )

m

m m

m

m m

42 Solve the equation for b

48 Solve the equation for x

x x

50 Solve the equation for m

Because the linear equation is an identity, every

real number is a solution

54 Solve the equation for k

k

k k

=

12 48

12 124

58 Solve the equation for n

4 25

254

n n

n

=

=

=Check:

60 Solve the equation for t

t

t t

w w

x

x x

66 Solve the equation for y

x

x x

=

76 Solve the equation for t

= −Check:

78 Mistake: In the check, neglected to multiply 5

by 3 after dividing out 2

Correct: 5

2is correct; the second to the last line

of the check should be 15 1+ = − +5 21

80 Mistake: Did not multiply 3 by 12

n n

n n

n

n n n

82 Let h be the crate’s height Since there are two

types of units, convert all the units to feet:

V lwh

h h h h

84 Substitute 76.8 for V and 6.4 for A, then solve for h

( ) ( )

13176.8 6.431

3 76.8 3 6.4

3230.4 6.4

10 230.4 10 6.4

2304 64

2304 64

64 6436

V Ah

h h h h h h h

86 Let w be the width of the building and w + 16 be

the length of the building

=

=

=The width of the building is 52.25 ft and the length is 52.25 + 16 = 68.25 ft

88 Substitute 1008 for A, 24 for h, and 48 for b

The length of side a is 36 inches

90 Substitute 1992 for SA, 22 for l, and 18 for w

Then solve for h

The height will be 15 in

92 Substitute 26.4 for C Then solve for d

The diameter is approximately 8.4 m

94 Since we are given the diameter, we must first find the radius Since the radius is half the diameter, the radius is 3 cm Substitute 355 for

V and 3 for r Then solve for h

( )

2 2

V r h

h h h

h h

ππππ

96 By looking at the figure, we can see that

+ =

=+

a a c

a c c c c

+ + =+ =+ =+ =

=Also, because the area of the figure is 192 square inches, we have

98 Substitute 15 for V and 2.5 for i Then solve for R

15 2.5

15 2.52.5 2.5

6

V iR R R

100 Substitute 9.8− for a and 44.1− for F Then

The velocity is 39.2 m/sec

106 Since Laura has 100 free miles, we must

subtract that amount from her total miles:

421 100− =321 She will be charged for 321

miles Substitute 321 for m

The total cost is $286.67

108 Substitute 82.4 for F and solve for C

( )

9

325

2

2 22

n a

n a

a n

=

=

=

6 Solve for m 3

33

b b h b

A bh

A bh

h h A b h

h

A a b h

2

0

V h r lw

V r h lwh lwh lwh

ππ

πππ

40 Solve for t

I Prt

I Prt

Pr Pr I t Pr

=

=

=

59325

2

kMn F d kMn

k Mn

x x

x x x x

+ =+ =

x x

x x x x

h h h

h h

− =

⋅ − = ⋅

−++ =

=

=+

=

22 Let x be the number

x x

x x

x x x

x

x x x

x x

36 Let x be the number

42 Eight times the difference of a number and two

will yield three times the number

44 Half of the sum of a number and one is one-third

the difference of the number and five

46 Five-hundredths of a number added to hundredths of the difference of the number and four and five-tenths is equal to four hundred sixty-five thousandths

three-48 The sum of one-half, one-third, and one-sixth of the same number will equal five

50 Mistake: Division translated in reverse order Correct: n÷12= − 8

52 Mistake: “three subtracted from” indicates that the 3 should be after the minus sign

SA SA SA SA

2 442