College Algebra 11th Edition Gustafson Solutions Manual by a522238902

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Preface

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

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Contents

Chapter 0

Sets of Real Numbers

Chapter 1

Equations and Inequalities

Chapter 2

The Rectangular Coordinate System and Graphs of Equations

174

Chapter 3

Functions

236

Chapter 4

Exponential and Logarithmic Functions

309

Chapter 5

Solving Polynomial Equations

359

Chapter 6

Linear Systems

410

Chapter 7

Conic Sections and Quadratic Systems

505

Chapter 8

Sequence, Series and Probability

551

Chapter 9

The Mathematics of Finance

585

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SECTION 0.1

Exercises 0.1

(page 13)

set

subset

union

intersection

decimal

variable

even

composite

10.

rational

11.

decimals

12.

13.

negative

14.

15.

B C D

16.

17.

&7 & † #

18.

commutative, multiplication

19.

interval

20.

21.

two

22.

half-open

23.

positive

24.

distance

25.

Every natural number is a whole number, so N § W. TRUE

26.

Every rational number is a real number, so Q § R. TRUE

27.

The rational number "# is not a natural ¸ N. FALSE number, so Q §

28.

Every integer is a rational number, so Z § Q. TRUE

29.

Every whole number is an integer, so W § Z. TRUE

30.

31.

E ∪ F œ ea, b, c, d, e, f, gf

32.

The real number È# is not an integer, ¸ Z. FALSE so R §

E ∩ F œ ed, ef

33.

E ∩ G œ ea, c, ef

34.

F ∪ G œ ea, c, d, e, f, gf

35.

* œ !Þ&'#&; terminates "'

36.

$ œ !Þ$(&; terminates )

37.

$ œ !Þ#(#(#(ÞÞÞ; repeats ""

38.

& œ !Þ%"''''ÞÞÞ; repeats "#

39.

natural: ", #, ', (

40.

whole: !, ", #, ', (

41.

integers: &, %, !, ", #, ', (

42.

43.

irrational: È#

rational: &, %, #$ , !, ", #, #Þ(&, ', (

44.

prime: #, (

45.

composite: '

46.

even: %, !, #, '

47.

odd: &, ", (

48.

negative: &, %, #$

49.

oqñqñqñqp # $ %

50.

oñqqñqqñqñp ' ) * %

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SECTION 0.1 51.

oñqñqqñqñp "" "$ "( "*

52.

oñqñqñqñqñqñqñp # " ! " # $ %

53.

oñqñqñqñp % $ # "

54.

oñqñqñqñp ) ' % #

55.

oñqñqñqñqñp & $ " " $

56.

oñqqqñqqqqñqp !Þ( "Þ(& $

57.

B # p #, ∞

60.

58.

íïïÑqqp

61.

oqÐïïÑqp #

63.

# Ÿ B ! # p c #, #

64.

oqÒïïÑqp #

66.

B ! % p ∞, %

oqqÐïïî # ! B ! $ p #, $

67.

% ! B Ÿ " p %, "d

! 70.

$ Ÿ B ! % p c $, %

68.

oqÒïïÑqp

% Ÿ B Ÿ % p c %, %d

oqÒïïÓqp %

72.

$ B # p # Ÿ B Ÿ $ p c #, $d #

B & and B ! %p &, ∞ ∩ ∞, %

oqÐïïïî & íïïïÑqp % oqÐïïÑqp &

oqÒïïÓqp

&, ∞ ∩ ∞, %

oqÐïïÓqp

' B # p # Ÿ B Ÿ ' p c#, 'd

∞, %

íïïÓqqp

& ! B Ÿ ! p &, !d

&, ∞

B Ÿ & p ∞, &d

65.

oqÒïïÓqp 73.

B ! $ p ∞, $

62.

íïïÑqqp

# Ÿ B Ÿ $ p c #, $d

oqÒïïÓqp 71.

oqqÐïïî

oqÐïïÑqp

B % p %, ∞

oqqÒïïî 69.

! ! B ! & p !, &

59.

oqÐïïÓqp

B " p c ", ∞

( )

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SECTION 0.1 74.

B $ and B ! 'p c $, ∞ ∩ ∞, ' c $, ∞

oqÒïïïî $ íïïïÑqp ' oqÒïïÑqp

∞, '

c $, ∞ ∩ ∞, ' 75.

B ) and B Ÿ $p c ), ∞ ∩ ∞, $d c ), ∞

∞, $d

c ), ∞ ∩ ∞, $d 76.

oqÒïïïî ) íïïïÓqp $ oqÒïïÓqp )

B " and B Ÿ (p ", ∞ ∩ ∞, (d ", ∞

∞, (d

", ∞ ∩ ∞, (d 77.

oqÐïïïî " íïïïÓqp ( oqÐïïÓqp "

(

B ! # or B # p ∞, # ∪ #, ∞

78.

íïÑqqÐïî #

79.

íïÓqqÐïî

B Ÿ " or B $ p ∞, "d ∪ c$, ∞

80.

íïÓqqÒïî "

81.

B ! $ or B # p ∞, $ ∪ c#, ∞

íïÑqqÒïî

Since "$ !, k"$k œ "$.

B Ÿ & or B ! p ∞, &d ∪ !, ∞

82.

83.

Since ! !, k!k œ !.

84.

85.

Since ) ! !, k )k œ ) œ ). k )k œ ) œ )

86.

Since "( ! !, k "(k œ "( œ "(. Since '$ !, k'$k œ '$. k'$k œ '$ œ '$

Since #& ! !, k #&k œ #& œ #&.

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SECTION 0.1 87.

89.

91.

Since $# !, k$#k œ $#. k$#k œ $# œ $#

88.

Since 1 & ! !, k1 &k œ 1 & œ 1 & œ & 1.

k1 1k œ k!k œ !

Since ' ! !, k 'k œ ' œ '. k 'k œ ' œ '

90.

Since ) 1 !, k) 1k œ ) 1.

92.

Since #1 !, k#1k œ #1.

93.

If B #, then B " !. Then kB "k œ B ".

94.

If B Ÿ #, then B " ! !. Then kB "k œ B " .

95.

If B ! !, then B % ! !. Then kB %k œ B % .

96.

If B "!, then B ( !. Then kB (k œ B (.

97. 99.

distance œ k) $k œ k&k œ &

distance œ k $ ) k œ k&k œ &

98.

distance œ k"# & k œ k"(k œ "(

100. distance œ k #! 'k œ k #'k œ #'

101. Since population must be positive and never has a fractional part, the set of natural numbers should be used.

102. Since the subdivisions on a ruler are measured in fractions of an inch, the set of rational numbers should be used.

103. Since temperatures are usually reported without fractional parts and may be either positive or negative (or zero), the set of integers should be used.

104. Since the financial condition of a business is usually described in terms of dollars and cents (fractional parts of a dollar), the set of rational numbers should be used.

105. B will represent a positive number if B itself is negative. For instance, if B œ $, then B œ $ œ $, which is a positive number.

106. Every integer is a rational number because every integer is equal to itself over 1.

107. The statement is always true.

108. The statement is always true.

109. The statement is not always true. For example, let + œ & and , œ #.

110. The statement will be true if + ! and , !, or if + Ÿ ! and , Ÿ !.

111. The statement + ! , - could be interpreted to mean that + -, when this is not necessarily true.

Exercises 0.2 1.

factor

112. k, +k œ k " + , k œ k "k † k+ , k œ k+ , k

(page 24) 2.

natural

$, #B

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exponential

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SECTION 0.2 7.

B7 B8 œ B7 8

B7 8 œ B78

11.

B! œ "

12.

B 8 œ

"$# œ "$ † "$ œ "'*

14.

"!$ œ "! † "! † "! œ ",!!!

15.

&# œ " † & † & œ #&

16.

& # œ & & œ #&

17.

%B$ œ % † B † B † B

18.

19.

&B % œ &B &B &B &B

%B $ œ %B %B %B

20.

'B# œ ' † B † B

21.

)B% œ ) † B † B † B † B

22.

)B % œ )B )B )B )B

23.

(BBB œ (B$

24.

)CCCC œ )C%

25.

B B œ " " B# œ B#

26.

#+ #+ #+ œ # † # † # † +$ œ )+$

scientific, integer

BC 8 œ B8 C8

10.

13.

Answers may vary. B7 œ B7 8 B8

" B8

27.

$> $> $> œ $ $ $ >$ œ #(>$

29.

BBBCC œ B$ C#

30.

+++,,,, œ +$ , %

31.

#Þ#$ œ "!Þ'%)

32.

(Þ"% œ #&%"Þ"')"

33.

!Þ&% œ !Þ!'#&

34.

!Þ# % œ !Þ!!"'

35.

B# B$ œ B# $ œ B&

36.

C$ C% œ C$ % œ C(

37.

38.

>' œ >'†( œ >%#

39.

C& C# œ C( œ C#"

40.

41. 43. 45. 47.

(

D # D % œ D ' D #! œ D #' &

51.

46.

B# C œ B# C$ œ B' C$ $

+# +# +' Œ  œ $ œ $ , , , $

49.

44.

$B $ œ $$ B$ œ #(B$ $

B ! œ "

42.

+# +% œ +' +) œ +"%

D # œ D #†$ œ D' $

+$ +' +% œ +* +% œ +"$

>$ >& œ >"# >"! œ >## %

+# +$ œ +) +* œ +"( %

#C % œ # % C% œ "'C%

48.

B$ D % œ B$ D % œ B") D #%

50.

52.

#, #, #, #, œ " † # † # † # † # † , % œ "', %

28.

%B! œ % † " œ %

B B% B% œ œ  % C$ C"# C$ %

53.

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%B ! œ "

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SECTION 0.2 54.

#B! œ # † " œ #

57.

C # C $ œ C & œ

59.

B$ B %

61.

63.

D % œ

55.

" D%

" C&

58.

7 # 7$ œ 7" œ 7

60.

C # C$

B( œ B( $ œ B% B$

62.

<& œ <& # œ <$ <#

+#" œ +#" "( œ +% +"(

64.

>"$ œ >"$ % œ >* >%

66.

=* =$ ="# œ % œ ="# % œ =) # = =#

68.

>% % $ $ " $ $ Œ $  œ ˆ> ‰ œ ˆ> ‰ œ > >

70.

<* < $ <' œ œ <' ' œ <"# < ' < # $

72.

74.

B $ B# B " B # " œ œ œ B "" œ "" $ $ * # & $ B B B B B

76.

B ( C& C& C% C* C#( Œ ( %  œ Œ ( (  œ Œ "%  œ %# BC BB B B

œ B "

œ B#

B# B% œ œ B% $ œ B" œ B B# B B$ #

65.

67.

7$ 7$ 7* œ œ  $ 8# 8' 8# $

+$ ++#

69.

" œ ># > #

56.

+ $  , "

+ ' " œ + ' $ œ + * œ * +$ +

73.

75.

B& C # B& B$ B) B$# Œ $ #  œ Œ # #  œ Œ %  œ "' B C C C C C

77.

&B $ C # Œ # $  $B C

œŒ

$B# C $ $B# B$ C# $B& *B"!  œŒ  œŒ  œ $ # $ &B C &C &C #&C#

78.

œŒ

#B # C ' #C& # ) œ  Œ  œŒ %  œ # & # # ' $B C $B B C $B C #(B"# C$

79.

$B& C $ Œ & $  'B C

, " %

+"# ,%

<% < ' < # # # % œ  Œ  œ ˆ< ‰ œ < $ $ ! < < < " œ % < #

$B# C &  #B # C '

" C%

> %  > $

> % >) œ œ ># >' > $ #

71.

œ C % œ

+ $

œ C"

œ #

'B & C$ #C$ C$ #C' %C"# œ Œ & $  œ Œ & &  œ Œ "!  œ #! $B C "B B B B #

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SECTION 0.2

80.

"#B % C$ D & $C$ C$ $C' #(C") œ œ œ  Œ  Œ  %B% C $ D & "B% B% D & D & B) D "! B#% D $!

81.

) # D $ C )# D $ C " '%D $ C " '%D $ D% '%D( œ $ ' ' " " # œ # & % œ œ $ " & " & C D †& C D & C D #&C C #&C' &C# D # &CD #

82.

7 # 8$ :% 78 # :$

83.

84.

'$ % ( # ‘ '$ $ # ‘ 'c$ *d 'c 'd $' ") œ œ œ œ œ # & # % & # "' & "% (! (! $&

85. 87. 89. 91.

92. 93.

78 # :$ % 78# : "

7% 8 ' : ) † 7% 8 ) :"# 7) 8 "% :% 7) 7& :% :"$ 7"$ :"( œ & ' "$ œ œ % ) "# " # " ' "% 7 8 : †7 8 : 7 8 : 8 8 8#!

&c'# * & d &c$' %d &c%!d #!! œ œ œ &! # # œ % " % % # $ % "

B# œ # # œ %

B$ œ # $ œ )

BD $ œ c " † # † $d$ œ '$ œ #"'

86. 88. 90.

B# œ # # œ " † % œ %

B$ œ # $ œ " † ) œ )

BD$ œ " † # † $$ œ # † #( œ &%

 # # † $$ ‘ B# D $ c% † #(d "!) œ œ œ œ "# # # # # D C $ ! * ! *

$#  # # !# ‘ D # B# C# * % ! * % $' $ œ œ œ œ œ $ B$ D ) $ #% #% # # $

&B# $C$ D œ & # # $ ! $ $ œ & % $ ! $ œ #! ! œ #!

94.

$ B D # # C D $ œ $ # $ # # ! $ $ œ $ & # # $ $ œ $ #& # #( œ (& &% œ #"

95.

$B $ D # "D $ D $ $ $ $ œ œ & œ œ œ & œ 'B# D $ #B# B$ D # #B # $# '% '% # #

&B# D $ #&B% D ' &B% &B$ & # $ & ) %! %! œ œ œ œ œ œ œ &BD # &BD # BD # D ' D% $% )" )" )" #

96. 97.

$(#,!!! œ $Þ(# ‚ "!&

98.

99.

"((,!!!,!!! œ "Þ(( ‚ "!)

100. #$,%(!,!!!,!!! œ #Þ$%( ‚ "!"!

101. !Þ!!( œ ( ‚ "! $

)*,&!! œ )Þ*& ‚ "!%

102. !Þ!!!&# œ &Þ# ‚ "! %

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SECTION 0.2 103. !Þ!!!!!!'*$ œ 'Þ*$ ‚ "! (

104. !Þ!!!!!!!)* œ )Þ* ‚ "! )

105. ",!!!,!!!,!!!,!!! œ " ‚ "!"#

106. !Þ!!!!!" œ " ‚ "! '

107. *Þ$( ‚ "!& œ *$(,!!!

108. %Þ#' ‚ "!* œ %,#'!,!!!,!!!

109. #Þ#" ‚ "! & œ !Þ!!!!##"

110. #Þ((% ‚ "! # œ !Þ!#((%

111. !Þ!!!$# ‚ "!% œ $Þ#

112. *,$!!Þ! ‚ "! % œ !Þ*$

113. $Þ# ‚ "! $ œ !Þ!!$#

114. (Þ#& ‚ "!$ œ (,#&!

115.

116.

117.

118.

'&,!!! %&,!!! 'Þ& ‚ "!% %Þ& ‚ "!% 'Þ& %Þ& œ œ ‚ "!% % & œ ""Þ( ‚ "!$ & #&!,!!! #Þ& ‚ "! #Þ& œ "Þ"( ‚ "!" ‚ "!$ œ "Þ"( ‚ "!% !Þ!!!!!!!%& !Þ!!!!!!"# %Þ& ‚ "! ) "Þ# ‚ "! ( %Þ& "Þ# œ œ ‚ "! ) ( ( ( %&,!!!,!!! %Þ& ‚ "! %Þ& œ "Þ# ‚ "! ## !Þ!!!!!!$& "(!,!!! $Þ& ‚ "! ( "Þ( ‚ "!& $Þ& "Þ( œ œ ‚ "! ( & ( !Þ!!!!!!)& )Þ& ‚ "! ( )Þ& œ !Þ( ‚ "!& œ ( ‚ "! " ‚ "!& œ ( ‚ "!% !Þ!!!!!!!"%% "#,!!! "Þ%% ‚ "! ) "Þ# ‚ "!% "Þ%% "Þ# œ œ ‚ "! ) % & '!!,!!! ' ‚ "!& ' œ !Þ#)) ‚ "! * œ #Þ)) ‚ "! " ‚ "! * œ #Þ)) ‚ "! "!

119.

%&,!!!,!!!,!!! #"#,!!! %Þ& ‚ "!"! #Þ"# ‚ "!& %Þ& #Þ"# œ œ ‚ "!"! & % !.!!!") "Þ) ‚ "! % "Þ) œ &Þ$ ‚ "!"*

120.

!Þ!!!!!!!!#(& %,(&! #Þ(& ‚ "! * %Þ(& ‚ "!$ #Þ(& %Þ(& œ œ ‚ "! * $ "" "" &!!,!!!,!!!,!!! & ‚ "! & œ #Þ'"#& ‚ "! "(

121. $Þ$" ‚ "!% cm/sec œ

$Þ$" ‚ "!% cm "m '! sec $Þ$" ‚ "!% ' ‚ "!" † † œ m/min " sec "!! cm " min " ‚ "!# $Þ$" ' œ ‚ "!% " # m/min " œ "*Þ)' ‚ "!$ m/min œ "Þ*)' ‚ "!% m/min 8

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SECTION 0.2 122. Z œ 6A2 œ ',!!! mm *,(!! mm %,(!! mm œ ˆ' ‚ "!$ ‰ˆ*Þ( ‚ "!$ ‰ˆ%Þ( ‚ "!$ ‰ mm$ œ ' *Þ( %Þ( ‚ "!$ $ $ mm$ œ #($Þ&% ‚ "!* mm$ œ #Þ($&% ‚ "!"" mm$

123. mass œ ",!!!,!!!,!!! !Þ!!!!!!!!!!!!!!!!!!!!!!!"'(#%) g œ ˆ" ‚ "!* ‰ˆ"Þ'(#%) ‚ "! #% g‰ œ "Þ'(#%) ‚ "! "& g $!,!!!,!!!,!!! cm " mile '! sec '! min † † † " sec "'!,*$%Þ% cm " min " hr $ ‚ "!"! ' ‚ "!" ' ‚ "!" œ mile/hr "Þ'!*$%% ‚ "!& $ ' ' œ ‚ "!"! " " & mile/hr "Þ'!*$%% ¸ '(Þ"" ‚ "!( mile/hr œ 'Þ("" ‚ "!) mile/hr

124. $!,!!!,!!!,!!! cm/sec œ

125. Earth: 8 œ $ . œ *,#(&,#!!$ˆ#8 # ‰ %‘ œ *,#(&,#!!$ˆ#$ # ‰ %‘

œ *,#(&,#!!$ˆ#" ‰ %‘ œ *,#(&,#!!c"!d œ *#,(&#,!!! ¸ *$,!!!,!!! *Þ$ ‚ "!( mi

Mars: 8 œ % . œ *,#(&,#!!$ˆ#8 # ‰ %‘ œ *,#(&,#!!$ˆ#% # ‰ %‘

œ *,#(&,#!!$ˆ## ‰ %‘ œ *,#(&,#!!c"'d œ "%),%!$,#!! ¸ "%),!!!,!!! "Þ%) ‚ "!) mi

126. "! † "! † "! † #' † #' † #' œ "!$ † #'$ ; "!$ † #'$ œ "(,&(',!!! œ "Þ(&(' ‚ "!( 127. polar radius œ 'Þ$&'(&!& ‚ "!$ km equatorial radius œ 'Þ$(8135 ‚ "!$ km

128. polar radius œ $Þ*%"")& ‚ "!$ mi equatorial radius œ $Þ*&%%%$( ‚ "!$ mi

129. B8 B# œ B8 #

130.

B7 œ B7 $ B$

132.

B$7 & œ B$7 & # œ B$7 $ B#

131.

B7 B# B7 # œ œ B7 # $ œ B7 " $ B B$

133. B7 " B$ œ B7 " $ œ B7 %

134. +8 $ +$ œ +8 $ $ œ +8

135. In the expression B% , the base of the exponent is B, while in the expression

136. $# ‚ "!# is not in scientific notation because $# is not a number between 1 and 10.

B % , the base of the exponent is B.

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SECTION 0.2 137. #, % Ê

138. ∞, $d ∪ c$, ∞ Ê

oqÐïïÑqp #

íïÓqqÒïî

139. Since 1 & ! !, k1 &k œ 1 & œ 1 & œ & 1.

Exercises 0.3

140. distance œ k & ( k œ k#k œ #

(page 38)

positive

+"Î8

k+k

11.

*"Î# œ $#

13.

" Œ  #&

15.

"Î%

17.

"!,!!! "Î% œ "!%

19.

#( Œ  )

21.

10.

not

"Î$

8 È +,

8 È + 8 È ,

ÈB

)"Î$ œ #$

14.

"' Œ  '#&

16.

) Œ  #(

18.

",!#% "Î& œ %&

œ%

20.

'%"Î$ œ ˆ%$ ‰

œ %

'% "Î# Ê not a real number

22.

23.

"'+#

œ  %+ # ‘

"#& "Î$ œ  & $ ‘

œ %k+k

24.

#&+%

25.

"'+%

œ ’ #+ % “

œ #k+k

26.

'%+$

27.

$#+&

28.

'%+'

29.

#"', '

30.

#&'>)

œ$ # "Î#

" œ –Œ  — &

"Î#

œ $

% "Î%

"Î#

"Î&

œ "! $ "Î$

$ œ –Œ  — #

"Î#

œ  #+ & ‘

"Î$

"Î&

œ ’ ', # “

$ #

œ #+

$ "Î$

œ ', #

œ# % "Î%

# œ –Œ  — &

"Î%

" &

œ $

"Î%

"Î$

"Î%

"Î$

12.

"Î#

, ˆ'"Î$ ‰

"Î$

"Î'

"Î$

œ ’ &+# “

œ  %+ $ ‘

œ  #+ ' ‘

"Î%

"Î'

œ ’ %># “

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

# $

œ & œ &k+# k œ &+#

# "Î#

"Î$

# &

$ "Î$

# œ –Œ  — $ "Î&

"Î#

"Î$

œ %+

œ #k+k

% "Î%

œ %k># k œ %>#

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.3 "'+% Œ  #&, #

"Î#

31.

œ –Œ

# "Î#

%+# — &,

œº

"Î$

33.

37.

+&  $#, "!

34.

%*># Œ  "!!D %

"Î&

"Î#

œ ”Š

+ & ‹ • #, #

"Î&

# "Î#

(> œ –Œ  "!D # —

"!B# $C

œº

+ #, #

"'$Î# œ ˆ"'"Î# ‰ œ % $ œ '%

",!!!#Î$ œ ˆ",!!!"Î$ ‰ œ "! # œ "!!

41.

'% "Î# œ

43.

'% $Î# œ

45.

* $Î# œ

36.

)#Î$ œ ˆ)"Î$ ‰ œ ## œ %

38.

) #Î$ œ ’ ) "Î$ “ œ # # œ %

39.

(> º "!D#

(k>k "!D #

%$Î# œ ˆ%"Î# ‰ œ #$ œ )

40.

"!!$Î# œ ˆ"!!"Î# ‰ œ "!$ œ ",!!!

" " œ "Î# '% )

42.

#& "Î# œ

" " œ "Î# #& &

" " " " œ œ $ œ $ $Î# '% ) &"# '%"Î#

44.

%* $Î# œ

" " " " œ œ $ œ $ $Î# %* ( $%$ %*"Î#

46.

#( #Î$ œ

" " " œ $ œ $ "Î# *$Î# $ * " œ #( "Î# &

47.

% Œ  *

% œ –Œ  *

49.

#( Œ  '%

'% œ Œ  #(

50.

"#& Œ  )

) œŒ  "#&

51.

"!!=%

œ "!!"Î# =%

&Î#

$ "Î$

"!B# œ –Œ — $C œ

35.

32.

%+# &k, k

œ ",!!!B' Œ  #(C$

%+# º &,

#Î$

%Î$

"Î#

#& Œ  )"

%Î$

$Î#

48. "Î$ #

'% œ –Œ  #(

œ "!=#

’ #( "Î$ “

" " # œ * $

"Î# $

#& œ –Œ  )"

& "#& — œ Œ *  œ (#* $

% "' — œ Œ $  œ * #

"Î$ %

) œ –Œ  "#&

"Î#

#Î$

# $# — œ Œ $  œ #%$ #Î$

# "' — œ Œ &  œ '#& %

52.

'%?' @$

"Î$

œ '%"Î$ ?'

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

"Î$

œ %?# @

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.3 53.

$#C"! D &

54.

'#&+% , )

55.

B"! C&

56.

"Î&

"Î%

$Î&

$#C"! D & "Î&

"Î% '#&+% , )

$#"Î& C"! "Î& D & "Î&

"Î% '#&"Î% +% , ) "Î%

ˆ )B* C"# ‰ #Î$ œ ) #Î$ B ")Î$ C #%Î$ œ

59.

60.

"'B% Œ  '#&C)

61.

#(<' Œ  ",!!!="#

62.

63.

+#Î& +%Î& +'Î& œ "Î& œ +&Î& œ + "Î& + +

)+'  "#&, *

" <' ="# "

)

#Î$

B ' C ) œ

) #Î$ +"#Î$ # # +% %+% œ œ #Î$ ")Î$ # ' "#& , & , #&, '

#Î$

$Î%

" " # ' ) œ %B' C) # B C

"'$Î% B"#Î% #$ B$ )B$ œ $ ' œ $Î% #%Î% '#& C & C "#&C'

#Î$

œŒ

$#7"!  #%$8"&

#Î&

",!!!="#  #(<'

œŒ

#Î$

#%$8"&  $#7"!

#Î&

",!!!#Î$ =#%Î$ "!# =) "!!=) œ # % œ #Î$ "#Î$ #( < $ < *<% #%$ #Î& 8$!Î& $ # 8' *8' œ œ $##Î& 7#!Î& # # 7% %7%

È%* œ È(# œ (

64. 66.

$ $ È "#& œ È &$ œ &

68.

$ $ È "#& œ É & $ œ &

70.

71.

73.

È$'B# œ É 'B # œ k'Bk œ 'kBk

" &+, #

&Î'

58.

69.

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

'%+' , "#

ˆ<) ="' ‰ $Î% œ < #%Î% = %)Î% œ < ' = "# œ

67.

" #C# D

œ B$!Î& C"&Î& œ B' C$

57.

65.

$# # # " & œ ËŒ  œ œ "!!,!!! "! "! &

B'Î( B$Î( B*Î( œ (Î( œ B#Î( #Î( &Î( B B B

È)" œ È*# œ *

$ $ È '% œ É % $ œ %

& & È #%$ œ É $ & œ $

72.

74.

È#&C# œ É &C # œ k&Ck œ &kCk

#&' % % % œ ËŒ  œ '#& & &

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.3 75. 77.

79. 81. 82. 83. 84. 85.

86.

87. 88. 89. 90.

91.

92.

È*C% œ É $C# # œ k$C# k œ $C# $ $ È )C$ œ É #C $ œ #C

Ê %

76. 78.

B% C) BC# BC# kBkC# % œ œ œ Ë Œ  º º D "# D$ D$ kD $ k %

80.

È ) È # œ È %È # È # œ #È # È # œ È #

È+% , ) œ É +# , % # œ k+# , % k œ +# , % $ $ È #(D* œ É $D$ $ œ $D$

Ê &

+"! , & +# , +# , & œ œ Ë Œ  -"& -$ -$

È(& #È#( œ È#&È$ #È*È$ œ &È$ # $ È$ œ &È$ 'È$ œ È$ È#!!B# È*)B# œ È"!!B# È# È%*B# È# œ "!BÈ# (BÈ# œ "(BÈ#

È"#)+$ +È"'#+ œ È'%+# È#+ +È)"È#+ œ )+È#+ *+È#+ œ +È#+

#È%)C& $CÈ"#C$ œ #È"'C% È$C $CÈ%C# È$C œ #ˆ%C# ‰È$C $C #C È $C œ )C# È$C 'C# È$C œ #C# È$C CÈ""#C %È"(&C$ œ CÈ"'È(C %È#&C# È(C œ C % È(C % &C È(C œ %CÈ(C #!CÈ(C œ #%CÈ(C

$ $ $ $ $ $ $ $ $ $ $ #È )" $È #% œ #È #(È $ $È )È $ œ # $ È $ $ # È $ œ 'È $ 'È $ œ "#È $ % % % % % % % % % % $È $# #È "'# œ $È "'È # #È )"È # œ $ # È # # $ È # œ 'È # 'È #œ! % % % % % % % % % È (')D & È %)D & œ È #&'D % È $D È "'D% È $D œ %DÈ $D #DÈ $D œ 'DÈ $D

& & & & & & & & #È '%C# $È %)'C# œ #È $#È #C# $È #%$È #C# œ # # È #C# $ $ È #C# & & & œ %È#C# *È#C# œ &È #C#

È)B# C BÈ#C È&!B# C œ È%B# È#C BÈ#C È#&B# È#C œ #BÈ#C BÈ#C &BÈ#C œ 'BÈ#C

$BÈ")B #È#B$ È(#B$ œ $BÈ*È#B #ÈB# È#B È$'B# È#B œ $B $ È#B #BÈ#B 'BÈ#B œ *BÈ#B #BÈ#B 'BÈ#B œ &BÈ#B

93.

$ $ $ $ $ $ $ $ È "'BC% CÈ #BC È &%BC% œ È )C$ È #BC CÈ #BC È #(C$ È #BC $ $ $ œ #CÈ#BC CÈ#BC $CÈ#BC œ !

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.3 94.

95.

97.

99.

101.

102.

103.

% % % % % % % % % È &"#B& È$#B& È ",#&!B& œ È#&'B% È #B È"'B% È #B È'#&B% È #B % % % % È È È È œ %B #B #B #B &B #B œ (B #B

$ $ È$ $È $ È œ † œ œ $ È$ È$ È$ $

' ' È& 'È & œ † œ È& È& È& &

96.

ÈB #È B # # œ † œ ÈB ÈB ÈB B

)È C ) ) ÈC œ † œ ÈC ÈC ÈC C

98.

$ $ $ # # È % #È % #È % È $ œ † œ œ œ % $ $ $ $ È È È È # ) # # %

$ $ $ %. %. È $ %. È $ %. È $ œ † œ œ $ $ $ $ È È È È $ * * $ #(

100.

$ $ $ È &+ &+ &+# &+È &+# &+È &+# $ œ † œ œ œ È&+# $ $ $ $ È#&+ È#&+ È&+# È"#&+$ &+

$ $ $ È ( ( '-# (È '-# (È '-# œ † œ œ $ $ $ $ È$'È$'- È'-# È#"'-$ '-

% % % È #, #, #(+# #, È #(+# #, È #(+# œ † œ œ % % % % È$+# È$+# È#(+# È)"+% $+

ÈB ÈB È#C È#BC B 104. Ê œ œ † œ È#C È#C È#C #C #C

$ $ $ $ $ $ È È #?% #?% ?$ È #? È $@# ?È '?@# ?È '?@# œ $ œ † œ œ $ $ $ È*@ È*@ È$@# È#(@$ *@ $@

105. Ê $

106. Ê $

107.

È&

109.

$ È *

110.

111.

$ $ $ $ $ $ È È $=& $=& =$ È $=# È #< =È '<=# =È '<=# œ œ † œ œ # $ $ $ $ È%<# È%<# È#< È)<$ %< #<

$ È "', #

& È "', $

'%+

È& È& & " † œ œ "! È& "!È& #È &

108.

ÈC $

$ $ $ È È * È $ #( $ " † $ œ $ œ $ œ $ È$ $ È$ $È $ $È $

$ È "', #

& È "', $

'%+

†

$ È %, $ È %,

& È #, #

È#, # &

$ È '%, $

$ "'È %,

& È $#, &

& '%+È #, #

$ "'È %,

ÈC ÈC C † œ $ ÈC $È C

$ %È %,

#, , œ & È È # '%+ #, $#+ & #, # 14

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.3 112. Ê

È$B È$B È$B $B $B $B $B B œ œ † œ œ œ œ È&( È&( È$B È"("B È*È"*B È È &( $ "*B "*B

È" È" È$ È$ È$ È$ È$ " " " È$ " 113. Ê Ê œ œ † † œ œ È$ È#( È$ È$ È#( È$ È)" $ #( $ $ * $È $ È $ #È $ œ œ * * * $ $ $ $ $ $ $ $ È È È È È È " " " " È % " % % % % È % $ " $ œ $ $ œ $ † $ $ † $ œ $ $ œ 114. Ê Ê È# È"' È# È% È"' È% È) È'% # "' # % $ $ $ È # % È % $È % œ œ % % %

115. Ê

ÈB ÈB ÈB ÈB È# ÈB È# ÈB È# B B B Ê Ê œ œ † † † È) È# È$# È) È# È# È# È$# È# ) # $# È#B È#B È#B œ È"' È% È'% œ

È#B

% # ) È#B #È#B %È#B È#B œ œ ) ) ) )

$ 116. Ê

$ $ $ $ C $ C $ C $ C $ C $ C È È È È È È È È È C C C # # # $ $ Ê Ê œ $ $ $ œ $ † $ $ † $ $ † $ È% È$# È&!! È% È# È$# È# È&!! È# % $# &!! $ $ $ È È #C È #C #C œ $ $ $ È) È'% È",!!!

$ È #C

# % "! $ $ $ $ "!È #C &È #C #È #C "$È #C œ œ #! #! #! #!

"Î% % 117. È * œ *"Î% œ $# œ $#Î% œ $"Î# œ È$

"Î' ' 118. È #( œ #("Î' œ $$ œ $$Î' œ $"Î# œ È$

"Î"! "Î"! "Î& "! & 119. È "'B' œ "'B' œ #% B' œ #%Î"! B'Î"! œ ##Î& B$Î& œ ## B$ œ È %B$

"Î' "Î' "Î# ' 120. È #(B* œ #(B* œ $$ B* œ $$Î' B*Î' œ $"Î# B$Î# œ $B$ œ È$B$ œ BÈ$B ' ' ' $ ' ' 121. È#È # œ #"Î# † #"Î$ œ #$Î' † ##Î' œ È #$ È ## œ È )È %œÈ $#

' ' ' ' $ ' 122. È$È & œ $"Î# &"Î$ œ $$Î' &#Î' œ È $$ È &# œ È #(È #& œ È '(&

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.3

123.

% È $

124.

$ È #

È#

È&

% % % % % % È È È È È $"Î% $"Î% $ $ $ È % "# "# œ œ œ œ † œ œ % % % % % È È È È È # #"Î# ##Î% # "' % % % #

' ' ' ' ' ' È È È È È #"Î$ ##Î' ## % % È "#& &!! &!! œ œ œ œ † œ œ ' ' ' ' ' È È È È È $ &"Î# &$Î' & "&,'#& "#& "#& "#& &

% 125. ÈB% œ kBk. Since kBk œ B if B !, then % È B% œ B if B !.

B 127. Œ  C

7Î8

B B 8 126. Ê œŒ  C C

"Î8

8 È B B"Î8 œ "Î8 8 È C C

B 7Î8 B 7Î8 B7Î8 C7Î8 C7Î8 C7 "Î8 C7 œ † œ œ œ Œ  C 7Î8 C 7Î8 B7Î8 C7Î8 B7Î8 B7 B7 "Î8

"Î8

œÊ 8

C7 B7

128. Consider the case when 8 is even, 7 is odd and B is negative. Then 7 7 8 8 B7Î8 œ ˆB"Î8 ‰ œ ˆÈ B‰ . Thus, È B must be a real number for the expression to be defined. 129. # ! B Ÿ & Ê #, &d

131. B# C# œ # # $# œ % * œ & 132.

130. If B %, then $ B ! !. Then k$ Bk œ $ B œ $ B œ B $.

BC %C # $ % $ ' "# ' œ œ œ œ $ B # # #

133. '"(,!!!,!!! œ 'Þ"( ‚ "!)

Exercises 0.4

134. !Þ!!#$& ‚ "!% œ #$Þ&

(page 50)

monomial, variables

degree, variables

trinomial

binomial

one

zero

degree

coefficients, variables

10.

$È B #

12.

yes, binomial, 3rd degree

13.

15.

yes, binomial, 3rd degree

18.

21.

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

11.

yes, trinomial, 2nd degree

14.

16.

yes, monomial, 5th degree

17.

yes, monomial, 0th degree

19.

yes, monomial, no degree

20.

yes, none, 3rd degree

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.4 22.

ˆ#B% &B$ ‰ ˆ(B$ B% #B‰ œ #B% &B$ (B$ B% #B

œ #B% B% &B$ (B$ #B œ B% #B$ #B

23.

ˆC& #C$ (‰ ˆC& #C$ (‰ œ C& #C$ ( C& #C$ (

œ C& C& #C$ #C$ ( ( œ %C$ "%

24.

ˆ$>( (>$ $‰ ˆ(>( $>$ (‰ œ $>( (>$ $ (>( $>$ (

œ $>( (>( (>$ $>$ $ ( œ %>( %>$ %

25.

#ˆB# $B "‰ $ˆB# #B %‰ % œ #ˆB# ‰ # $B # " $ˆB# ‰ $ #B $ % % œ #B# 'B # $B# 'B "# % œ #B# $B# 'B 'B # "# % œ B# "%

26.

&ˆB$ )B $‰ #ˆ$B# &B‰ ( œ &ˆB$ ‰ & )B & $ #ˆ$B# ‰ # &B (

œ &B$ %!B "& 'B# "!B ( œ &B$ 'B# %!B "!B "& ( œ &B$ 'B# $!B )

27.

)ˆ># #> &‰ %ˆ># $> #‰ 'ˆ#># )‰ œ )ˆ># ‰ ) #> ) & %ˆ># ‰ % $> % # 'ˆ#># ‰ ' ) œ )># "'> %! %># "#> ) "#># %) œ )># %># "#># "'> "#> %! ) %) œ #)> *'

28.

$ˆB$ B‰ #ˆB# B‰ $ˆB$ #B‰ œ $ˆB$ ‰ $ B #ˆB# ‰ # B $ˆB$ ‰ $ #B œ $B$ $B #B# #B $B$ 'B œ $B$ $B$ #B# $B #B 'B œ #B# B

29.

CˆC# "‰ C# C # C #C # œ CˆC# ‰ C " C# C C# # C #C C # œ C$ C C$ #C# #C# #C œ C$ C$ #C# #C# C #C œ %C# C

30.

%+# + " $+ˆ+# %‰ +# + #

œ %+# + %+# " $+ˆ+# ‰ $+ % +# + +# #

œ %+$ %+# $+$ "#+ +$ #+# œ %+$ $+$ +$ %+# #+# "#+ œ #+$ '+# "#+

31.

BC B %C CˆB# $BC‰ BC #B $C œ BC B BC %C CˆB# ‰ C $BC BC #B BC $C

œ B# C %BC# B# C $BC# #B# C $BC# œ B# C B# C #B# C %BC# $BC# $BC# œ #B# C %BC#

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.4 32.

33.

$78 7 #8 '7 $78 " #8 %78 " œ $78 7 $78 #8 '7 $78 '7 " #8 %78 #8 " œ $7# 8 '78# ")7# 8 '7 )78# #8 œ $7# 8 ")7# 8 '78# )78# '7 #8 œ "&7# 8 #78# '7 #8 #B# C$ %BC% œ # % B# BC$ C% œ )B$ C(

34.

"&+$ , ˆ #+# , $ ‰ œ "& # +$ +# ,, $ œ $!+& , %

35.

$7# 8ˆ#78# ‰Š

36.

37.

%<= <# =# œ %<= <# %<= =# œ %<$ = %<=$

38. 39.

78 " ' % % 7% 8% 7 8 œ ‹ œ $ # Œ 7# 7788# 8 œ "# "# "# #

$<# =$ #<# = "&<=# $ # "& # # $ # & ' Œ Œ  œ Œ Œ Œ < < <= == œ $< = & $ # & $ #

'?# @ #?@# C œ '?# @ #?@# '?# @ C œ "#?$ @$ '?# @C

'+, # -ˆ#+- $,-# %+, # -‰ œ '+, # - #+- '+, # -ˆ$,-# ‰ '+, # -ˆ %+, # -‰ œ "#+# , # -# ")+, $ -$ #%+# , % -#

78# 78# 78# 78# ˆ%78 '7# )‰ œ ˆ '7# ‰ %78 ) # # # # # $ $ # # œ #7 8 $7 8 %78

40.

41.

+ # + # œ +# #+ #+ % œ +# %+ %

43.

+ ' # œ + ' + ' œ +# '+ '+ $' œ +# "#+ $'

42.

44.

C & C & œ C# &C &C #& œ C# "!C #& > * # œ > * > * œ ># *> *> )" œ ># ")> )"

45.

B % B % œ B# %B %B "' œ B# "'

46.

D ( D ( œ D # (D (D %* œ D # %*

47.

B $ B & œ B# &B $B "& œ B# #B "&

48.

D % D ' œ D # 'D %D #% œ D # #D #%

49.

? # $? # œ $?# #? '? % œ $?# %? %

50.

%B " #B $ œ )B# "#B #B $ œ )B# "!B $

51.

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

52.

%B " #B ( œ )B# #)B #B ( œ )B# $!B (

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SECTION 0.4 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65.

$+ #, # œ $+ #, $+ #, œ *+# '+, '+, %, # œ *+# "#+, %, #

%+ &, %+ &, œ "'+# #!+, #!+, #&, # œ "'+# #&, #

$7 %8 $7 %8 œ *7# "#78 "#78 "'8# œ *7# "'8#

%< $= # œ %< $= %< $= œ "'<# "#<= "#<= *=# œ "'<# #%<= *=# #C %B $C #B œ 'C# %BC "#BC )B# œ 'C# "'BC )B#

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

*B C B# $C œ *B$ #(BC B# C $C# œ *B$ B# C #(BC $C# )+# , + #, œ )+$ "'+# , +, #, #

&D #> D # > œ &D$ &>D #>D# #># œ &D$ #>D# &>D #>#

C #B# B# $C œ B# C $C# #B% 'B# C œ #B% &B# C $C#

ŠÈ& $B‹Š# È&B‹ œ #È& &B 'B $È&B# œ $È& B# B #È& ŠÈ# B‹Š$ È#B‹ œ $È# #B $B È#B# œ È# B# &B $È# $B " $ œ $B " $B " $B " œ ˆ*B# $B $B "‰ $B " œ ˆ*B# 'B "‰ $B "

œ *B# $B *B# " 'B $B 'B " " $B " " œ #(B$ *B# ")B# 'B $B " œ #(B$ #(B# *B "

66.

#B $ $ œ #B $ #B $ #B $ œ ˆ%B# 'B 'B *‰ #B $ œ ˆ%B# "#B *‰ #B $

œ %B# #B %B# $ "#B #B "#B $ * #B * $ œ )B$ "#B# #%B# $'B ")B #( œ )B$ $'B# &%B #(

67.

$B " ˆ#B# %B $‰ œ $Bˆ#B# ‰ $B %B $B $ "ˆ#B# ‰ " %B " $

œ 'B$ "#B# *B #B# %B $ œ 'B$ "%B# &B $

68.

#B & ˆB# $B #‰ œ #BˆB# ‰ #B $B #B # &ˆB# ‰ & $B & #

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

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.4 69.

$B #C ˆ#B# $BC %C# ‰ œ $Bˆ#B# ‰ $B $BC $Bˆ%C# ‰ #Cˆ#B# ‰ #C $BC #Cˆ%C# ‰

œ 'B$ *B# C "#BC# %B# C 'BC# )C$ œ 'B$ &B# C 'BC# )C$

70.

%< $= ˆ#<# %<= #=# ‰ œ %<ˆ#<# ‰ %< %<= %<ˆ #=# ‰ $=ˆ#<# ‰ $= %<= $=ˆ #=# ‰

œ )<$ "'<# = )<=# '<# = "#<=# '=$ œ )<$ "!<# = #!<=# '=$

71. 72.

#C8 $C8 C 8 œ #C8 $C8 #C8 C 8 œ 'C8 8 #C8 8 œ 'C#8 #C! œ 'C#8 # $+ 8 ˆ#+8 $+8 " ‰ œ $+ 8 #+8 $+ 8 ˆ$+8 " ‰ œ '+ 8 8 *+ 8 8 " œ '+! *+ " * œ' +

73.

&B#8 C8 ˆ#B#8 C 8 $B #8 C8 ‰ œ &B#8 C8 ˆ#B#8 C 8 ‰ &B#8 C8 ˆ$B #8 C8 ‰

74.

#+$8 , #8 ˆ&+ $8 , +, #8 ‰ œ #+$8 , #8 ˆ&+ $8 , ‰ #+$8 , #8 ˆ +, #8 ‰

75.

B8 $ B8 % œ B8 B8 %B8 $B8 "# œ B#8 B8 "#

76.

œ "!B#8 #8 C8 8 "&B#8 #8 C8 8 œ "!B%8 C! "&B! C#8 œ "!B%8 "&C#8

œ "!+$8 $8 , #8 " #+$8 " , #8 #8 œ "!+! , #8 " #+$8 " , ! œ "!, #8 " #+$8 "

+8 & +8 $ œ +8 +8 $+8 &+8 "& œ +#8 )+8 "&

77.

#<8 ( $<8 # œ #<8 $<8 #<8 # ( $<8 "% œ '<#8 %<8 #"<8 "% œ '<#8 #&<8 "%

78.

%D 8 $ $D 8 " œ %D8 $D8 %D8 " $ $D8 $ œ "#D #8 %D 8 *D8 $ œ "#D#8 "$D8 $

79. 80. 81.

B"Î# ˆB"Î# C BC"Î# ‰ œ B"Î# B"Î# C B"Î# BC"Î# œ B#Î# C B$Î# C"Î# œ BC B$Î# C"Î#

+, "Î# ˆ+"Î# , "Î# , "Î# ‰ œ +, "Î# +"Î# , "Î# +, "Î# , "Î# œ +$Î# , #Î# +, #Î# œ +$Î# , +, ˆ+"Î# , "Î# ‰ˆ+"Î# , "Î# ‰ œ +"Î# +"Î# +"Î# , "Î# +"Î# , "Î# , "Î# , "Î# œ +#Î# , #Î# œ + ,

82.

ˆB$Î# C"Î# ‰ œ ˆB$Î# C"Î# ‰ˆB$Î# C"Î# ‰ œ B$Î# B$Î# B$Î# C"Î# B$Î# C"Î# C"Î# C"Î# #

œ B'Î# #B$Î# C"Î# C#Î# œ B$ #B$Î# C"Î# C

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.4 È$ "

È& #

# ŠÈ $ " ‹

ŠÈ $ ‹ " #

# ŠÈ $ " ‹

ŠÈ & ‹

È& #

$BŠÈ( #‹

# ŠÈ $ " ‹

œ È$ "

È$ "

È$ " È$ "

È& #

È& # È& #

85.

È( #

86.

"%CŠÈ# $‹ "%CŠÈ# $‹ È# $ "%C "%C œ † œ œ œ #CŠÈ# $‹ # È# $ È# $ È# $ # * # È Š #‹ $

83.

84.

†

È( #

È( # È( # $B

†

" ŠÈ & # ‹ #

$BŠÈ( #‹ ŠÈ ( ‹ # # #

$ "

& %

È& #

( %

œ È& #

$BŠÈ( #‹ $

87.

BŠB È$‹ BŠB È$‹ B B B È$ œ † œ œ # B# $ B È$ B È$ B È$ B# ŠÈ$‹

88.

#C È(

89.

ŠC È#‹ŠC È#‹ C È# C È# C È# C# #CÈ# # œ † œ œ # C# # C È# C È# C È# C # ŠÈ # ‹

90.

91.

œ BŠÈ( #‹

CŠ#C È(‹ CŠ#C È(‹ #C È( œ œ # %C# ( #C È( #C È( #C # ŠÈ(‹ C

†

ŠB È$‹ŠB È$‹ B È$ B È$ B È$ B# #BÈ$ $ œ † œ œ # B# $ B È$ B È$ B È$ B# ŠÈ$‹

È # È ' È $ ŠÈ $ ‹ È# È$ " È$ È# È' È$ $ œ † œ œ # " $ " È$ " È$ " È$ " # ŠÈ $ ‹

È# È$

œ œ œ

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È# È' È$ $

# È Š # È ' È $ $‹ # È$ $ È# È' #

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SECTION 0.4

92.

È $ È ' È # ŠÈ # ‹ È$ È# " È# È$ È' È# # œ † œ œ # " # " È# " È# " È# " # ŠÈ # ‹

È$ È#

È$ È' È# #

" œ ŠÈ $ È ' È # # ‹

93.

ÈB ÈC

94.

È#B C

95.

È# "

96.

ÈB $

ÈB ÈC È#B C

œ È' È# È$ #

ÈB# ÈBC ÈBC ÈC# ÈB ÈC ÈB ÈC B #ÈBC C † œ œ # # ÈB ÈC ÈB ÈC B C ˆÈB‰ ˆÈC‰

È%B# CÈ#B CÈ#B C# È#B C È#B C #B #CÈ#B C# † œ œ # È#B C È#B C #B C# ŠÈ#B‹ C#

ŠÈ # ‹ " # È# " È# " # " " œ † œ œ œ È# " # # ŠÈ # " ‹ # ŠÈ # " ‹ # ŠÈ # " ‹ #

ÈB $ ÈB $ ˆÈB‰# $# B * † œ œ È ˆ È ‰ ˆ È $ B $ $ B $ $ B $‰

C # ŠÈ $ ‹ C È$ C È$ C È$ C# $ œ † œ œ C È$ C È$ C È$ C# CÈ$ CÈ$ È* C# #CÈ$ $ #

97.

ˆÈ+‰# ŠÈ, ‹ È+ È, È+ È, È+ È, + , œ † œ œ È+# È+, È+, È, # È+ È, È+ È, È+ È, + #È+, , #

98.

99.

ÈB $ ÈB $

# ÈB $ ÈB ÈB $ ÈB ˆÈB $‰ ˆÈB‰# † œ ÈB $ ÈB $ $ˆÈB $ ÈB‰ B $ B œ È $ˆ B $ ÈB‰ $ " œ œ È È $ˆ B $ ÈB‰ B $ ÈB

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SECTION 0.4

100.

È# 2 È# 2

# ˆÈ# 2‰ ŠÈ#‹ È# 2 È# È# 2 È# œ † œ È# 2 È# 2 2 ŠÈ # 2 È # ‹

œ œ

# 2 # 2 ŠÈ # 2 È # ‹

$'+# , $ #+ œ #+# " , $ ' œ #+" , $ œ $ ' ")+, ,

102.

%&<# =& >$ & # ' & # $ ) & % $ & &=$ œ < = > œ < = > œ #(<' =# >) $ $ $<% >&

103.

"'B' C% D * # # #D * œ B' * C% ' D * ! œ B $ C # D * œ $ # * ' ! #%B C D $ $ $B C

104.

$#7' 8% :# "' ' ' % ( # # "' ! $ ! "' œ 7 8 : œ 7 8 : œ #'7' 8( :# "$ "$ "$8$ &B$ C# "&B$ C% &B$ C# "&B$ C% œ "!B# C$ "!B# C$ "!B# C$ B $BC œ #C #

106.

2 ŠÈ # 2 È # ‹

101.

105.

" È# 2 È#

*7% 8* '7$ 8% *7% 8* '7$ 8% œ "#7$ 8$ "#7$ 8$ "#7$ 8$ $78' 8 œ % #

107.

#%B& C( $'B# C& "#BC #%B& C( $'B# C& "#BC #C$ $C " œ œ $ % $ & % & % & % & % '!B C '!B C '!B C '!B C & &B &B C

108.

*+$ , % #(+# , % ")+# , $ *+$ , % #(+# , % ")+# , $ + $ " œ œ $ $ % # ( # ( # ( ")+ , ")+ , ")+ , ")+# , ( #, #, ,

109.

$B # B $ $B# ""B ' $B# *B #B ' #B ' !

111.

B ( #B & #B# "*B #B# &B "%B "%B

# #B &

110.

B $ $B # $B# ""B ' $B# #B *B ' *B ' !

112.

#B & B ( #B# "*B $& #B# "%B &B $& &B $& !

$( $( $& #

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SECTION 0.4 113.

#B# #B # B " #B$ !B# !B #B$ #B# #B# !B #B# #B #B #B

$ B "

114.

" " " # $

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

" #B (

#! #! #! #" "

116.

B # B " B# $ B# $ B$ #B# %B & B$ $B #B# B & #B# ' B "

& B# # B B$ # $ & % $ B # B !B #B $B# !B * B& #B# $ #B B# !B * #B$ % B# &

118.

B# # B$$ $ B $ B& !B% #B$ $B# !B * B& $B# $ #B !B * #B$ ' $

119.

B% #B$ %B# )B "' B # B& !B% !B$ !B# !B $# B& #B% #B% !B$ #B% %B$ %B$ !B# %B$ )B# )B# !B )B# "'B "'B $# "'B $# !

120.

121.

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

115.

B $ B B " B$ #B# %B $ B$ B# B $B# $B $ $B# $B $ !

117.

B$ B# B " B " B% !B$ !B# !B " B% B$ B$ !B# B$ B# B# !B B# B B " B " !

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SECTION 0.4 122.

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

123. Area œ length † width œ B & B # ft# œ B# #B &B "! ft# œ B# $B "! ft# 124.

" † base † height # " B# $B %! œ B ) † height # #ˆB# $B %!‰ œ B ) † height Area œ

#B# 'B )! œ B ) † height #B# 'B )! œ height B )

125. Volume œ 6 † A † 2 œ "# #B "# #B B in.$ œ ˆ"%% %)B %B# ‰B in.$ œ ˆ"%%B %)B# %B$ ‰ in.$

#B "! B ) #B# 'B )! #B# "'B "!B )! "!B )! ! The height is #B "! ft.

. $B# "*B #! œ < $B % B & $B % $B# "*B #! $B# %B "&B #! "&B #! ! > œ B &

126. > œ

127. + , - # œ + , - + , - œ + + , - , + , - - + , - œ +# +, +- +, , # ,- +- ,- -# œ +# , # -# #+, #,- #+128. + , - . # œ + , - . + , - . œ + + , - . , + , - . - + , - . . + , - . œ +# +, +- +. +, , # ,- ,. +- ,- -# -. +. ,. -. .# œ +# , # -# . # #+, #+- #+. #,- #,. #-. 129. Answers may vary.

130. Multiply the numeratior and denominator by the conjugate of the numerator ˆÈB #‰. 131. Check the formula with + œ " and , œ #.

132. Check the formula with + œ $ and , œ %.

133. *$Î# œ ˆ*"Î# ‰ œ $$ œ #( $

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SECTION 0.4 134. Œ

)  "#&

135. Œ

'#&B%  "'C)

#Î$

œŒ

$Î%

"#&  )

#Î$

œ Œ

'#&$Î% B%

"#&  )

$Î%

"'$Î% C) $Î%

"Î$

& #&  œ Œ# œ %

"#&B$ )C'

136. È)!B% œ È"'B% È& œ %B# È&

$ $ $ $ $ $ $ $ $ $ 137. È"'+, % , È &%+, œ È), $ È #+, , È #(È #+, œ #, È #+, , $ È #+, œ #, È #+, $, È #+, $ È œ , #+, % % % % % % % % % 138. BÈ ",#)!B È)!B& œ BÈ #&'È &B È"'B% È &B œ %BÈ &B #BÈ &B œ 'BÈ &B

Exercises 0.5

(page 61)

factor

integer, prime

+B ,B œ B + ,

B# C# œ B C B C

5. 7. 9. 11. 13. 15. 17. 18. 19. 21. 23. 24. 25.

B# #BC C# œ B C B C œ B C #

B$ C$ œ B C B# BC C#

$B ' œ $ B #

6. 8. 10.

)B# %B$ œ %B# # B

(B# C# "%B$ C# œ (B# C# " #B

+ B C , B C œ B C + ,

12. 14. 16.

B# #BC C# œ B C B C œ B C #

B$ C$ œ B C B# BC C#

&C "& œ & C $

*C$ 'C# œ $C# $C #

#&C# D "&CD# œ &CD &C $D

, B C + B C œ B C , +

%+ , "#+# $+, œ %+ , $+ %+ , œ " %+ , $+ %+ , œ %+ , " $+ B# %B BC %C œ B B % C B % œ B % B C %B# * œ #B # $# œ #B $ #B $

% *<# œ ## $< # œ # $< # $<

20. 22.

$'D # %* œ 'D # (# œ 'D ( 'D (

"' %*B# œ %# (B # œ % (B % (B

)"B% " œ *B# "# œ *B# " *B# " œ *B# " $B " $B " #

)" B% œ *# B# œ * B# * B# œ * B# $ B $ B #

B D # #& œ B D # &# œ B D & B D &

26.

B C # * œ B C # $# œ B C $ B C $

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SECTION 0.5 27. 29. 31.

B# )B "' œ B % B % œ B % #

, # "!, #& œ , & , & œ , & #

28. 30.

C# "%C %* œ C ( C ( œ C ( #

7# %78 %8# œ 7 #8 7 #8

32.

<# )<= "'=# œ < %= < %=

"#B# BC 'C# œ %B $C $B #C

34.

)B# "!BC $C# œ %B C #B $C

œ 7 #8

33.

+# "#+ $' œ + ' + ' œ + ' #

œ < %= #

35.

B# "!B #": + œ ", , œ "!, - œ #" key number œ +- œ " #" œ #" B# "!B #" œ B# (B $B #" œ B B ( $ B ( œ B ( B $

36.

B# (B "!: + œ ", , œ (, - œ "! key number œ +- œ " "! œ "! B# (B "! œ B# &B #B "! œ B B & # B & œ B & B #

37.

B# %B "#: + œ ", , œ %, - œ "# key number œ +- œ " "# œ "# B# %B "# œ B# 'B #B "# œ B B ' # B ' œ B ' B #

38.

B# #B '$: + œ ", , œ #, - œ '$ key number œ +- œ " '$ œ '$ B# #B '$ œ B# *B (B '$ œ B B * ( B * œ B * B (

39.

':# (: $: + œ ', , œ (, - œ $ key number œ +- œ ' $ œ ") ':# (: $ œ ':# *: #: $ œ $: #: $ #: $ œ #: $ $: "

40.

%; # "*; "#: + œ %, , œ "*, - œ "# key number œ +- œ % "# œ %) %; # "*; "# œ %; # $; "'; "# œ ; %; $ % %; $ œ %; $ ; %

41. 42. 43. 44. 45. 46. 47. 48. 49.

>$ $%$ œ >$ ($ œ > ( c># > ( (# d œ > ( ># (> %*

<$ )=$ œ <$ #= $ œ < #= <# < #= #= # ‘ œ < #= <# #<= %=# )D $ #( œ #D $ $$ œ #D $  #D # #D $ $# ‘ œ #D $ %D# 'D *

"#&+$ '% œ &+ $ %$ œ &+ %  &+ # &+ % %# ‘ œ &+ % #&+# #!+ "' $+# ,- '+, # - *+,-# œ $+,- + #, $-

&B$ C$ D $ #&B# C# D # "#&BCD œ &BCD B# C# D# &BCD #&

$B$ $B# B " œ $B# B " " B " œ B " $B# "

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

#>BC #->B $>C $-> œ > #BC #-B $C $- œ >c#B C - $ C - d œ > C - #B $ 27

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SECTION 0.5 50. 51. 52.

53.

55.

56.

57. 58.

#+B %+C ,B #,C œ #+ B #C , B #C œ B #C #+ ,

+B ,B +C ,C +D ,D œ B + , C + , D + , œ + , B C D

'B# C$ ")BC $B# C# *B œ $Bˆ#BC$ 'C BC# $‰ œ $B#CˆBC# $‰ "ˆBC# $‰‘ œ $BˆBC# $‰ #C "

B# C D # œ cB C D dcB C D d œ B C D B C D

54.

D# C $ # œ cD C $ dcD C $ d œ D C $ D C $

B C # B C # œ c B C B C dc B C B C d œ B C B C B C B C œ #B #C œ %BC #+ $ # #+ $ # œ c #+ $ #+ $ dc #+ $ #+ $ d œ #+ $ #+ $ #+ $ #+ $ œ %+ ' œ #%+

B% C% œ B# C# œ B# C# B# C# œ B# C# B C B C #

D % )" œ D # *# œ D# * D# * œ D# * D# $# œ D# * D $ D $ #

$B$ C $BC œ $BCˆB# "‰ œ $BC B " B "

59.

$B# "# œ $ B# % œ $ B # B #

60.

61.

")BC# )B œ #Bˆ*C# %‰ œ #B $C # $C #

62.

#(B# "# œ $ˆ*B# %‰ œ $ $B # $B #

63.

B# #B "& Ê prime

64.

B# B # Ê prime

65.

"& #+ #%+# œ #%+# #+ "& œ '+ & %+ $

66.

$# ')B *B# œ *B# ')B $# œ *B % B )

67. 69. 70. 71. 72. 73. 74.

'B# #*BC $&C# œ $B (C #B &C

68.

"!B# "(BC 'C# œ &B 'C #B C

"#:# &):; (!; # œ # ':# #*:; $&; # œ # ': $&; : ; $B# 'BC *C# œ $ B# #BC $C# œ $ B $C B C

'7# %(78 $&8# œ '7# %(78 $&8# œ '7 &8 7 (8 "%<# ""<= "&=# œ "%<# ""<= "&=# œ (< &= #< $=

'B$ #$B# $&B œ B 'B# #$B $& œ B 'B ( B & C$ C# *!C œ C C# C *! œ C C "! C *

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SECTION 0.5 75. 76. 77. 79. 81. 83.

85.

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

"#B "(B# (B$ œ (B$ "(B# "#B œ B (B# "(B "# œ B B $ (B %

B% #B# "& œ B# & B# $

B% B# ' œ B# $ B# #

78.

+#8 #+8 $ œ +8 $ +8 "

+#8 '+8 ) œ +8 % +8 #

80.

'B#8 (B8 # œ $B8 # #B8 "

*B#8 *B8 # œ $B8 # $B8 "

82.

%B#8 *C#8 œ #B8 # $C8 # œ #B8 $C8 #B8 $C8

"!C#8 ""C8 ' œ &C8 # #C8 $

84.

)B#8 #B8 $ œ %B8 $ #B8 "

86.

"'C%8 #&C#8 œ C#8 ˆ"'C#8 #&‰ œ C#8  %C8 # &# ‘

œ C#8 %C8 & %C8 &

87. 88. 89.

90.

91.

#B$ #,!!! œ # B$ ",!!! œ # B$ "!$ œ # B "! B# "!B "!!

$C$ '%) œ $ C$ #"' œ $ C$ '$ œ $ C ' C# 'C $'

B C $ '% œ B C $ %$ œ c B C %d B C # % B C %# ‘ œ B C % ˆB# #BC C# %B %C "'‰

B C $ #( œ B C $ $$ œ c B C $d B C # $ B C $# ‘ œ B C $ ˆB# #BC C# $B $C *‰

# # '%+' C' œ ˆ)+$ ‰ ˆC$ ‰ œ ˆ)+$ C$ ‰ˆ)+$ C$ ‰ œ #+ C ˆ%+# #+C C# ‰ #+ C ˆ%+# #+C C# ‰

œ #+ C #+ C ˆ%+# #+C C# ‰ˆ%+# #+C C# ‰

92. 93. 94.

+' , ' œ +# , # œ +# , # Š +# +# , # , # ‹= +# , # +% +# , # , % $

+$ , $ + , œ + , +# +, , # + , " œ + , +# +, , # " +# C# & + C œ + C + C & + C œ + C + C &

95.

'%B' C' œ ˆ%B# ‰ ˆC# ‰ œ ˆ%B# C# ‰Šˆ%B# ‰ %B# C# ˆC# ‰ ‹

96.

D # 'D * ##&C# œ D $ D $ ##&C# œ D $ # "&C # œ D $ "&C D $ "&C

œ ˆ%B# C# ‰ˆ"'B% %B# C# C% ‰

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SECTION 0.5 97.

B# 'B * "%%C# œ B $ B $ "%%C# œ B $ # "#C # œ B $ "#C B $ "#C

98.

B# #B *C# " œ B# #B " *C# œ B " B " *C#

99.

+ , # $ + , "! œ c + , &dc + , #d œ + , & + , #

œ B " # $C # œ B " $C B " $C

100. # + , # & + , $ œ c# + , "dc + , $d œ #+ #, " + , $ 101. B' (B$ ) œ B$ ) B$ " œ B # B# #B % B " B# B "

102. B' "$B% $'B# œ B# B% "$B# $' œ B# B# * B# % œ B# B $ B $ B # B # 103. B% B# " œ B% #B# " B# œ ˆB# "‰ˆB# "‰ B#

104. B% $B# % œ B% %B# % B# œ ˆB# #‰ˆB# #‰ B#

105. B% (B# "' œ B% )B# "' B# œ ˆB# %‰ˆB# %‰ B#

106. C% #C# * œ C% 'C# * %C# œ ˆC# $‰ˆC# $‰ %C#

# œ ˆB# "‰ B# œ ˆB# " B‰ˆB# " B‰

# œ ˆB# %‰ B# œ ˆB# % B‰ˆB# % B‰

# œ ˆB# #‰ B# œ ˆB# # B‰ˆB# # B‰

# œ ˆC# $‰ #C # œ ˆC# $ #C‰ˆC# $ #C‰

107. %+% " $+# œ %+% %+# " +# œ ˆ#+# "‰ˆ#+# "‰ +# œ ˆ#+# "‰ +# œ ˆ#+# " +‰ˆ#+# " +‰ #

108. B% #& 'B# œ B% "!B# #& %B# œ ˆB# &‰ˆB# &‰ %B#

œ ˆB# &‰ #B # œ ˆB# & #B‰ˆB# & #B‰ #

% $ % $ 1< 1< $ " $ # % œ 1ˆ<"$ <#$ ‰ $ % œ 1 <" <# ˆ<"# <" <# <## ‰ $

109. Z œ

111-114. Answers may vary.

115. $B # œ #ˆ $B ## ‰ œ #ˆ $# B "‰ # 117. B# #B % œ #Š B# #

#B #

%# ‹

œ #ˆ "# B# B #‰

110. 0 œ "%% "'># œ "'ˆ* ># ‰ œ "' $ > $ >

116. &B $ œ &ˆ &B $& ‰ œ &ˆB $& ‰ & 118. $B# #B & œ $Š $B$ #

#B $

&$ ‹

œ $ˆB# #$ B &$ ‰

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SECTION 0.5 119. + , œ +ˆ ++ +, ‰ œ +ˆ" +, ‰

121. B B"Î# œ B"Î# ˆB" "Î# B"Î# "Î# ‰ œ B"Î# ˆB"Î# "‰ 123. #B È#C œ È#

È#C #B È# È# 

œ È#ŠÈ#B C‹

125. +, $Î# +$Î# , œ +, 

+, $Î# +$Î# , +, +, 

œ +, ˆ, "Î# +"Î# ‰

120. + , œ , ˆ +, ,, ‰ œ , ˆ +, "‰

122. B$Î# B"Î# œ B"Î# ˆB$Î# "Î# B"Î# "Î# ‰ œ B"Î# B "

124. È$+ $, œ È$

È$+ È$

$, È$ 

œ È$Š+ È$, ‹

126. +, # , œ , " Œ

+, # , "  , " , œ , " ˆ+, $ , # ‰

127. B# B ' BC #C œ B $ B # C B # œ B # B $ C

128. #B# &B # BC #C œ #B " B # C B # œ B # #B " C

129. +% #+$ +# + " œ +# ˆ+# #+ "‰ + " œ +# + " + " " + " œ + " +# + " "‘ œ + " ˆ+$ +# "‰

130. +% +$ #+# + " œ +# ˆ+# + #‰ + " œ +# + # + " " + " œ + " +# + # "‘ œ + " ˆ+$ #+# "‰

131. The number 1 is neither prime nor composite.

132. c #, $ Ê

oqÒïïÑqp #

+$ +# +* +) +"( # $ œ $ œ "& œ + # $ & + + + +

133. B$ B# œ B& œ B#!

134.

135. Œ

136. È#!B& œ È%B% È&B œ #B# È&B

$B% B$  œ" 'B # B% !

137. È#!B È"#&B œ È%È&B È#&È&B œ #È&B &È&B œ $È&B 138.

$ $ $ $ $ È * $È * $È * È œ † œ œ œ $ * $ $ $ $ È$ È$ È* È#( $

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SECTION 0.6

Exercises 0.6

(page 71)

numerator

denominator

+. œ ,-

zero

+,.

+. ,-

+ ,

)B ? "'B œ $C 'C ? )B † 'C œ $C † "'B

10.

$B# ? "#C# œ %C# "'B# ? %C# † "#C# $B# † "'B# œ %)B% Á %)C% NOT EQUAL

%)BC œ %)BC EQUAL 11.

#&BCD ? &!+# ,œ "#+, # #%BCD ? #&BCD † #%BCD œ "#+, # - † &!+# ,-

12.

'!!B# C# D # Á '!!+$ , $ -# NOT EQUAL

"&<=# ? $(Þ&+$ œ %<=# "!+$ ? "&<=# † "!+$ œ %<=# † $(Þ&+$ "&!<=# +$ œ "&!<=# +$ EQUAL

13.

(+# , + † (+, + (+, + œ œ † œ #"+, # $, † (+, $, (+, $,

14.

$&:$ ; # &; † (:$ ; &; (:$ ; &; œ œ † œ % $ %*: ; (: † (: ; (: (:$ ; (:

15.

%B # %B † # )B † œ œ ( &+ ( † &+ $&+

16.

&C % &C † % #!C "! † œ œ œ #D C# #D † C# #C# D CD

17.

)7 $7 )7 "!8 )!78 "' ƒ œ † œ œ &8 "!8 &8 $7 "&78 $

18.

"&: &: "&: "'; # #%!:; # ƒ œ † œ œ '; # ); "'; ); &: %!:;

19.

$D #D $D #D &D D œ œ œ &&&&-

20.

(+ $+ (+ $+ %+ + œ œ œ %, %, %, %, ,

21.

"&B# C B# C "%B# C #B# C œ œ (+# , $ (+# , $ (+# , $ +# , $

22.

)<=># (<=># "&<=># <= œ œ % "&7% ># "&7% ># "&7% ># 7

23.

#B % # B # # œ œ B# % B # B # B #

24.

B# "' B % B % B % œ œ )B "' B % B % B %

25.

% B# # B # B B # œ œ B# &B ' B $ B # B $

27.

'B$ B# "#B B 'B# B "# B #B $ $B % $B % œ œ œ $ # # %B %B $B B %B %B $ B #B $ #B " #B "

26.

#& B# & B & B œ B# "!B #& B & B & & B B & œ œ B & B &

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SECTION 0.6 28.

29.

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

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

B$ ) B$ #$ B# #B % B # B# #B % œ œ œ +B #B #+ B B + # B + B + B # B +

BC #B $C ' B C # $ C # C # B $ C # œ œ œ # B $ B# $B * B$ #( B$ $$ B $B * B " B " B# " B# B# B B " † # œ † œ B " B " B B #B " B B "

C# #C " C # C " C " C # C " † # œ † œ C # C " C C C # C C $B# (B # B# B B " $B " B # B B " † # œ † œ B# #B $B B B B # B $B " B

B# B #B# B $ B B " #B $ B " † œ † œ" #B# $B B# " B #B $ B " B " B# B B# " B B " B " B " B B " # † œ † œ B " B # B " B # B #

B# &B ' B # B # B # B # B $ † # œ † œ # B 'B * B % B $ B $ B # B # B $ B # #B# $# B# "' #B# $# # # B# "' # " ƒ œ † # œ † # œ ) # ) B "' ) B "' #

B# B ' B# % B# B ' B# * B $ B # B $ B $ ƒ œ † # œ † # # # B 'B * B * B 'B * B % B $ B $ B # B # B $ # œ B $ B #

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

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.6 40.

41.

42.

43.

44.

45.

+B ,B + , B# " +B ,B + , B# #B " ƒ # œ # † # # + #+, , B #B " + #+, , # B# " B + , " + , B " B " œ † + , + , B " B " + , B " B " B " B " † œ œ + , + , B " B " + , $B# &B # 'B# "$B & $B# &B # #B$ &B# ƒ œ † # $ # $ # $ # B #B #B &B B #B 'B "$B & $B " B # B# #B & œ † œ" $B " #B & B# B # B# "$B "# #B# B $ B# "$B "# )B# "%B & ƒ œ † )B# 'B & )B# "%B & )B# 'B & #B# B $ B "# B " %B & #B " B "# #B " œ † œ %B & #B " #B $ B " #B " #B $ B# (B "# B# $B "! B$ %B# $B † † # B$ B# 'B B# #B $ B B #! B $ B % B & B # B B $ B " œ † † œ" B B $ B # B $ B " B & B %

B B # $ B B " # B# #B $ B# B # † œ # † # B B ( $ B " B B ( $ B " B (B $B $ B (B $B $ B# #B $ B# B # œ # † B %B $ B# %B $ B # B $ B " B # B " œ † œ B $ B $ B " B $ B " B# #B $ $B ) B# 'B & B# #B $ $B ) (B# $$B "! † ƒ œ † † #"B# &!B "' B $ (B# $$B "! #"B# &!B "' B $ B# 'B & B $ B " $B ) (B # B & œ † † (B # $B ) B $ B & B " B & œ B &

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.6 46.

47.

49. 51.

53.

54.

55.

B$ #( B# %B $ B# B ' B$ #( B# %B $ B# $B * ƒŒ ƒ # ƒŒ † # œ #  # # B % B #B B $B * B % B# #B B B ' $ # B #( B $ B " B $B * œ # ƒŒ †  B $ B # B % B B # B$ #( B " B# $B * œ # ƒ B % B B # B # # B $ B $B * B B # B # œ † B # B # B " B# $B * B B $ œ B " $ B # $ B # B & œ œ B $ B $ B $ B $

%B % %B % % B " œ œ œ% B " B " B " B "

# " # " " œ œ & B B & B & B & B &

48.

50. 52.

$ B # $ B # B & œ œ B " B " B " B "

'B $ 'B $ $ #B " œ œ B # B # B # B #

$ # $ # & œ œ B ' ' B B ' B ' B '

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

+ $ + + $ + œ +# (+ "# +# "' + $ + % + % + % " + œ + % + % + % " + % + œ + % + % + % + % + % + œ + % + % + % + % #+ % # + # œ œ + % + % + % + %

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.6 56.

57.

58.

59.

60.

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

B " B " B " B # œ œ % B # B # B # B # B # B # B # B # B B # œ B # B # B # B # # œ B # B #

,# % ,# % , # , % , # # œ œ , # , # , , # % , #, , , # , # , , # , # ,$ %, ) œ , , # , # , , # , # , $ %, ) œ , , # , #

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

#> > " #> > " #> > > " > & œ œ ># #& ># &> > & > & > > & > > & > & > > & > & #># ># %> & œ > > & > & > > & > & ># %> & œ > > & > &

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SECTION 0.6 61.

62.

63.

64.

65.

# " # $ œ C " C " C# " C " # œ C " C " # œ C " C " $C# C # œ C " C " #

$ " " C " $ C " C " " C " " C " C " C " C " $C# $ C " C " C " C " C " $C # C " $C # œ œ C " C " C "

% " # % " œ % > # " > # > # > # # > # > # % " > # œ " > # > # > # > # > # > # #># ) % > # œ > # > # > # > # > # > # #># > ' #> $ > # #> $ œ œ œ > # > # > # > # > #

" $ $B # " $ $B # # œ B # B # B % B # B # B # B # " B # $ B # $B # œ B # B # B # B # B # B # B # $B ' $B # œ B # B # B # B # B # B # B # " œ œ B # B # B #

B & $ $B " B & *B $ œ B $ B $ B# * B $ B $ B $ B $ B B $ & B $ *B $ œ B $ B $ B $ B $ B $ B $ B# $B &B "& *B $ œ B $ B $ B $ B $ B $ B $ B# (B "# B $ B % B % œ œ œ B $ B $ B $ B $ B $ Œ

" " B $ " B $ " B # œŒ † † B # B $ #B B # B $ B $ B # B $ B # œŒ † B # B $ B # B $ #B & B $ #B & œ † œ B # B $ #B #B B #

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B $ #B B $ #B

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SECTION 0.6 66.

67.

68.

69.

" " " " B # " B " B # œŒ ƒ † B " B # B # B " B # B # B " " B # B " B # œŒ † B " B # B " B # " $ B # $ œ † œ B " B # " B "

$B B $B " $B B $B " œ # B % B % "' B B % B % % B % B $B B $B " œ B % B % B % B % $B B % B B % $B " œ B % B % B % B % B % B % B# %B $B " $B# "#B œ B % B % B % B % B % B % #B# "*B " œ B % B % (B $B $B " (B $B $B " œ B & & B B# #& B & B & B & B & %B $B " œ B & B & B & %B B & $B " œ B & B & B & B & %B# #!B $B " %B# #$B " œ œ B & B & B & B & B & B & " # " B# $B # B# %B $ B# &B ' " # " œ B # B " B $ B " B # B $ " B $ # B # " B " œ B # B " B $ B $ B " B # B # B $ B " B $ #B % B " œ B # B " B $ B # B " B $ B # B " B $ B $ #B % B " ! œ œ œ! B # B " B $ B # B " B $

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.6 70.

71.

72.

73.

75.

# # #D #C # # #D #C œ B C B D C B D B C B D B C B D B # D B # C B #D #C œ C B D B D B C B C B D B #D #B #C #B #D #C œ C B D B C B D B C B D B #D #B #C #B #D #C ! œ œ œ! C B D B C B D B B#

$B # %B# # $B# #& # # B #! B #& B "' $B # %B# # $B# #& œ B & B % B & B & B % B % $B # B & B % %B# # B % B % œ â B & B % B & B % B & B & B % B % $B# #& B & B & B % B % B & B & $ # % # $B &B &)B %! %B '#B $# œ â B & B % B & B % B & B % B & B % $B% "!!B# '#& B & B % B & B % $B$ &B# &)B %! %B% '#B# $# $B% "!!B# '#& œ B & B % B & B % B% $B$ %$B# &)B '*( œ B & B % B & B %

)B#

$+ , '+,#

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

$+# , +, #(

$+ '+$+ , # , ƒ # œ † œ , , , '+#-

$+# , +, $+# , #( ƒ œ † œ )"+ " #( " +,

74.

76.

$># *B > ")B $?# @ %>

$?@

$># > $># ")B ƒ œ † œ '> *B ")B *B >

$?# @ $?@ $?# @ " ? ƒ œ † œ %> " %> $?@ %>

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.6 77.

B C +, C B +,

78.

B# &B ' #B# C B# * #B# C

B C C B B C +, ƒ œ † œ " +, +, +, C B

B# &B ' B# * B# &B ' #B# C ƒ œ † # #B# C #B# C #B# C B * œ

79.

80.

81.

" B

" C

"" B

" B " B

BCŠ B" C" ‹ BC BC

BCˆ B" ‰ BCŠ C" ‹ B# C#

83.

84.

85.

86.

88.

89.

C B B# C#

" C " C

BCŠ B" C" ‹ BCŠ B" C" ‹

BCˆ B" ‰ BCŠ C" ‹ BCˆ B" ‰ BCŠ C" ‹

82.

C B C B

" B " B

" C " C

BCŠ B" C" ‹ BCŠ B" C" ‹

BCˆ B" ‰ BCŠ C" ‹

BCˆ B" ‰ BCŠ C" ‹ C B œ C B œ

%+ %+ # ‰ +,BŠ $+ +,Bˆ $+ %+B $+# B %+$ , +# $B %+, , B ‹ , +,BŠ B ‹ œ œ œ œ " " " " " +B , +B , +B +,Bˆ , +B ‰ +,Bˆ , ‰ +,Bˆ +B ‰ #

" B# C#

BC BC BC B# C# B# C# B# C# œ œ œ "" œ "" "" ""C ""B "" C B C ‰ BCŠ "" BCˆ "" B C ‹ B BC Š C ‹

œ $+ , " ,

B $ B # #B# C B # † œ # #B C B $ B $ B $

B C

B " B &

' B ' B

C# Š" BC ‹

C# Š BC# "‹ #

C# " C# Š BC ‹

C# Š BC# ‹ C# " #

C# BC C C B C œ œ B# C# B C B C B C

BˆB " B' ‰ B B B " Bˆ B' ‰ B# B ' B # B $ B # œ œ œ œ '‰ '‰ # ˆ ˆ B &B ' B # B # B $ B B & B B B B & B B

#D D #D #D # $ œ ˆ $‰ œ " D D " D D " D ˆ $D ‰ #D # œ D $

87.

$BC BC $BC $B# C# œ " œ " " " BC BCŠ" BC BC " BCŠ BC ‹ ‹ œ

B $ B" BˆB $ B" ‰ B# $B " B# $B " œ œ œ œ " " " # " B $B B# $B " B B $ Bˆ B B $‰

$B B $B $B# " œ ˆ "‰ œ # B " B B B B B

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

$B# C# BC "

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 0.6 90.

91.

#B# % & #B# % "!B# #! # &B# "! &B# "! œ œ œ %B œ %B "! %B # & #B & #B # & &ˆ# & ‰ B B # $ B #

# B " B B "

B B # B " ˆ B # $ B # B " ˆ B #

# ‰ B " B ‰ B "

B ‰ # ‰ B # B " ˆ B # B # B " ˆ B " B ‰ $ ‰ B # B " ˆ B # B # B " ˆ B "

B " B B # # B " $ B # B B# B #B % B# $B % œ œ # # $B $ B #B B &B $ œ

92.

#B B $ $ B $

" B # B B #

#B B $ B # ˆ B $ $ B $ B # ˆ B $

" " œ " " B "

95.

$ B # " # B " " œ B # "

" B

#B ‰ " ‰ B $ B # ˆ B $ B $ B # ˆ B # $ ‰ B ‰ B $ B # ˆ B $ B $ B # ˆ B # B # #B B $ " œ B # $ B $ B #B# %B B $ œ $B ' B# $B #B# $B $ #B# $B $ œ œ B# 'B ' B# 'B '

B " B œ " B " Bˆ" B ‰

93.

" ‰ B # B ‰ B #

$ B #

# B "

94.

" B #

C " œ B " C "

" C " B

" C

$ # ‰ B # B " ˆ B # B " " B # B " ˆ B # ‰

BCŠ B" C" ‹

$ ‰ # ‰ B # B " ˆ B # B # B " ˆ B " B " B " $ B # # œ B " $B $ #B % &B " œ œ B " B "

96.

#B B $ " $ B # " œ B $ " B # "

#B B $

$ B #

" B $ B #

#B B $ B # ˆ B $

" 5"

" 5#

5" 5# "

5" 5# Š 5""

" 5# ‹

B # #B B $ $ " œ #B# %B $B * œ #B# B *

5" 5#

5" 5# Š 5"" ‹

$ ‰ B #

B $ B # Š B $ " B # ‹

97.

BCŠ "C ‹

5" 5# Š 5"# ‹

5" 5# 5# 5"

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

B C B

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SECTION 0.6 98.

99.

" " V"

" V#

" V$

V" V# V$ "

V" V# V$ Š V""

102.

" V$ ‹

B $

V" V# V$

V" V# V$ Š V"" ‹ V" V# V$ Š V"# ‹ V" V# V$ Š V"$ ‹

V" V# V$ V# V$ V" V$ V" V#

$B $B B‰ œ ˆ $ B $ " $

+, +, +, +, #+, #+, œ œ œ $ $+ œ ˆ $+ ‰ œ $ + $ % $+ # #+ " # # # # # # # # +ˆ # ‰ +

101.

B B B B œ œ œ " " B " " " $B " " $ " Bˆ $ ‰ B

100.

" V#

B " "

œ œ B œ B ‰ œ B " B œ #B " B " " B " B " ˆ" B " " " " " " Bˆ" " ‰ B B "

œ # # # # # C

C #

C Š# #C ‹

C #

#C #C #

B "

#C # C

#C # Š#

#C #C # ‹

B "

#C# #C #C # # #C

#C C " %C % #C #C C " C C " œ œ # $C # $C #

107. Since ' ! !, k 'k œ ' œ '.

103-106. Answers may vary.

108. If B ! !, then & B !. Then k& Bk œ & B. 109. Œ

B$ C #  B " C

110. #(B'

#Î$

œŒ

B " C C# C C$ C* œ œ œ  Œ  Œ  B$ C # B$ B B% B"# $

œ #(#Î$ B'

#Î$

œ ˆ#("Î$ ‰ B"#Î$ œ $# B% œ *B% #

111. È#! È%& œ È%È& È*È& œ #È& $È& œ È&

112. # B# % $ #B# & œ # B# # % $ #B# $ & œ #B# ) 'B# "& œ %B# (

Chapter 0 Review

(page 75)

natural: $, ', )

whole: !, $, ', )

integers: ', $, !, $, ', )

rational: ', $, !, "# , $, ', )

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

CHAPTER 0 REVIEW 5.

irrational: 1, È&

real: ', $, !, "# , $, 1, È&, ', )

prime: $

composite: ', )

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

18.

oñqñqqñqñp "" "$ "( "*

19.

oñqñqñqñqñp ' ) "! "# "%

20.

$ ! B Ÿ &

21.

B ! or B ! "

oqÐïïÓqp $ 22.

íïÑqqÒïî

Ð #, %Ó

oqÐïïÓqp #

23.

∞, # ∩ &, ∞ ∞, # &, ∞

∞, # ∩ &, ∞ 24.

∞, % ∪ Ò', ∞Ñ

íïïïÑqp # oqÐïïïî & oqÐïïÑqp &

íïÑqqÒïî %

25. 27.

29.

Since ' !, k'k œ '.

Since " È# ! !, ¹" È #¹ œ Š" È #‹ œ È # ".

26. 28.

distance œ k( & k œ k"#k œ "#

Since #& ! !, k #&k œ #& œ #&. Since È$ " !, ¹ È $ "¹ œ È $ " .

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

CHAPTER 0 REVIEW &+ # œ &+ &+

30.

&+$ œ &+++

31.

32.

$>>> œ $>$

33.

34.

8# 8% œ 8# % œ 8'

35.

:$ œ :$†# œ :'

36.

B$ C# œ B$ C# œ B"# C)

37.

38.

ˆ7 $ 8! ‰# œ ˆ7 $ † "‰# œ 7 ' œ

39.

: # ; # ;# ; # ;' Œ  œ Œ # œ $ œ # # #: ):' #:

40.

+& " œ +& ) œ + $ œ $ ) + +

41.

+# Œ $ ,

42.

$B# C #  B# C#

43.

+ $ , #  +, $

44.

$B$ C Œ  BC$

œŒ

45.

œŒ

#7 # 8!  %7# 8 "

#, $, œ # $ ,, œ ', # #

+% +% +"#  œ # $ œ ' # , , , $

" 7'

œŒ

,$ ,'  œ % # + + #

B# C# B# C# C# C% C) œ œ œ  Œ  Œ  $B# C # $B# $ * #

+, $ ++$ +% +) œ œ œ  Œ  Œ  + $ , # ,#,$ ,& , "! #

BC$ C# C%  œŒ  œ % $ # $B C $B *B #

œ Œ

%7# 8 " #7# 7# #7% )7"# œ œ œ  Œ  Œ  #7 # 8! 8" 8! 8 8$ $

46.

B# BC# œ $ # $ $ # œ * $ * œ * #( œ * #( œ ")

47.

',(&! œ 'Þ(&! ‚ "!$

48.

!Þ!!!#$ œ #Þ$ ‚ "! %

49.

%Þ) ‚ "!# œ %)!

50.

!Þ#& ‚ "! $ œ !Þ!!!#&

51.

%&,!!! $&!,!!! %Þ& ‚ "!% $Þ& ‚ "!& %Þ& ‚ $Þ& ‚ "!% ‚ "!& "&Þ(& ‚ "!* œ œ œ % % !Þ!!!"!& "Þ!& ‚ "! "Þ!& ‚ "! "Þ!& ‚ "! % œ "& ‚ "!"$ œ "Þ& ‚ "!"% œ ""

# "Î#

"Î#

52.

"#"

54.

$#B&

"Î&

53.

#( Œ  "#&

55.

)"+%

"Î$

œ ""

œ $#"Î& B&

"Î&

œ #B

"Î%

$ "Î$

$ œ –Œ  — &

œ )""Î% +%

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

"Î%

$ &

œ $k+k

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CHAPTER 0 REVIEW ˆ ",!!!B' ‰"Î$ œ ",!!! "Î$ ˆB' ‰"Î$

57.

ˆ #&B# ‰"Î# œ #& "Î# ˆB# ‰"Î# Ê not a real number

58.

B"# C#

59.

B"# Œ % C

60.

-#Î$ -&Î$  - #Î$ 

61.

+ "Î% +$Î%  +*Î# 

62.

'%#Î$ œ ˆ'%"Î$ ‰ œ %# œ "'

64.

"' Œ  )"

66.

) Œ  #(

67.

"' Œ  '#&

68.

#"'B$

56.

œ "!B#

œ B"#

"Î#

78. 79.

-(Î$ œ  #Î$  -

"Î#

"Î$

"Î#

œ ˆ -*Î$ ‰

"Î$

+*Î# œ  "Î% $Î%  + +

"Î#

#Î$

œŒ

'#&  "'

"Î$

"Î#

$ È #( #( $ œ $ œ È"#& "#& &

œŒ

C%  B"#

"Î#

C# B'

œ -

+*Î# œ  "Î#  +

63.

$# $Î& œ

65.

$# Œ  #%$

"Î#

œ ˆ+)Î# ‰

"Î#

œ ˆ+% ‰

"Î#

œ +#

" " " " œ $ œ $ œ "Î& $#$Î& # ) $#

ˆ$#"Î& ‰ $##Î& ## % œ œ # œ # #Î& #%$ $ * #%$"Î& #

#Î&

ˆ#("Î$ ‰ #(#Î$ $# * œ #Î$ œ œ œ # # "Î$ ) # % ) #

ˆ'#&"Î% ‰ '#&$Î% &$ "#& œ œ $ œ $ $Î% "' # ) "'"Î% $

$Î%

œ #"' #Î$ B$

È$' œ ' Ê

œ ˆ -$ ‰

+*Î# œ  #Î%  +

ˆ"'"Î% ‰ "'$Î% #$ ) œ œ $ œ $ $Î% )" $ #( )""Î%

#( œŒ  )

$Î%

76.

œ B' kCk

#Î$

73.

"Î#

$Î%

70.

"Î$

#Î$

71.

74.

% % È ) % 7) È 8% 7# k8k % 7 8 œ Ë :"' œ È % :% :"'

œ $'B#

69.

:+Î# :+Î$ :$+Î' :#+Î' :&+Î' œ œ +Î' œ :%+Î' œ :#+Î$ +Î' +Î' : : :

È%* œ (

72.

ÈB# C% œ ÈB# ÈC% œ kBkC# 77.

Ê &

75.

È* * $ œ œ È#& #& &

$ È B$ œ B

& & È +"& , "! +"& È , "! +$ , # œ œ & È -& -&

È&! È) œ È#&È# È%È# œ &È# #È# œ (È#

È"# È$ È#( œ È%È$ È$ È*È$ œ #È$ È$ $È$ œ $È$ $È$ œ !

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

CHAPTER 0 REVIEW 80. 81.

83.

$ $ $ $ $ $ $ $ $ È #%B% È $B% œ È )B$ È $B È B$ È $B œ #BÈ $B BÈ $B œ BÈ $B

È( È&

È( È& È$& † œ È& È& &

82.

$ $ $ È È " " È % % % œ † œ œ $ $ $ $ È È È È # ) # # %

84.

$ $ $ È # # & #È & #È & œ † œ œ $ $ $ $ È È È È & #& #& & "#&

85.

È#

87.

È#B

89.

3rd degree, binomial

90.

2nd degree, trinomial

91.

2nd degree, monomial

92.

4th degree, trinomial

93.

# B $ $ B % œ #B ' $B "# œ &B '

94. 95. 96. 97. 98. 99.

È# È# # † œ È È & # & #

) ) È# )È # )È # œ † œ œ È) È) È# È"' % È œ# #

86.

È#B È#B #B † œ È#B $ $È#B

88.

È& &

È& È& & " † œ œ È È È & & & & &

$ $ $ $ $È (B $È (B È %*B# $È $%$B$ œ † $ œ $ È%*B# # # #È%*B# #"B œ $ È # %*B#

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

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

%+ #, #+ $, œ )+# "#+, %+, ', # œ )+# )+, ', #

D $ $D # D " œ $D$ D# D *D# $D $ œ $D$ "!D# #D $ +8 # +8 " œ +#8 +8 #+8 # œ +#8 +8 #

100. ŠÈ# B‹ œ ŠÈ# B‹ŠÈ# B‹ œ ŠÈ#‹ BÈ# BÈ# B# œ # #BÈ# B# #

101. ŠÈ# "‹ŠÈ$ "‹ œ È' È# È$ "

$ $ $ $ $ $ $ $ 102. ŠÈ $ #‹ŠÈ * #È $ %‹ œ È #( #È * %È $ #È * %È $ ) œ $ ) œ &

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

CHAPTER 0 REVIEW È$ "

# ŠÈ $ " ‹

œ È$ "

È$ "

104.

#ŠÈ$ È#‹ #ŠÈ$ È#‹ È$ È# # # œ † œ œ # # È$ È# È$ È# È$ È# $ # ŠÈ $ ‹ ŠÈ # ‹

È$ " È$ "

# ŠÈ $ " ‹

103.

†

ŠÈ $ ‹ " # #

$ "

#ŠÈ$ È#‹

" œ #ŠÈ$ È#‹

105.

ÈB # #BˆÈB #‰ #BˆÈB #‰ #B #B œ † œ œ # ÈB # ÈB # ÈB # B % ˆÈB‰ ##

106.

ÈB ÈC

107.

ÈB #

108.

109.

111.

ÈB ÈC

ÈB# ÈBC ÈBC C ÈB ÈC ÈB ÈC B #ÈBC C † œ œ # # ÈB ÈC ÈB ÈC B C ˆÈB‰ ˆÈC‰

ÈB # ÈB # ˆÈB‰# ## B % † œ œ È ˆ È ‰ ˆ È & B # & B # & B #‰

# " È+ " È+ " È+ "# ˆÈ+‰ " + œ † œ œ + + " È+ +ˆ" È+‰ +ˆ" È+‰

$B# C# C œ $ 'B C #B

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

110.

112.

%+# , $ '+, % %+# , $ '+, % œ #, # #, # #, # œ #+# , $+, # B$ #B $ B ' # " B " B& !B% B$ $B# #B $ B& B$ #B$ $B# #B #B$ #B $B# $ $B# $ ' #

113. $>$ $> œ $> ># " œ $> > " > "

114. &<$ & œ & <$ " œ & <$ "$ œ & < " <# < "

115. 'B# (B #% œ $B ) #B $

116. $+# +B $+ B œ + $+ B " $+ B œ $+ B + " 47

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CHAPTER 0 REVIEW 117. )B$ "#& œ #B $ &$ œ #B &  #B # #B & &# ‘ œ #B & %B# "!B #&

118. 'B# #!B "' œ # $B# "!B ) œ # $B # B %

119. B# 'B * ># œ B $ B $ ># œ B $ # ># œ B $ > B $ > 120. $B# " &B œ $B# &B " Ê prime

121. )D $ $%$ œ #D $ ($ œ #D (  #D # #D ( (# ‘ œ #D ( %D# "%D %* 122. " "%, %*, # œ %*, # "%, " œ (, " (, " œ (, " #

123. "#"D # % %%D œ "#"D # %%D % œ ""D # ""D # œ ""D # #

124. '%C$ ",!!! œ ) )C$ "#& œ ) #C $ &$ ‘ œ ) #C & %C# "!C #&

125. #BC %DB AC #DA œ #B C #D A C #D œ C #D #B A 126. B) B% " œ B) #B% " B% œ ˆB% "‰ˆB% "‰ B%

# # œ ˆB% "‰ ˆB# ‰ œ ˆB% " B# ‰ˆB% " B# ‰

œ ˆB% #B# " B# ‰ˆB% B# "‰ œ ˆB# "‰ˆB# "‰ B# ‘ˆB% B# "‰

œ ˆB# " B‰ˆB# " B‰ˆB% B# "‰

127.

129.

130.

131.

132.

# B B # " œ œ %B % B # B # B #

128.

+# * + $ + $ + $ œ œ '+ * + $ + $ + $

B# %B % B# &B ' B # B # B # B $ † œ † œ B # B $ B # B # B # B # #C# ""C "& C# #C ) #C & C $ C % C # #C & † # œ † œ C# 'C ) C C ' C % C # C $ C # C # #># > $ "!> "& #># > $ $># > % ƒ œ † $># (> % $># > % $># (> % "!> "& #> $ > " $> % > " > " œ † œ $> % > " & #> $ &

:# (: "# :# * :# (: "# :# : $ : % :# ƒ œ † œ † :$ ):# %: :# :$ ):# %: :# * : :# ): % : $ : $ : : % œ # : ): % : $ 48

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CHAPTER 0 REVIEW 133.

B# B ' B# B ' B# % † # ƒ # # B B ' B B # B &B ' B# B ' B# B ' B# &B ' œ # † † B B ' B# B # B# % B $ B # B $ B # B # B $ B $ B # B $ œ œ † † B $ B # B # B " B # B # B # # B "

134. Œ

135.

136.

137.

138.

#B ' #B# #B % B# B # #B ' B# #& B# B # ƒ œ † † #  # # # B & B #& B #B "& B & # B B # B #B "& # B $ B & B & B # B " œ † † œ" B & # B # B " B & B $

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

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

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

CHAPTER 0 REVIEW 139.

140.

141.

143.

144.

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

&B # $B# ) " B

" C

B C

&B $B# &B ) #! ƒ œ † # œ # ) # $B $B

BCŠ B" C" ‹ BC B C

B " C " œ C " B "

" B " C

" C " B

Chapter 0 Test

142.

BCˆ B" ‰ BCŠ C" ‹ BC B C

BCŠ B" C" ‹ BCŠ "C

" B‹

$B C 'B C#

$B 'B $B C# C ƒ # œ † œ C C C 'B #

C B B C

C B BC B C

BCˆ B" ‰ BCŠ C" ‹ BCŠ "C ‹

BCˆ B" ‰

(page 82)

odd integers: (, ", $

prime numbers: $

commutative property of addition

distributive property

% ! B Ÿ # Ê

Ð ∞, $Ñ ∪ Ò', ∞Ñ Ê

oqÐïïÓqp %

íïÑqqÒïî

Since "( ! !, k "(k œ "( œ "(

distance œ k"# % k œ k"'k œ "'

10.

distance œ k "# #! k œ k)k œ )

11.

B% B& B# œ B% & # œ B""

12.

<# <$ = <& = < œ œ < % =# < % =# =

14.

16.

!Þ!!!$%& œ $Þ%& ‚ "! %

+ " +# + $

13. 15.

+" + $

%&!,!!! œ %Þ& ‚ "!&

+ # œ+ + $

If B ! !, then B ( ! !. Then kB (k œ B ( .

B! B# B# % ' #% œ  Œ  œ ˆB ‰ œ B # # B B '

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

CHAPTER 0 TEST 17.

$Þ( ‚ "!$ œ $,(!!

19.

#&+%

21.

)>' Œ  #(=*

"Î#

œ #&"Î# +%

"Î#

#Î$

22.

24.

25.

26.

œŒ

œ &+#

#(=*  )>'

#Î$

$ $ $ È #(+' œ È #(È +' œ $+#

#(#Î$ =*

#Î$

)#Î$ >' #Î$

18.

"Þ# ‚ "! $ œ !Þ!!"#

20.

$'  )"

ˆ#("Î$ ‰# =' # )"Î$ >%

23.

ˆ$'"Î# ‰ $'$Î# #"' œ $ œ $Î# "Î# )" (#* )" $

$Î#

œ *=' %>%

È"# È#( œ È%È$ È*È$

œ #È $ $È $ œ &È $

$ $ $ $ $ $ $ $ #È$B% $BÈ #%B œ #ÈB$ È $B $BÈ )È $B œ #BÈ $B $B # È $B œ #BÈ $B 'BÈ $B $ œ %BÈ$B $

ÈB # BˆÈB #‰ BˆÈB #‰ B B œ † œ œ # ÈB # ÈB # ÈB # B % ˆÈB‰ ##

ÈB ÈC ÈB ÈC

ÈB ÈC ÈB ÈC ˆÈB‰# ˆÈC‰# B C † œ œ ÈB ÈC ÈB ÈC ÈB# ÈBC ÈBC ÈC# B #ÈBC C

ˆ+# $‰ ˆ#+# %‰ œ +# $ #+# %

28.

$+$ , # #+$ , % œ '+' , '

29.

$B % #B ( œ 'B# #"B )B #) œ 'B# "$B #)

30.

+8 # +8 $ œ +#8 $+8 #+8 ' œ +#8 +8 '

31.

B# % B# % œ B% %B# %B# "' œ B% "'

27.

œ +# (

32. 33.

35. 37.

B# B # #B $ œ #B$ $B# #B# $B %B ' œ #B$ &B# (B ' $% 'B "* B $ B $ 'B# B #$ 'B# ")B "*B #$ "*B &( $%

$B 'C œ $ B #C

"!># "*>A 'A# œ &> #A #> $A

34.

36. 38.

B# #B " #B " #B$ $B# !B " #B$ B# %B# !B %B# #B #B " #B " !

B# "!! œ B# "!# œ B "! B "! $+$ '%) œ $ˆ+$ #"'‰ œ $ + ' ˆ+# '+ $'‰

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 39.

B% B# "# œ ˆB# %‰ˆB# $‰ œ B # B # ˆB# $‰

41.

B # B # œ œ" B # B # B #

42.

43.

44.

45.

46.

40.

'B% ""B# "! œ $B# # #B# &

B B B B " B B " B# B B# B #B œ œ œ B " B " B " B " B " B " B " B " B " B "

B# B #! B# #& B & B % B & B & B & # † œ † œ B# "' B & B % B % B & B % B# " +

B # B# % B # B " " ƒ œ † œ #B " B " B " B " B # B # B " B #

" ,

+, ˆ +" ", ‰ +, ˆ +" ‰ +, ˆ ", ‰ , + œ œ "‰ ˆ + + +, ,

B " œ B " C "

" B " B

Exercises 1.1

" C

BCˆ B" ‰

BCŠ B"

" C‹

BCˆ B" ‰

BCŠ C" ‹

C C B

(page 93)

root, solution

identity

conditional

linear

rational

one

denominator

B $ œ " no restrictions

10.

" B ( œ "% # no restrictions

11.

13.

15.

) & œ B $ B # B $ Á ! B # Á ! BÁ$ B Á # B Á $, B Á # " &B œ # B $ B "' " &B œ B % B % B $ B $ Á ! B % Á ! B % Á ! BÁ$ B Á % BÁ% B Á $, B Á %, B Á %

14.

16.

" œ "# B BÁ!

12.

$ œ *B B # BÁ#

B % œ B $ B % B $ Á ! B % Á ! BÁ$ B Á % B Á $, B Á % " & œ # B# $B % B " & œ # B " B % B B " Á ! B % Á ! BÁ ! B Á " BÁ% B Á ", B Á %, B Á !

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 17.

20.

23.

25.

#B & œ "& #B & & œ "& & #B œ "! #B "! œ # # Bœ& conditional equation

18.

$ 7 # œ # 7 $ 7 21. $7 ' œ #7 ' 7 $7 ' œ $7 ' identity

# + " œ $ + # + #+ # œ $+ ' + #+ # œ #+ ' #+ #+ # œ #+ #+ ' # Á ' contradiction $ B $ œ

'B ") # 'B ") $B * œ # 'B ") # $B * œ # † # 'B ") œ 'B ") identity

$B # œ B ) $B B # œ B B ) #B # œ ) #B # # œ ) # #B œ ' #B ' œ # # Bœ$ conditional equation B ( œ( # B ( #† œ # ( # B ( œ "% B ( ( œ "% ( Bœ( conditional equation

24.

26.

19.

22.

# 8 # & œ #8 #8 % & œ #8 #8 " œ #8 #8 #8 " œ #8 #8 " Á ! contradiction

B ( œ "% # B ( ( œ "% ( # B œ #" # B # † œ # #" # B œ %# conditional equation

B# œ B % B % "' B# œ B# "' "' B# œ B# identity

B B # œ B " # B# #B œ B " B " B# #B œ B# #B " B# B# #B œ B# B# #B " #B œ #B " #B #B œ #B #B " !Á" contradiction

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 27.

29.

31.

33.

35.

$ œ" , $ $ , $ † œ , $ " , $ $œ, $ $ $œ, $ $ 'œ, conditional equation

#B# &B $ œ #B " B $ #B# &B $ œ #B# &B $ identity

#B ( œ "! B $B ( œ "! $B œ $ Bœ" & B # œ # B % &B "! œ #B ) $B "! œ ) $B œ ") Bœ' ( #B & ' B ) œ ( "%B $& 'B %) œ ( )B "$ œ ( )B œ #! #! & Bœ œ ) #

28.

30.

32.

34.

36.

B# )B "& œ B $ B & B# )B "& œ B# #B "& B# B# )B "& œ B# B# #B "& )B "& œ #B "& )B )B "& œ #B )B "& "& œ "!B "& "& "& œ "!B "& "& $! œ "!B $! "!B œ "! "! $œB conditional equation #B# &B $ œ #BŒB

"*  # #B# &B $ œ #B# "*B #B# #B# &B $ œ #B# #B# "*B &B $ œ "*B &B &B $ œ "*B &B $ œ "%B $ "%B œ "% "% $ œB "% conditional equation *+ $ œ "& $+ '+ $ œ "& '+ œ ") +œ$ & < % œ & < % &< #! œ &< #! "!< #! œ #! "!< œ %! <œ% ' B & % B # œ " 'B $! %B ) œ " #B $) œ " #B œ $( $( Bœ #

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 37.

40.

43.

45.

& D )œ( $ & D œ "& $ & $ † D œ $ "& $ &D œ %& Dœ* $: : œ % ( $: (Œ : œ ( % ( $: (: œ #) %: œ #) :œ(

38.

41.

$B " " œ #! # $B " " #! † œ #! † #! # $B " œ "! $B œ * Bœ$

$ B B ( œ %B " $ # $ B B ( 'Œ  œ ' %B " $ # # $ B $ B ( œ #%B ' ' #B $B #" œ #%B ' &B #( œ #%B ' "*B #( œ ' "*B œ #" #" Bœ "*

% C "# œ % $ % C œ "' $ % $ † C œ $ "' $ %C œ %) C œ "#

39.

$B # ( œ #B $ $ $B # ( $† œ $Œ#B  $ $ $B # œ 'B ( $B # œ ( $B œ * B œ $ 44.

46.

42.

D #œ% & D œ# & D & † œ & # & D œ "!

( "& B & œ B # #

( "& #Œ B & œ #ŒB  # # (B "! œ #B "& &B "! œ "& &B œ & Bœ"

( B %B $ œ ' ' ' ( B %B $ 'Œ#B  œ ' † ' ' ' "#B ( B œ %B $ "$B ( œ %B $ *B ( œ $ *B œ "! "! Bœ * #B

$B $ % B œ # # $B $ % B #”# #B " •œ#† # # % #B " $B œ $ % B )B % $B œ "# $B &B % œ "# $B )B % œ "# )B œ "' B œ # # #B "

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 47.

$ $B # "!B % œ ! #

48.

$ #” $B # "!B %• œ # ! # $ $B # #!B ) œ ! *B ' #!B ) œ ! ""B "% œ ! ""B œ "% "% Bœ "" 49.

C # # C# œC # $ $ C # # C# $– œ $ C # Œ  — $ $

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

50.

C # # œ $C ' C# C# %C % œ C# $C ' %C % œ $C ' C %œ' Cœ#

51.

53.

B B # œ B " # " B# #B œ B " B " " B# #B œ B# #B " " B# #B œ B# #B ! œ ! Ê identity

+ + $ & + " # œ 7 7 + + $ & + " # 7” œ 7 • – — 7 7

52.

> " > " œ > # > $ % > # " œ ># > ' % " œ > # > " œ # > œ "

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

# = # = $ # œ = = & #Œ

"( = # #= % =# '= * œ =# &= "( #= =# )= "$ œ =# (= "( )= "$ œ (= "( =œ%

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 54.

56.

58.

59.

$ " % œ B # B $ " % #BŒ  œ #B † B # B ' Bœ) Bœ#

$ " $ œ B # B B # $ " $ B B # Œ  œ B B # † B # B B # $B " B # œ $B $B B # œ $B %B # œ $B Bœ# The answer does not check. Ê no solution

55.

57.

# " " œ B " $ B " # " " $ B " Œ  œ $ B " † B " $ B " ' " B " œ $ " ' B " œ $ B ( œ $ B œ % *> ' ( œ > $ > > $ *> ' ( > > $ ” • œ > > $ † > > $ > $ *> ' œ (> #> ' œ ! #> œ ' > œ $ The answer does not check. Ê no solution

# #B " $B# œ $B & $B & # #B " $B# $B & ”B • œ $B & † $B & $B & # B $B & # #B " œ $B $B# &B %B # œ $B# B # œ ! B œ # B

# % œ + ( + # + $ + # # % + ( + # + $ † œ + ( + # + $ † + ( + # + $ + # # + $ œ % + ( #+ ' œ %+ #) #+ œ $% + œ "(

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 60.

61.

62.

# " " œ # 8 # 8 " 8 8 # # " " œ 8 # 8 " 8 # 8 " # " " 8 # 8 " Œ  œ 8 # 8 " † 8 # 8 " 8 # 8 " # 8 " " 8 # œ " #8 # 8 # œ " $8 œ " " 8œ $ #B $ $B # &B # # œ # &B ' B B ' B % #B $ $B # &B # œ B $ B # B $ B # B # B # B # #B $ B # $B # œ B $ &B # #B# B ' $B# %B % œ &B# "$B ' &B# $B "! œ &B# "$B ' $B "! œ "$B ' "!B œ % % # Bœ œ "! & B#

emultiply by common denominatorf

$B #B B # œ # B# B B# &B B 'B & $B #B B # œ B & B " B B " B B & $ # B # œ B " B & B & B " emultiply by common denominatorf $ B & # B " œ B # $B "& #B # œ B # B "$ œ B # "$ Á # Ê no solution

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 63.

$B & $ # $B # # œ $ B ) B % B # B# #B % $B & $ # $B # œ B # B# #B % B # B # B # B# #B % B # $B & ˆB# #B %‰ $ œ # B # $B # emultiply by common denominatorf $B# B "! $B# 'B "# œ 'B# )B ) 'B# (B # œ 'B# )B ) "&B œ "! "! # Bœ œ "& $

64.

65.

66.

" $8 % " œ 8 ) &8# %#8 "' &8 # " $8 % " œ 8 ) &8 # 8 ) &8 # &8 # " $8 % œ 8 ) emultiply by common denominatorf &8 # $8 % œ 8 ) #8 ' œ 8 ) 8œ# " # $8 " " œ "" 8 (8# (%8 $$ (8 $ " # $8 " " # œ 8 "" (8 (%8 $$ (8 $ " '8 # " œ 8 "" (8 $ 8 "" (8 $ (8 $ '8 # œ 8 "" " (8 $ '8 # œ 8 "" 8 & œ 8 "" #8 œ ' 8œ$

emultiply by common denominatorf

% # " # œ # "$+ %) + ")+ $# + + ' % # " œ + "' + $ + "' + # + $ + # % + # # + $ œ " + "' emultiply by common denominatorf %+ ) #+ ' œ + "' #+ "% œ + "' + œ # +#

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 67.

68.

69.

70.

& # ' " œ C % C # C # C# 'C ) & % " œ C % C # C # C % & C # œ % C % " emultiply by common denominatorf &C "! œ %C "' " &C "! œ %C "& Cœ& ' $ " œ # #+ ' $ $+ + %+ $ ' $ " œ # + $ $ " + + $ + " $ " " œ + $ + " + $ + " $ + " " + $ œ " emultiply by common denominatorf $+ $ + $ œ " %+ ' œ " %+ œ ( ( +œ % $C #C ) œ ' $C #C % % C# $C #C ) œ $ # C # C # # C # C C C ) œ # C # C # C # C emultiply by common denominatorf C # C C # C œ ) #C C# #C C# œ ) %C œ ) C œ # Ê The solution does not check, so the equation has no solution. $ #+ # $+ &+ # œ # +# ' &+ +# ' + + % #+ $ $+ # &+ # œ + # + $ + $ + # + # + # + # #+ $ + # $+ # œ + $ &+ # #+# + ' $+# %+ % œ &+# "$+ ' &+# $+ "! œ &+# "$+ ' "!+ œ % % # +œ œ "! &

emultiply by common denominatorf

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 71.

+ $+ # "œ # + # + %+ % + " $+ # œ + # + # + # " + $+ # + # + # ” "• œ + # + # † ” • + # + # + # + + # + # + # œ $+ # +# #+ ˆ+# %+ %‰ œ $+ # +# #+ +# %+ % œ $+ # #+ % œ $+ # +œ#

72.

73.

76.

B " B # " #B œ B $ B $ $ B B " B # #B " œ B $ B $ B $ B $ B " B $ B # œ B $ #B " B# %B $ B# B ' œ #B# &B $ #B# $B $ œ #B# &B $ )B œ ! ! Bœ œ! ) 5 œ #Þ#: 5 #Þ#: œ #Þ# #Þ# 5 œ: #Þ# " # 1< 2 $ " œ $ † 1 <# 2 $ œ 1 <# 2 1 <# 2 œ 1 <#

Z œ $Z

$Z $Z 1 <# $Z œ2 1 <#

74.

77.

+B , œ ! +B œ , , Bœ +

" # 1< 2 $ " œ $ † 1 <# 2 $ œ 1 <# 2 1 <# 2 œ 12

Z œ $Z

emultiply by common denominatorf

75.

78.

$Z $Z 12 $Z œ <# 12

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

: œ #6 #A : #6 œ #A : #6 #A œ # # : #6 œA # B . 5 B . D5 œ †5 5 D5 œ B . . D5 œ B . œ B D5 Dœ

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 T8 œ P

79.

T8 P œ

0 T8 P œ =3 0 T8 P =3 œ 3 3 0 T8 P œ= 3

85.

87.

" 0 " 0 :; † 0 :; :; :; ; : :; ; :

T8 œ P

80.

=3 0

0 T8 P œ 0 †

82.

=3 0

T8 P œ

" " : ; " " œ 0 :; Œ  : ; œ 0; 0: œ 0 ; : 0 ; : œ ; : œ

81.

=3 0

0 T8 P œ 0 †

=3 0

J <#

J <# J <# Q1 J <# œ7 Q1

=3 0

0 T8 P œ =3 0 T8 P =3 œ T8 P T8 P =3 0œ T8 P 83.

B C + , C , C ,† , C

œ"

84.

B + B œ , Š" ‹ + B œ , Š" ‹ +

œ"

œ0

" < " <<" <# † < <" <# <" <# <" <# <# <" <" <# <# <"

" " <" <# " " œ <<" <# Œ  <" <# œ <<# <<" œ < <# <" < <# <" œ <# <" œ

86.

œ<

6 œ + 8 " . 6 œ + 8. . 6 + . œ 8. 6 + . 8. œ . . 6 + . œ8 .

88.

7Q 1 <# 7Q 1 # œ †< <# œ 7Q 1 7Q 1 œ Q1

J œ

B C œ" + , B C +, Š ‹ œ +, † " , + ,B +C œ +, ,B œ +, +C ,B œ + , C ,B + , C œ , C , C ,B œ+ , C

" " " œ < <" <# " " " <<" <# † œ <<" <# Œ  < <" <# <" <# œ <<# <<" <" <# <<" œ <<# <" <# < œ <<# <" <# < <<# œ <# < <# < <<# <" œ <# <

6 œ + 8 " . 6 + œ 8 " . 6 + 8 " . œ 8 " 8 " 6 + œ. 8 "

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1 89.

+ œ 8 #

")! 8 ")! +8 œ 8 # †8 8 +8 œ 8 # ")! +8 œ ")!8 $'! $'! œ ")!8 +8 $'! œ 8 ")! + $'! œ8 ")! + Vœ

91.

90.

+ 6< " < + 6< W " < œ " < " < W " < œ + 6< W W< 6< œ + Wœ

" " <"

" <#

" <$

<" <# <$ "

<" <# <$ Š <"" <"# <"$ ‹ <" <# <$ Vœ <# <$ <" <$ <" <# V <# <$ <" <$ <" <# œ <" <# <$ V<# <$ V<" <$ V<" <# œ <" <# <$ V<" <$ V<" <# <" <# <$ œ V<# <$ <" V<$ V<# <# <$ œ V<# <$ V<# <$ <" œ V<$ V<# <# <$ Vœ

Vœ

92.

" " <"

" <#

" <$

<" <# <$ "

<" <# <$ Š <"" <"# <"$ ‹ <" <# <$ Vœ <# <$ <" <$ <" <# V <# <$ <" <$ <" <# œ <" <# <$ V<# <$ V<" <$ V<" <# œ <" <# <$ V<# <$ V<" <$ <" <# <$ œ V<" <# <$ V<# V<" <" <# œ V<" <# V<" <# <$ œ V<# V<" <" <# Vœ

93.

Answers may vary.

95.

#&B

# "Î#

# ‘"Î#

œ  &B

œ &kBk

94.

Answers may vary.

96.

#&:# Œ  "'; %

"Î#

# "Î#

&: œ –Œ #  — %;

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

&k:k %; #

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.1

97.

"#&B$  )C'

#Î$

œŒ

)C'  "#&B$

#Î$

98.

)#Î$ C

' #Î$

99.

"#&#Î$ B$ #Î$

"Î$

#( "Î$ C$

"Î$

",!!!"Î$ B' "Î$ $C $C œ œ "!B# "!B# œ

$ $ 100. È "#&C* œ É &C$ $ œ &C$

+% , "# +, $ k+, $ k % œ œ Ë Œ  D) D# D#

Exercises 1.2

#(C$  ",!!!B'

%C% #&B#

È#&C# œ É &C # œ &kCk

101. Ê

102. Ê

B"! C& B# C B# C & œ œ Ë Œ  D "& D$ D$ &

(page "!")

add

perimeter

amount

break point

rate, time

!Þ!& $! œ "Þ&

Let B œ the score on the first exam. Then B & œ the score on the midterm, and B "$ œ the score on the final. Sum of scores œ *! $ B B & B "$ œ *! $ $B ") œ *! $ $B ") œ #(! $B œ #&# B œ )% His score on the first exam was 84.

Let B œ the score on the first exam. Then her scores on the following tests were B $, B ' and B *. Sum of scores œ '*Þ& % B B $ B ' B * œ '*Þ& % %B ") œ '*Þ& % %B ") œ #() %B œ #'! B œ '& Her score on the first exam was 65%.

Let B œ the program development score. Sum of scores œ )' % )# *! B () œ )' % B #&! œ )' % B #&! œ $%% B œ *% The program development score was 94.

10.

Let B œ the score on the final round. Sum of scores œ (# % (' ') (! B œ (# % B #"% œ (# % B #"% œ #)) B œ (% She needs to shoot 74 on the final round.

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.2 11.

Let B œ the number of locks replaced. %! #) †

Number of locks

12.

œ #$'

Let B œ the number of interviews. #! !Þ(& †

%! #)B œ #$' #)B œ "*' Bœ( 7 locks can be changed for $236.

Number of interviews

œ &'

#! !Þ(&B œ &' !Þ(&B œ $' B œ %) He interviewed 48 people.

13.

Let B œ the width. Then B #' œ the height. Perimeter œ *# #B # B #' œ *# #B #B &# œ *# %B œ %! B œ "! The dimensions are 10 ft by 36 ft.

15.

Perimeter œ "% B B # B B # œ "% %B % œ "% %B œ "! & " " B œ œ # Ê The width is 2 feet. # # #

16.

Total Fence Length œ # † Square Fence Length B B #% B B #% œ # † B B B B %B %) œ )B %) œ %B B œ "# The total fencing required is %B %) œ % "# %) œ *' feet.

17.

Total Area œ # † Triangular Area " " #!B "' #! œ # † "' #! # # #!B "'! œ $#! #!B œ "'! Bœ) The dimensions are 8 feet by 20 feet.

14.

18.

Let B œ the width. Then B ""& œ the length. Perimeter œ &(! #B # B ""& œ &(! #B #B #$! œ &(! %B œ $%! B œ )& The dimensions are 85 ft by 200 ft.

Sum of angles œ ")! B B $! B $! œ ")! $B '! œ ")! $B œ "#! B œ %! The angles measure %!°, (!° and (!°.

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.2 19.

20.

New Area

Old Area

!Þ&! †

Old Area

"# B "! "#B œ "# B "! !Þ&! † "# B "! "#B "#! "#B œ "#B "#! 'B '! #%B "#! œ ")B ")! 'B œ '! B œ "! Ê The length of the living room is B "! œ #! feet. Area œ &%

" . "# ) œ &% # "!. œ &% . œ &Þ% Ê The depth is 5.4 inches

21.

Let B œ the amount invested at 7%. Then ##!!! B œ the amount invested at 6%. Interest at 7% Interest at 6% œ Total interest !Þ!(B !Þ!' ##!!! B œ "%#! !Þ!(B "$#! !Þ!'B œ "%#! !Þ!"B œ "!! B œ "!!!! $10,000 was invested at 7% and $12,000 was invested at 6%.

22.

Let B œ the amount invested at 7%. Interest at 7% Interest at 9% œ Total interest !Þ!(B !Þ!* #!!!! œ &!!! !Þ!(B ")!! œ &!!! !Þ!(B œ $#!! B ¸ %&("%Þ#* She needs to invest $45,714.29 at 7% to reach her goal.

23.

Let B œ the amount invested at each rate. Interest at 6% Interest at 7% Interest at 8% œ Total interest !Þ!'B !Þ!(B !Þ!)B œ #!$( !Þ#"B œ #!$( B œ *(!! $9,700 was invested at each rate, for a total investment of $#*,100.

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.2 24.

Let B œ the amount invested at 8%. Then $(,!!! B œ the amount invested at 9 "# %. Interest at 9 12 % œ Interest at 8% %&#Þ&!

!Þ!*& $(,!!! B œ !Þ!)B %&#Þ&! $&"& !Þ!*&B œ !Þ!)B %&#Þ&! $!'#Þ&! œ !Þ"(&B "(&!! œ B $17,500 is invested at 8% and $19,500 is invested at 9 12 %. 25.

Let B œ the number of full-price tickets sold. Then &)& B œ the number of student tickets sold. #Þ&! †

26.

# of full-price

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.

Let B œ the cost of a student ticket. Cost of full-price

27.

# of student

"Þ(& †

†

# of full-price

Cost of student

†

œ %*'!

%)! ( B )!! %)! œ %*'! $$'! $#!B œ %*'! $#!B œ "'!! B œ & Ê A student ticket cost $5.

Let : œ the original price. Original price

# of student

Discount œ

28. New price

Wholesale cost

: !Þ#!: œ '$Þ*' !Þ)!: œ '$Þ*' : œ (*Þ*& The original price was $79.95. 29.

Let B œ # of plates for equal costs. Cost of 1st machine

Let A œ the wholesale cost. Markup œ

Selling price

A !Þ$!A œ &))Þ*! "Þ$!A œ &))Þ*! A œ %&$ The wholesale cost is $453. 30.

Cost of 2nd machine

Let B œ # of fasteners for equal costs. Cost of 1st machine

'!! $B œ )!! #B B œ #!! The break point is 200 plates.

Cost of 2nd machine

"#!! !Þ!!&B œ "&!! !Þ!!"&B !Þ!!$&B œ $!! B ¸ )&("% The break point is about 85,714 fasteners.

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual

SECTION 1.2 31.

Let B œ # of computers to break even. Income œ Expenses "#(&B œ )*#& )&!B %#&B œ )*#& B œ #" 21 computers need to be sold to break even.

32.

Let B œ # of meals to break even. Income œ Expenses 'B œ "$(Þ&! %Þ(&B "Þ#&B œ "$(Þ&! B œ ""! More than 110 meals need to be sold to make a profit.

33.

Let B œ days for both working together.

34.

Let B œ hours for both working together.

Man in 1 day

Roofer in 1 day

Total in 1 day

Crew 1 in 1 hour

Let B œ hours for both working together. Woman in 1 hour

Man in 1 hour

Crew 2 in 1 hour

Total in 1 hour

" " " œ ) "! B " " " %!BŒ  œ %!BŒ  ) "! B &B %B œ %! *B œ %! %! % Bœ œ% * * They can seal the parking lot in 4 49 hours.

" " " œ ( % B " " " #)BŒ  œ #)BŒ  ( % B %B (B œ #) ""B œ #) #) ' Bœ œ# "" "" 6 They can roof the house in 2 11 days. 35.

36.

Total in 1 hour

Let B œ days for both hoses to fill the pool. 1st hose in 1 day

" " " œ # % B " " " %BŒ  œ %BŒ  # % B #B B œ % $B œ % % " Bœ œ" $ $ They can mow the lawn in 1 "$ hours.

2nd hose in 1 day

Total in 1 day

" " " œ $ # B " " " 'BŒ  œ 'BŒ  $ # B #B $B œ ' &B œ ' ' " Bœ œ" & & The pool can be filled in 1 15 days.

Full file at https://testbankuniv.eu/College-Algebra-11th-Edition-Gustafson-Solutions-Manual