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Preface 1 Foundations 2 Solving Linear Equations and Inequalities 3 Math Models 4 Graphs 5 Systems of Linear Equations 6 Polynomials 7 Factoring 8 Rational Expressions and Equations 9 Roots and Radicals 10 Quadratic Equations Answer Key Index Library Elementary Algebra Preface 1 Foundations 2 Solving Linear Equations and Inequalities 3 Math Models 4 Graphs 5 Systems of Linear Equations 6 Polynomials 7 Factoring 8 Rational Expressions and Equations 9 Roots and Radicals 10 Quadratic Equations Answer Key Index
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Show solution 5.1
Show solution 5.2
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Show solution 5.15
infinitely many solutions
Show solution 5.16
infinitely many solutions
Show solution 5.17
no solution, inconsistent, independent
Show solution 5.18
no solution, inconsistent, independent
Show solution 5.19
one solution, consistent, independent
Show solution 5.20
one solution, consistent, independent
Show solution 5.21
infinitely many solutions, consistent, dependent
Show solution 5.22
infinitely many solutions, consistent, dependent
Show solution 5.23
Manny needs 3 quarts juice concentrate and 9 quarts water.
Show solution 5.24
Alisha needs 15 ounces of coffee and 3 ounces of milk.
Show solution 5.25
Show solution 5.26
Show solution 5.27
Show solution 5.28
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Show solution 5.36
(
−
1
2
,
−2
)
(
−
1
2
,
−2
)
Show solution 5.37
infinitely many solutions
Show solution 5.38
infinitely many solutions
Show solution 5.39
Show solution 5.40
Show solution 5.41
Show solution 5.42
The numbers are 2 and −8.
Show solution 5.43
The length is 12 and the width is 8.
Show solution 5.44
The length is 23 and the width is 6.
Show solution 5.45
The measure of the angles are 22 degrees and 68 degrees.
Show solution 5.46
The measure of the angles are 36 degrees and 54 degrees.
Show solution 5.47
There would need to be 160 policies sold to make the total pay the same.
Show solution 5.48
Kenneth would need to sell 1,000 suits.
Show solution 5.49
Show solution 5.50
Show solution 5.51
Show solution 5.52
Show solution 5.53
Show solution 5.54
Show solution 5.55
Show solution 5.56
Show solution 5.57
Show solution 5.58
Show solution 5.59
infinitely many solutions
Show solution 5.60
infinitely many solutions
Show solution 5.61
Show solution 5.62
Show solution 5.63
The numbers are 25 and 17.
Show solution 5.64
The numbers are −25 and 10.
Show solution 5.65
The bag of diapers costs $11 and the can of formula costs $13.
Show solution 5.66
There are 105 calories in a banana and 5 calories in a strawberry.
Show solution 5.67
ⓐ Since both equations are in standard form, using elimination will be most convenient. ⓑ Since one equation is already solved for x x
Show solution 5.68
ⓐ Since one equation is already solved for y y ⓑ Since both equations are in standard form, using elimination will be most convenient.
Show solution 5.69
{
m
+
n
=
−23
m
=
n
−
7
{
m
+
n
=
−23
m
=
n
−
7
Show solution 5.70
{
m
+
n
=
−18
m
=
n
+
40
{
m
+
n
=
−18
m
=
n
+
40
Show solution 5.71
{
w
+
h
=
84,000
h
=
2
w
−
18,000
{
w
+
h
=
84,000
h
=
2
w
−
18,000
Show solution 5.72
{
s
=
2
n
−
5
s
+
n
=
43
{
s
=
2
n
−
5
s
+
n
=
43
Show solution 5.73
Ali is 28 and Jameela is 16.
Show solution 5.74
Jake is 9 and his dad is 33.
Show solution 5.75
Mark burned 11 calories for each minute of yoga and 7 calories for each minute of jumping jacks.
Show solution 5.76
Erin burned 11 calories for each minute on the rowing machine and 5 calories for each minute of weight lifting.
Show solution 5.77
The angle measures are 55 degrees and 35 degrees.
Show solution 5.78
The angle measures are 5 degrees and 85 degrees.
Show solution 5.79
The angle measures are 42 degrees and 138 degrees.
Show solution 5.80
The angle measures are 66 degrees and 114 degrees.
Show solution 5.81
The length is 60 feet and the width is 35 feet.
Show solution 5.82
The length is 60 feet and the width is 38 feet.
Show solution 5.83
It will take Clark 4 hours to catch Mitchell.
Show solution 5.84
It will take Sally 1 1 2 1 1 2
Show solution 5.85
The rate of the boat is 11 mph and the rate of the current is 1 mph.
Show solution 5.86
The speed of the canoe is 7 mph and the speed of the current is 1 mph.
Show solution 5.87
The speed of the jet is 235 mph and the speed of the wind is 30 mph.
Show solution 5.88
The speed of the jet is 408 mph and the speed of the wind is 24 mph.
Show solution 5.89
There were 206 adult tickets sold and 347 children tickets sold.
Show solution 5.90
There were 521 adult tickets sold and 842 children tickets sold.
Show solution 5.91
Matilda has 13 dimes and 29 quarters.
Show solution 5.92
Juan has 36 nickels and 63 dimes.
Show solution 5.93
Greta should use 3 pounds of peanuts and 2 pounds of cashews.
Show solution 5.94
Sammy should purchase 10 pounds of beans and 10 pounds of ground beef.
Show solution 5.95
LeBron needs 120 ml of the 25% solution and 30 ml of the 50% solution.
Show solution 5.96
Anatole should mix 125 ml of the 10% solution and 125 ml of the 40% solution.
Show solution 5.97
Leon should put $42,000 in the stock fund and $8000 in the savings account.
Show solution 5.98
Julius invested $1,750 at 11% and $5,250 at 13%.
Show solution 5.99
The principal amount for the bank loan was $4,000. The principal amount for the federal loan was $14,000.
Show solution 5.100
The principal amount for was $41,200 at 4.5%. The principal amount was, $24,000 at 7.2%.
Show solution 5.101
Show solution 5.102
Show solution 5.103
Show solution 5.104
Show solution 5.105
Show solution 5.106
Show solution 5.107
Show solution 5.108
Show solution 5.109
no solution
Show solution 5.110
no solution
Show solution 5.111
y ≥ 3 x + 1 y ≥ 3 x + 1
Show solution 5.112
x + 4 y ≤ 4 x + 4 y ≤ 4
Show solution 5.113
ⓐ { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 { 30 m + 20 p ≤ 160 2 m + 3 p ≤ 15 ⓑ
ⓒ yesⓓ no
Show solution 5.114
ⓐ { a ≥ p + 5 a + 2 p ≤ 400 { a ≥ p + 5 a + 2 p ≤ 400 ⓑ
ⓒ noⓓ no
Show solution 5.115
ⓐ { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 { 0.75 d + 2 e ≤ 25 360 d + 110 e ≥ 1000 ⓑ
ⓒ yesⓓ no
Show solution 5.116
ⓐ { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 { 140 p + 125 j ≥ 1000 1.80 p + 1.25 j ≤ 12 ⓑ
ⓒ yesⓓ no
Section 5.1 Exercises
Show solution 1 .
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Show solution 7 .
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Show solution 15 .
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Show solution 45 .
infinitely many solutions
Show solution 47 .
infinitely many solutions
Show solution 49 .
Show solution 51 .
Show solution 53 .
Show solution 55 .
no solutions, inconsistent, independent
Show solution 57 .
Show solution 59 .
infinitely many solutions
Show solution 61 .
infinitely many solutions
Show solution 63 .
Molly needs 16 ounces of strawberry juice and 48 ounces of water.
Show solution 65 .
Enrique needs 8 ounces of nuts and 16 ounces of water.
Show solution 67 .
Leo should plant 50 tulips and 300 daffodils.
Show solution 69 .
Given that it is only known that the slopes of both linear equations are the same, there are either no solutions (the graphs of the equations are parallel) or infinitely many.
Section 5.2 Exercises
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(
1
2
,
−
3
4
)
(
1
2
,
−
3
4
)
Show solution 99 .
Infinitely many solutions
Show solution 101 .
Infinitely many solutions
Show solution 103 .
Show solution 105 .
Show solution 107 .
Show solution 109 .
The numbers are −7 and −19.
Show solution 111 .
The length is 20 and the width is 10.
Show solution 113 .
The length is 34 and the width is 8.
Show solution 115 .
The measures are 16° and 74°.
Show solution 117 .
The measures are 45° and 45°.
Show solution 119 .
80 cable packages would need to be sold.
Show solution 121 .
Mitchell would need to sell 120 stoves.
Show solution 123 .
ⓐ t = 2 t = 2 ⓑ s = 2 1 2 s = 2 1 2
Show solution 125 .
Section 5.3 Exercises
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Show solution 145 .
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Show solution 151 .
Show solution 153 .
Show solution 155 .
Show solution 157 .
infinitely many solutions
Show solution 159 .
infinitely many solutions
Show solution 161 .
infinitely many solutions
Show solution 163 .
inconsistent, no solution
Show solution 165 .
inconsistent, no solution
Show solution 167 .
The numbers are 20 and 45.
Show solution 169 .
The numbers are 16 and −43.
Show solution 171 .
A shirt costs $16 and a sweater costs $33.
Show solution 173 .
There are 860 mg in a hot dog. There are 1,000 mg in a cup of cottage cheese.
Show solution 175 .
ⓐ elimination ⓑ substitution
Show solution 177 .
ⓐ substitution ⓑ elimination
Show solution 179 .
Show solution 181 .
ⓐ (8, 2)ⓑ
ⓒ Answers will vary.
Section 5.4 Exercises
Show solution 183 .
Show solution 185 .
The numbers are −5 and −25.
Show solution 187 .
Show solution 189 .
Show solution 191 .
Show solution 193 .
She put $15,000 into a CD and $35,000 in bonds.
Show solution 195 .
The amount of the first year’s loan was $30,000 and the amount of the second year’s loan was $12,000.
Show solution 197 .
Bethany is 16 years old and Alyssa is 28 years old.
Show solution 199 .
Noelle is 20 years old and her dad is 54 years old.
Show solution 201 .
The small container holds 20 gallons and the large container holds 30 gallons.
Show solution 203 .
There were 10 calories burned jogging and 10 calories burned cycling.
Show solution 205 .
Notebooks are $4 and thumb drives are $20.
Show solution 207 .
The measures are 60 degrees and 30 degrees.
Show solution 209 .
The measures are 125 degrees and 55 degrees.
Show solution 211 .
94 degrees and 86 degrees
Show solution 213 .
72.5 degrees and 17.5 degrees
Show solution 215 .
The measures are 44 degrees and 136 degrees.
Show solution 217 .
The measures are 34 degrees and 56 degrees.
Show solution 219 .
The width is 10 feet and the length is 25 feet.
Show solution 221 .
The width is 15 feet and the length is 15 feet.
Show solution 223 .
It took Sarah’s sister 12 hours.
Show solution 225 .
It took Lucy’s friend 2 hours.
Show solution 227 .
The canoe rate is 5 mph and the current rate is 1 mph.
Show solution 229 .
The boat rate is 6.5 mph and the current rate is 2.5 mph.
Show solution 231 .
The jet rate is 240 mph and the wind speed is 28 mph.
Show solution 233 .
The jet rate is 415 mph and the wind speed is 19 mph.
Show solution 235 .
s
=
183
,
a
=
242
s
=
183
,
a
=
242
Show solution 237 .
Section 5.5 Exercises
Show solution 239 .
There 1120 adult tickets and 530 child tickets sold.
Show solution 241 .
Josie bought 40 adult tickets and 32 children tickets.
Show solution 243 .
There were 125 adult tickets and 128 children tickets sold.
Show solution 245 .
Brandon has 12 quarters and 8 dimes.
Show solution 247 .
Peter had 11 dimes and 48 quarters.
Show solution 249 .
The cashier has fourteen $10 bills and sixteen $20 bills.
Show solution 251 .
Marissa should use 60 pounds of the $1.20/lb candy and 30 pounds of the $1.80/lb candy.
Show solution 253 .
Hannah needs 10 gallons of soda and 15 gallons of fruit drink.
Show solution 255 .
Julia and her husband should buy 12 pounds of City Roast Columbian coffee and 8 pounds of French Roast Columbian coffee.
Show solution 257 .
Jotham should mix 2 liters of the 30% solution and 28 liters of the 80% solution.
Show solution 259 .
The scientist should mix 15 liters of the 25% solution and 50 liters of the 12% solution.
Show solution 261 .
160 liters of the 40% solution and 80 liters of the 70% solution will be used.
Show solution 263 .
Hattie should invest $900 at 12% and $2,100 at 10%.
Show solution 265 .
Sam invested $28,000 at 10% and $20,000 at 6%.
Show solution 267 .
The federal loan is $62,500 and the bank loan is $3,300.
Show solution 269 .
$12,000 should be invested at 5.25% and $13,000 should be invested at 4%.
Show solution 271 .
14 boys paid the full-year fee. 4 boys paid the partial-year fee,
Show solution 273 .
Review Exercises
Show solution 327 .
Show solution 329 .
( 3 , −3 ) ( 3 , −3 )
Show solution 331 .
( 5 , 4 ) ( 5 , 4 )
Show solution 333 .
coincident lines
Show solution 335 .
infinitely many solutions, consistent system, dependent equations
Show solution 337 .
no solutions, inconsistent system, independent equations
Show solution 339 .
LaVelle needs 8 ounces of chocolate syrup and 40 ounces of coffee.
Show solution 341 .
Show solution 343 .
Show solution 345 .
Show solution 347 .
The numbers are 22 and 33.
Show solution 349 .
The measures are 23 degrees and 67 degrees.
Show solution 351 .
Show solution 353 .
Show solution 355 .
Show solution 357 .
The numbers are −37 −37 −53 −53
Show solution 359 .
Show solution 361 .
{
x
+
y
=
−32
x
=
2
y
−
2
{
x
+
y
=
−32
x
=
2
y
−
2
Show solution 363 .
{
j
+
d
=
7200
d
=
j
+
1600
{
j
+
d
=
7200
d
=
j
+
1600
Show solution 365 .
Show solution 367 .
The measures are 119 degrees and 61 degrees.
Show solution 369 .
The pergola is 8 feet high and 12 feet wide.
Show solution 371 .
It will take Lenore 3 hours.
Show solution 373 .
The rate of the boat is 10.5 mph. The rate of the current is 1.5 mph.
Show solution 375 .
Lynn bought 227 student tickets and 34 adult tickets.
Show solution 377 .
Yumi should use 4 cups of candies and 8 cups of nuts.
Show solution 379 .
Jack should put $3600 into savings and $8400 into the CD.
Show solution 381 .
Show solution 383 .
Show solution 385 .
Show solution 387 .
No solution
Show solution 389 .
ⓐ { b + n ≤ 40 12 b + 18 n ≥ 500 { b + n ≤ 40 12 b + 18 n ≥ 500 ⓑ
ⓒ yesⓓ no
Practice Test
Show solution 391 .
Show solution 393 .
Show solution 395 .
Show solution 397 .
infinitely many solutions
Show solution 399 .
The numbers are 40 and 64
Show solution 401 .
The measures of the angles are 28 degrees and 62 degrees.
Show solution 403 .
It will take Kathy 1 6 1 6
Show solution 405 .
Liz bought 23 children’s tickets and 5 adult tickets.
Show solution 407 .
ⓐ { C + 0.5 L ≤ 50 L ≥ 3 C { C + 0.5 L ≤ 50 L ≥ 3 C ⓑ
ⓒ Noⓓ Yes
3.6
3.6
Solve Applications with Linear Inequalities
Solve Applications with Linear Inequalities
4.6
4.6
Find the Equation of a Line
Find the Equation of a Line
5.6
5.6
Graphing Systems of Linear Inequalities
Graphing Systems of Linear Inequalities
7.6
7.6
Quadratic Equations
Quadratic Equations
8.6
8.6
Solve Rational Equations
Solve Rational Equations
Solve Equations with Square Roots
Solve Equations with Square Roots
Chapter Review
Chapter Review
Chapter 9
Chapter 9
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