Test bank and solution manual of college algebra 11e (2)

This manual contains detailed solutions to all of the exercises of the text CollegeAlgebra, eleventh edition, by R.. Many of the exercises in the text may be solved using more than one m

This manual contains detailed solutions to all of the exercises of the text College

Algebra, eleventh edition, by R David Gustafson and Jeff Hughes.

Many of the exercises in the text may be solved using more than one method, but it

is not feasible to list all possible solutions in this manual Also, some of the

exercises may have been solved in this manual using a method that differs slightly from that presented in the text There are a few exercises in the text whose solutions may vary from person to person Some of these solutions may not have been

included in this manual For the solution to an exercise like this, the notation

"answers may vary" has been included.

If you are a student using this manual, please remember that only reading a solution does not teach you how to solve a problem To repeat a commonly used phrase, mathematics is not a spectator sport You MUST make an honest attempt to solve each exercise in the text without using this manual first This manual should be viewed more or less as a last resort Above all, DO NOT simply copy the solution from this manual onto your own paper Doing so will not help you learn how to do the exercise, nor will it help you to do better on quizzes or tests.

I would like to thank Paul McCombs from Rock Valley College and Cynthia Ashton

of Brooks/Cole Publishing Company for their help and support This solutions manual was prepared using EXP 5.1.

This book is dedicated to John, who helps me to realize that mathematics cannot describe everything in life.

May your study of this material be successful and rewarding.

Michael G Welden

Chapter 0 Sets of Real Numbers 1

Graphs of Equations

Exercises 0.1 (page 13)

1. set 2. subset 3. union 4. intersection

5 decimal 6. variable 7. # 8. even

9. composite 10. rational 11. decimals 12. Ÿ

13. negative 14. 0 15. B  C  D
 16. CB

17 18. commutative, 19. interval . no

multiplication

&7  & † # 20

21. two 22. half-open 23. positive 24. distance

25. Every natural number is a whole number, 26. Every rational number is a real number,

43. irrational: È# 44. prime: , # ( 45. composite: '

46. even: % ! # ', , , 47. odd: & " (, , 48. negative: & % , , #

$

49. oqñqñqñqp# $ % 50. oñqqñqqñqñp% ' ) *

51. oñqñqqñqñp"" "$ "( "* 52. oñqñqñqñqñqñqñp# " ! " # $ %

53. oñqñqñqñp% $ # " 54. oñqñqñqñp) ' % #

55. oñqñqñqñqñp& $ " " $ 56. oñqqqñqqqqñqp!Þ( "Þ(&

$( )

oq ïï qp

Ð Ñ

oq ïï qp

Ò Ñ

oq ïï qp

Ò Ó

oq ïï qp

Ð Ó

97. distanceœ )  $ œ & œ &k k k k 98. distanceœ "#  & œ "( œ "(k
k k k

99. distanceœ $  ) œ & œ &k
k k k 100. distanceœ #!  ' œ #' œ #'k k k k

natural numbers

Since population must be positive and Since the

never has a fractional part, the set of

103 Since temperatures are usually reported

without fractional parts and may be either

positive or negative (or zero), the set of

integers

104.

should be used

Since the financial condition of a business

is usually described in terms of dollars andcents (fractional parts of a dollar), the set of

should be used

rational numbers

itself is negative For instance, if ,

107. The statement is always true 108. The statement is always true

109. The statement is not always true 110. The statement will be true if

For example, let and and , or if

+ œ & , œ # + € ! , € ! + Ÿ ! and , Ÿ !

111. The statement could be 112.

interpreted to mean that , when this

is not necessarily true

5. scientific, integer 6 Answers 7 8.

'& !!! %& !!!

'Þ& ‚ "! 
%Þ& ‚ "! 

'Þ& %Þ&

#&! !!! œ #Þ& ‚ "! œ #Þ& ‚ "! œ ""Þ( ‚ "!

!Þ!!!!!!!%& !Þ!!!!!!"#

%Þ& ‚ "! 
"Þ# ‚ "! 

%Þ& "Þ#

%& !!! !!! œ %Þ& ‚ "! œ %Þ& ‚ "!

117
!Þ!!!!!!$& "(! !!!
, 
$Þ& ‚ "! 
"Þ( ‚ "! 

$Þ& "Þ(

!Þ!!!!!!)& œ )Þ& ‚ "! œ )Þ& ‚ "!

!Þ!!!!!!!!#(& % (&!

#Þ(& ‚ "! 
%Þ(& ‚ "! 
#Þ(& %Þ(&


&!! !!! !!! !!! œ & ‚ "! œ & ‚ "!

œ "Þ*)' ‚ "!%

122 , mm , mm , mm mm

mm mm

8 œ % œ * #(& #!! $ #  %

127. polar radius km 128. polar radius mi

equatorial radius 8135 km equatorial radius

135. In the expression , the base of the 136.

exponent is , while in the expression

, the base of the exponent is

is not in scientific notation because

is not a number between 1 and 10

21.
'%"Î#Ênot a real number 22.
"#&"Î$œ
& $ "Î$‘ œ &

23.
"'+#"Î#œ
%+ # "Î#‘ œ % +k k 24.
#&+%"Î#œ’
&+# #“"Î#œ & + œ &+k k# #

25.
"'+%"Î%œ’
#+ %“"Î%œ # +k k 26.
'%+$"Î$œ
%+$‘"Î$œ %+

27.
$#+&"Î&œ
#+&‘"Î&œ #+ 28.
'%+'"Î'œ
#+ '‘"Î'œ # +k k

29.
#"','"Î$œ’
',#$“"Î$œ ',# 30.
#&'>)"Î%œ’
%># %“"Î%œ % > œ %>k k# #

47. Œ %* œ–Œ %* — œŒ #$ œ #%$$# 48. Œ #&)" œ–Œ #&)" — œŒ &* œ "#&(#*

55
B C"! &$Î&œ B$!Î& "&Î&C œ B C' $

56
'%+ ,' "#&Î'œ '%&Î' $!Î' '!Î'+ , œ '%ˆ "Î'‰&+ ,& "!œ # + ,& & "!œ $#+ ,& "!

"& "! #Î& #!Î& # % %

+ œ + œ + œ + B B œ B œ B

"Î& "Î& #Î( &Î( (Î(

65. È%* œÈ( œ (# 66. È)" œÈ* œ *#

67. È$ "#& œÈ$ & œ &$ 68. È$ '% œÉ
$ % $œ %

69. È$ "#& œÉ$
& $œ & 70. È& #%$ œÉ&
$ &œ $

#&+ œ #&+† &+ œ "#&+ œ &+ œ &+

& & & & " C

"! œ "! † & œ "! & œ# & $ œ $ † C œ$ C

"', "', #, $#, #, ,

'%+ œ '%+ † #, œ '%+ #, œ '%+ #, œ$#+ #,

# # # # % % "#& &!! &!!

& œ & œ & œ & œ "#&œ "#&† "#&œ "& '#& œ &

%

%

8

8 8

7

8

128 Consider the case when is even, is odd and is negative Then

Thus, must be a real number fo

5. one 6. zero 7. like 8. degree

9. coefficients, variables 10. $ÈB  # 11. yes, trinomial, 2nd degree

12. yes, binomial, 3rd degree 13. no 14. no

15. yes, binomial, 3rd degree 16. yes, monomial, 5th degree 17. yes, monomial, 0th degree

18. no 19. yes, monomial, no degree 20. yes, none, 3rd degree

21
B  $B  &B  )B œ B  $B  &B  )B œ B  &B  $B  )B œ 'B  $B  )B$ #
$  $ # $ $ $ # $ #

84 " " &  # &  # &  #

&  # œ &  #† &  # œ œ œ œ &  #

'!B C œ'!B C '!B C '!B C œ & &B &B C

& ( # & & ( # & $

& % & % & % & % $ % $

122 'B  ""B  "!

'B  B  "# $'B  (#B  "#"B  "%#B  "#!

$'B  'B  (#B''B  %*B  "%#B''B  ""B  "$#B

heightheightheightheight

129 Answers may vary.

134 Œ"#&)  œŒ"#&)  œŒ"#&)   œŒ &# œ#&%

67. 'B  #*BC  $&C œ $B  (C #B  &C# #

 68. "!B  "(BC  'C œ &B  'C #B  C# #



69 "#:  &):;  (!; œ # ':  #*:;  $&;# #
# #œ # ':  $&; :  ;



70 $B  'BC  *C œ $ B  #BC  $C# #
# #œ $ B  $C B  C



71 '7  %(78  $&8 œ  '7  %(78  $&8# #
# #œ  '7  &8 7  (8



72 "%<  ""<=  "&= œ  "%<  ""<=  "&=# #
# #œ  (<  &= #<  $=



73 'B  #$B  $&B œ B 'B  #$B  $& œ B 'B  ( B  &$ #
# 



74 C  C  *!C œ C C  C  *! œ C C  "! C  *$ #
# 



75 'B  ""B  $&B œ B 'B  ""B  $& œ B #B  ( $B  &% $ # #
#  #



œ B  &  #B œ B  &  #B B  &  #B

111-114 Answers may vary.

115. $B  # œ #ˆ$B#‰œ #ˆ$B  "‰ 116. &B  $ œ &ˆ&B$‰œ & B ˆ $‰

17. )7 $7 )7 "!8 )!78 "' 18. "&: &: "&: "'; #%!:;

&8 ƒ"!8 œ &8 † $7 œ"&78 œ $ ); ƒ"';# œ ); † &: œ %!:; œ ';

25. %  B #  B #  B B  # 26. #&  B &  B &  B

B  &B  ' œ B  $ B  # œ B  $ B  "!B  #& œ B  & B  &

39 D  D  #! D  #& D  D  #! D  & D  & D  % D  &

D  % ƒ D  & œ D  % †D  #&œ D  # D  # † D  & D  &

œ " +  %  ++  % +  % +  % +  %

œ +  %  ++  % +  % +  % +  %

œ #+  %+

56 + # + #

+  +  #+  &+  % œ +  # +  "  +  % +  "

œ + +  %  # +  #+  # +  " +  % +  % +  " +  #

œ +  %+  #+  %+  # +  " +  % +  # +  " + 

œ ,  %,  ), ,  # ,  # , ,  # ,  #

œ ,  %,  ), ,  # ,  #

$+ B  %+ , + $B  %+,+B  , +B  ,

90 #B  % & #B  % "!B  #! # &B  "! &B  "!

#  œ & #  œ "!  %B œ # &  #B œ &  #B

Chapter 0 Review (page 75)

1 natural: $ ' ), , 2. whole: ! $ ' ), , ,

3. integers: ' $ ! $ ' ), , , , , 4. rational: ' $ !, , , , , , "# $ ' )

5. irrational: , 1 È& 6. real: ' $ !, , , , , , "# $ 1 È& ' ), ,

7. prime: $ 8. composite: ' ),

9. even integers: ' ! ' ), , , 10. odd integers: $ $,

11. associative property of addition 12. commutative property of addition

13. associative property of multiplication 14. distributive property

15. commutative property of multiplication 16. commutative property of addition

17 double negative rule

30. &+ œ &+++$ 31.
&+#œ &+ &+



51
%& !!! $&! !!!, 
, 
%Þ& ‚ "! 
$Þ& ‚ "!  %Þ& ‚ $Þ& ‚ "! ‚ "! "&Þ(& ‚ "!

!Þ!!!"!& œ "Þ!& ‚ "! œ "Þ!& ‚ "! œ "Þ!& ‚ "!

83. " " % % % 84. # # & # & # &

# œ # † % œ ) œ # #& œ #&† & œ "#& œ &

# # # # & & & & "

& œ & † # œ & # & œ & † & œ & & œ &

89. 3rd degree, binomial 90. 2nd degree, trinomial

91. 2nd degree, monomial 92. 4th degree, trinomial

117 )B  "#& œ #B  & œ #B  &$
$ $

 #B  #B &  &#

 #‘œ #B  & %B  "!B  #&

# 

Chapter 0 Test (page 82)

1. odd integers: ( " $, , 2. prime numbers: $

3. commutative property of addition 4. distributive property

1. root, solution 2. identity 3. no 4. conditional

5. linear 6. rational 7. one 8. denominator

conditional equation

%  (B

27. $ 28.

,  $ œ " B  )B  "& œ B  $ B  &,  $ † $ œ ,  $ "

33. & B  # œ # B  % 34. & <  % œ & <  %

&B  "! œ #B  ) &<  #! œ &<  #!

&B  % œ "#  $B)B  % œ "#

)B œ "'

B œ #

”   •  

   

"! &

71 + $+  #

+  # " œ +  %+  %+ " $+  #+  #" œ  +  # +  #+  # +  # +  " œ +  # +  # †  $+  #

+  # +  # +  #+ +  #  +  # +  # œ  $+  #

#+  % œ $+  #+ œ #

5 . 55

5

œ B

œ B  D

C œ , " B

+

+, BC+

89. + œ 8  # ")! 90. W œ +  6<

8 "  <

+8 œ 8  # ")!† 8

8+8 œ 8  # ")!

95. #&B œ &B ‘ œ & Bk k 96. Œ#&:  œ–Œ&: — œ& :k k

"'; %; %;

"Î# # "Î#

1. add 2. perimeter 3. amount

4. break point 5. rate, time 6. !Þ!& $! œ "Þ& 

7 Let the score on the first exam

Then the score on the midterm,

and the score on the final

His score on the first exam was 84

Let the score on the first exam Then herscores on t

11. Let the number of locks replaced 12. Let th

7 locks can be changed for $236

13. Let the width 14. Let

Then the height

16 Total Fence Length Square Fence Length

The total fencing required is

17. Total Area Triangular Area 18. Sum of

The dimensions are 8 feet by 20 feet

19

The length

Area œ Area  !Þ&! † Area

$10,000 was invested at 7% and $12,000 was invested at 6%

22 Let the amount invested at 7%

Interest at 7% Interest at 9% Total interest

She needs to invest $45,714.29 at 7% to reach her goal

23 Let the amount invested at each rate

Interest at 6% Interest at 7% Interest at 8% Total interest

24 Let the amount invested at 8% Then , the amount invested at 9 %.

$17,500 is invested at 8% and $19,500 is invested at 9 %.12

25 Let B œthe number of full-price tickets sold Then &)&  B œthe number of student tickets sold

#Þ&! † full-price# of  "Þ(& † student# of œ "#"(Þ#&

#Þ&!B  "Þ(& &)&  B œ "#"(Þ#&

#Þ&!B  "!#$Þ(&  "Þ(&B œ "#"(Þ#&

!Þ(&B œ "*$Þ&!

B œ #&) Ê

 

There were 327 student tickets sold

26 Let B œthe cost of a student ticket

B œ & Ê A student ticket cost $5

27. Let the original price 28. Le

29. Let # of plates for equal costs 30.

The break point is 200 plates

B œ

œ'!!  $B œ )!!  #B

int is about 85,714 fasteners

31. Let # of computers to break even 32

Man in Roofer in Total in

1 day 1 day 1 day

They can roof the house in 2 days

Let hours for both working together

6 11

Crew 1 Crew 2 Total in

in 1 hour in 1 hour 1 ho

34.

ur

4 9

They can seal the parking lot in 4 hours

35 Let hours for both working together

Woman Man in Total in

in 1 hour 1 hour 1 hour

Œ  Œ 

ey can mow the lawn in 1 hours

Let days for both hoses to fill the pool

"

$

 œ

1st hose 2nd hose Total in

in 1 day in 1 day 1 day

" " "

$ # œ B'B " " œ 'B "