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Deck 9: Systems of Equations and Inequalities
Full screen (f)
Question
Solve the system of equations below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the system of equations below: 
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
Question
Solve each system of equations by the elimination method. 
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
Question
Question
Find the center of the circle whose graph passes through the points 
and 
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
Question
Solve the system of equations below by the substitution method. 
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
Question
Question
The number x of picture cell phones a manufacturer is willing to sell at price p is given by 
where p is the price, in dollars, per picture cell phone. The number x of picture cell phones a distributor is willing to purchase is given by 
where p is the price, in dollars, per picture cell phone. Find the equilibrium price.
A)
B)
C)
D)
E)
where p is the price, in dollars, per picture cell phone. The number x of picture cell phones a distributor is willing to purchase is given by where p is the price, in dollars, per picture cell phone. Find the equilibrium price.A)
B)
C)
D)
E)
Question
Solve the system of equations below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Question
Solve the system of equations below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve each system of equations by the substitution method. 
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
Question
Find the partial fraction decomposition of the rational expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The lines whose equations are 
and 
all intersect at the same point. What is the value of k ?
A)8
B)3
C)-5
D)-2
E)6
and all intersect at the same point. What is the value of k ?A)8
B)3
C)-5
D)-2
E)6
Question
A roundabout is a type of intersection that accommodates traffic flow in one direction, around a circular island. The graphic model below shows the numbers of cars per hour that are entering and leaving a roundabout where 
is 35 cars per hour, 
is 60 cars per hour, 
is 70 cars per hour, 
is 50 cars per hour, 
is 60 cars per hour, 
is 70 cars per hour, 
is 65 cars per hour, and 
is 50 cars per hour. 
What is the minimum number of cars per hour that can travel on 
?
A)25 cars per hour
B)0 cars per hour
C)20 cars per hour
D)15 cars per hour
E)10 cars per hour
is 35 cars per hour, is 60 cars per hour, is 70 cars per hour, is 50 cars per hour, is 60 cars per hour, is 70 cars per hour, is 65 cars per hour, and is 50 cars per hour. What is the minimum number of cars per hour that can travel on ?A)25 cars per hour
B)0 cars per hour
C)20 cars per hour
D)15 cars per hour
E)10 cars per hour
Question
Solve the system of equations below: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Solve the system of equations below: 
A)
B)
C)
D)no solution
E)
A)
B)
C)
D)no solution
E)
Question
A large, rectangular electronic advertising sign for a hotel has a diagonal of 29.2 feet. The height of the sign is 0.6 times its width. Find the height of the sign. Round to the nearest tenth of a foot.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find an equation of the form 
whose graph passes through the points 
and 
.
A)
B)
C)
D)
E)
whose graph passes through the points and .A)
B)
C)
D)
E)
Question
Sketch the graph of the solution set of each system of inequalities. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Sketch the graph of the inequality below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Question
Minimize 
with the constraints 
Round answer to the nearest hundredth.
A)45.89
B)70.80
C)78.00
D)48.00
E)45.50
with the constraints Round answer to the nearest hundredth.A)45.89
B)70.80
C)78.00
D)48.00
E)45.50
Question
Sketch the graph of the solution set of the system of inequalities below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Sketch the graph of the solution set of each system of inequalities. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A company makes two types of telephone answering machines: the standard model and the deluxe model. Each machine passes through three processes: 
, 
, and 
. One standard answering machine requires 1 hour in 
, 5 hours in 
, and 3 hours in 
. One deluxe answering machine requires 3 hours in 
, 6 hours in 
, and 3 hours in 
. Because of employee work schedules, 
, is available for 27 hours, 
, is available for 63 hours, and 
is available for 36 hours. If the profit is $5 for each standard model and $12 for each deluxe model, how many units of each type should the company produce to maximize profit?
A)9 standard models and 0 deluxe models
B)0 standard models and 9 deluxe models
C)9 standard models and 3 deluxe models
D)12 standard models and 0 deluxe models
E)3 standard models and 8 deluxe models
, , and . One standard answering machine requires 1 hour in , 5 hours in , and 3 hours in . One deluxe answering machine requires 3 hours in , 6 hours in , and 3 hours in . Because of employee work schedules, , is available for 27 hours, , is available for 63 hours, and is available for 36 hours. If the profit is $5 for each standard model and $12 for each deluxe model, how many units of each type should the company produce to maximize profit?A)9 standard models and 0 deluxe models
B)0 standard models and 9 deluxe models
C)9 standard models and 3 deluxe models
D)12 standard models and 0 deluxe models
E)3 standard models and 8 deluxe models
Question
Sketch the graph of the inequality below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the partial fraction decomposition of the rational expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the partial fraction decomposition of the rational expression below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
The sprinters on a track team use the following system of inequalities to determine their targeted exercise heart rate ranges for their workouts. 
In this system, y is the person s exercise heart rate in beats per minute and x is the person s age in years. Use the system of inequalities to determine the targeted exercise heart rate range for a sprinter who is 23 years old. Round the minimum and maximum targeted heart rates to the nearest beat per minute.
A)between 197 and 202 beats per minute
B)between 99 and 108 beats per minute
C)between 174 and 178 beats per minute
D)between 87 and 98 beats per minute
E)between 99 and 108 beats per minute.
In this system, y is the person s exercise heart rate in beats per minute and x is the person s age in years. Use the system of inequalities to determine the targeted exercise heart rate range for a sprinter who is 23 years old. Round the minimum and maximum targeted heart rates to the nearest beat per minute.A)between 197 and 202 beats per minute
B)between 99 and 108 beats per minute
C)between 174 and 178 beats per minute
D)between 87 and 98 beats per minute
E)between 99 and 108 beats per minute.
Question
Minimize 
with the constraints 
A)59
B)52
C)41
D)44
E)56
with the constraints A)59
B)52
C)41
D)44
E)56
Question
Sketch the graph of the inequality. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Maximize 
with the constraints 
. Round answer to the nearest hundredth.
A)59.50
B)126.00
C)69.00
D)40.50
E)91.80
with the constraints . Round answer to the nearest hundredth.A)59.50
B)126.00
C)69.00
D)40.50
E)91.80
Question
Graph the following inequality 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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Full screen (f)
Deck 9: Systems of Equations and Inequalities
1
Solve the system of equations below:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
2
Solve the system of equations below:
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
no solution
3
Solve each system of equations by the elimination method.
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
4
A painter leans a ladder against a vertical wall. The top of the ladder is 11 meters above the ground. When the bottom of the ladder is moved 1 meter farther away from the wall, the top of the ladder is 7 meters above the ground. What is the length of the ladder? Round to the nearest hundredth of a meter.
A)34.07 meters
B)27.87 meters
C)46.46 meters
D)43.36 meters
E)37.17 meters
A)34.07 meters
B)27.87 meters
C)46.46 meters
D)43.36 meters
E)37.17 meters
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5
Find the center of the circle whose graph passes through the points and
A)
B)
C)
D)
E)
and A)
B)
C)
D)
E)
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6
Solve the system of equations below by the substitution method.
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
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7
A company sells a large globe and a small globe. The volume of the large globe is four times the volume of the small globe. The difference between the volumes is 1161.36 cubic inches. Find the radius of the small globe. Round to the nearest tenth of an inch.
A)2.3 inches
B)4.5 inches
C)10.4 inches
D)7.2 inches
E)3.6 inches
A)2.3 inches
B)4.5 inches
C)10.4 inches
D)7.2 inches
E)3.6 inches
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8
The number x of picture cell phones a manufacturer is willing to sell at price p is given by where p is the price, in dollars, per picture cell phone. The number x of picture cell phones a distributor is willing to purchase is given by where p is the price, in dollars, per picture cell phone. Find the equilibrium price.
A)
B)
C)
D)
E)
where p is the price, in dollars, per picture cell phone. The number x of picture cell phones a distributor is willing to purchase is given by where p is the price, in dollars, per picture cell phone. Find the equilibrium price.A)
B)
C)
D)
E)
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9
Solve the system of equations below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
A rectangular brochure is designed so that it has an area of 17.5 square inches and a perimeter of 17 inches. Find the width of the brochure. Assume the height is greater than the width.
A)7 inches
B)2.5 inches
C)1.75 inches
D)10 inches
E)3.5 inches
A)7 inches
B)2.5 inches
C)1.75 inches
D)10 inches
E)3.5 inches
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11
One acetic acid solution is 80% water and another is 45% water. How many liters of each solution should be mixed to produce 15 liters of a solution that is 59% water?
A)10 liters of the 80% solution and 5 liters of the 45% solution
B)13 liters of the 80% solution and 2 liters of the 45% solution
C)5 liters of the 80% solution and 10 liters of the 45% solution
D)2 liters of the 80% solution and 13 liters of the 45% solution
E)6 liters of the 80% solution and 9 liters of the 45% solution
A)10 liters of the 80% solution and 5 liters of the 45% solution
B)13 liters of the 80% solution and 2 liters of the 45% solution
C)5 liters of the 80% solution and 10 liters of the 45% solution
D)2 liters of the 80% solution and 13 liters of the 45% solution
E)6 liters of the 80% solution and 9 liters of the 45% solution
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12
Solve the system of equations below:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
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13
Solve each system of equations by the substitution method.
A)no solution
B)
C)
D)
E)
A)no solution
B)
C)
D)
E)
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Unlock for access to all 35 flashcards in this deck.
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14
Find the partial fraction decomposition of the rational expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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15
The lines whose equations are and all intersect at the same point. What is the value of k ?
A)8
B)3
C)-5
D)-2
E)6
and all intersect at the same point. What is the value of k ?A)8
B)3
C)-5
D)-2
E)6
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Unlock Deck
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16
A roundabout is a type of intersection that accommodates traffic flow in one direction, around a circular island. The graphic model below shows the numbers of cars per hour that are entering and leaving a roundabout where is 35 cars per hour, is 60 cars per hour, is 70 cars per hour, is 50 cars per hour, is 60 cars per hour, is 70 cars per hour, is 65 cars per hour, and is 50 cars per hour. What is the minimum number of cars per hour that can travel on ?
A)25 cars per hour
B)0 cars per hour
C)20 cars per hour
D)15 cars per hour
E)10 cars per hour
is 35 cars per hour, is 60 cars per hour, is 70 cars per hour, is 50 cars per hour, is 60 cars per hour, is 70 cars per hour, is 65 cars per hour, and is 50 cars per hour. What is the minimum number of cars per hour that can travel on ?A)25 cars per hour
B)0 cars per hour
C)20 cars per hour
D)15 cars per hour
E)10 cars per hour
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17
Solve the system of equations below:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock Deck
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18
Solve the system of equations below:
A)
B)
C)
D)no solution
E)
A)
B)
C)
D)no solution
E)
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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19
A large, rectangular electronic advertising sign for a hotel has a diagonal of 29.2 feet. The height of the sign is 0.6 times its width. Find the height of the sign. Round to the nearest tenth of a foot.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
20
Find an equation of the form whose graph passes through the points and .
A)
B)
C)
D)
E)
whose graph passes through the points and .A)
B)
C)
D)
E)
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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21
Sketch the graph of the solution set of each system of inequalities.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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22
Sketch the graph of the inequality below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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23
An ice cream supplier has two machines that produce vanilla and chocolate ice cream. To meet one of its contractual obligations, the company must produce at least 78 gallons of vanilla ice cream and 22 gallons of chocolate ice cream per day. One machine makes 11 gallons of vanilla and 2 gallons of chocolate ice cream per hour. The second machine makes 6 gallons of vanilla and 5 gallons of chocolate ice cream per hour. It costs $38 per hour to run machine 1 and $38 per hour to run machine 2. How many hours should each machine be operated to fulfill the contract at the least expense?
A)Machine 1 for no hours and machine 2 for 2 hours.
B)Machine 1 for no hours and machine 2 for 6 hours.
C)Machine 1 for 6 hours and machine 2 for 2 hours.
D)Machine 1 for no hours and machine 2 for 13 hours.
E)Machine 1 for 2 hours and machine 2 for no hours.
A)Machine 1 for no hours and machine 2 for 2 hours.
B)Machine 1 for no hours and machine 2 for 6 hours.
C)Machine 1 for 6 hours and machine 2 for 2 hours.
D)Machine 1 for no hours and machine 2 for 13 hours.
E)Machine 1 for 2 hours and machine 2 for no hours.
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24
Minimize with the constraints Round answer to the nearest hundredth.
A)45.89
B)70.80
C)78.00
D)48.00
E)45.50
with the constraints Round answer to the nearest hundredth.A)45.89
B)70.80
C)78.00
D)48.00
E)45.50
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
25
Sketch the graph of the solution set of the system of inequalities below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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26
Sketch the graph of the solution set of each system of inequalities.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
27
A company makes two types of telephone answering machines: the standard model and the deluxe model. Each machine passes through three processes: , , and . One standard answering machine requires 1 hour in , 5 hours in , and 3 hours in . One deluxe answering machine requires 3 hours in , 6 hours in , and 3 hours in . Because of employee work schedules, , is available for 27 hours, , is available for 63 hours, and is available for 36 hours. If the profit is $5 for each standard model and $12 for each deluxe model, how many units of each type should the company produce to maximize profit?
A)9 standard models and 0 deluxe models
B)0 standard models and 9 deluxe models
C)9 standard models and 3 deluxe models
D)12 standard models and 0 deluxe models
E)3 standard models and 8 deluxe models
, , and . One standard answering machine requires 1 hour in , 5 hours in , and 3 hours in . One deluxe answering machine requires 3 hours in , 6 hours in , and 3 hours in . Because of employee work schedules, , is available for 27 hours, , is available for 63 hours, and is available for 36 hours. If the profit is $5 for each standard model and $12 for each deluxe model, how many units of each type should the company produce to maximize profit?A)9 standard models and 0 deluxe models
B)0 standard models and 9 deluxe models
C)9 standard models and 3 deluxe models
D)12 standard models and 0 deluxe models
E)3 standard models and 8 deluxe models
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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28
Sketch the graph of the inequality below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
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29
Find the partial fraction decomposition of the rational expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
30
Find the partial fraction decomposition of the rational expression below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
31
The sprinters on a track team use the following system of inequalities to determine their targeted exercise heart rate ranges for their workouts. In this system, y is the person s exercise heart rate in beats per minute and x is the person s age in years. Use the system of inequalities to determine the targeted exercise heart rate range for a sprinter who is 23 years old. Round the minimum and maximum targeted heart rates to the nearest beat per minute.
A)between 197 and 202 beats per minute
B)between 99 and 108 beats per minute
C)between 174 and 178 beats per minute
D)between 87 and 98 beats per minute
E)between 99 and 108 beats per minute.
In this system, y is the person s exercise heart rate in beats per minute and x is the person s age in years. Use the system of inequalities to determine the targeted exercise heart rate range for a sprinter who is 23 years old. Round the minimum and maximum targeted heart rates to the nearest beat per minute.A)between 197 and 202 beats per minute
B)between 99 and 108 beats per minute
C)between 174 and 178 beats per minute
D)between 87 and 98 beats per minute
E)between 99 and 108 beats per minute.
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
32
Minimize with the constraints
A)59
B)52
C)41
D)44
E)56
with the constraints A)59
B)52
C)41
D)44
E)56
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Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
33
Sketch the graph of the inequality.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
34
Maximize with the constraints . Round answer to the nearest hundredth.
A)59.50
B)126.00
C)69.00
D)40.50
E)91.80
with the constraints . Round answer to the nearest hundredth.A)59.50
B)126.00
C)69.00
D)40.50
E)91.80
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
35
Graph the following inequality .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 35 flashcards in this deck.
