Question 1

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\frac { x } { 3 } + \frac { y } { 3 } = 0$$
$x - y = - 8$

Accepted Answer

A)  $\{ ( - 4,4 ) \}$ 
B)  $\{ ( - 5,5 ) \}$ 
C)  $\{ ( x , y ) \mid x - y = - 8 \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 4,4 ) \}$ 
B)  $\{ ( - 5,5 ) \}$ 
C)  $\{ ( x , y ) \mid x - y = - 8 \}$ 
D)  $\varnothing$

Question 2

Graph a Nonlinear Inequality in Two Variables
-$$y \geq \log ( x - 2 )$$

Accepted Answer

A)   
B)   
C)   
D)   
A)   
B)   
C)   
D)

Question 3

Write the partial fraction decomposition of the rational expression.
-$$\frac { - 4 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$$

Accepted Answer

A)  $\frac { - 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } }$ 
B)  $\frac { 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 3 } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { - 2 } { x + 2 } + \frac { 2 } { x + 1 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } }$ 
D)  $\frac { - 3 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 2 } { ( x + 1 ) ^ { 2 } }$ 
A)  $\frac { - 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } }$ 
B)  $\frac { 2 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 3 } { ( x + 1 ) ^ { 2 } }$ 
C)  $\frac { - 2 } { x + 2 } + \frac { 2 } { x + 1 } + \frac { - 3 } { ( x + 1 ) ^ { 2 } }$ 
D)  $\frac { - 3 } { x + 2 } + \frac { - 2 } { x + 1 } + \frac { 2 } { ( x + 1 ) ^ { 2 } }$

Question 4

Solve Problems Using Systems of Nonlinear Equations
-A right triangle has an area of 36 square inches. The square of the hypotenuse is 145 . Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Accepted Answer

A)  8 inches and 9 inches 
B)  64 inches and 81 inches 
C)  4 inches and 18 inches 
D)  16 inches and $4.5$ inches 
A)  8 inches and 9 inches 
B)  64 inches and 81 inches 
C)  4 inches and 18 inches 
D)  16 inches and $4.5$ inches

Question 5

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
y = ( x + 5 ) ^ { 2 } + 1 \
2 x - y + 10 = 0
\end{array}$$

Accepted Answer

A)  $\{ ( - 4,2 ) \}$ 
B)  $\{ ( - 4,2 ) , ( 4,18 ) \}$ 
C)  $\{ ( 0,10 ) , ( 0,26 ) \}$ 
D)  $\{ ( - 5,0 ) \}$ 
A)  $\{ ( - 4,2 ) \}$ 
B)  $\{ ( - 4,2 ) , ( 4,18 ) \}$ 
C)  $\{ ( 0,10 ) , ( 0,26 ) \}$ 
D)  $\{ ( - 5,0 ) \}$

Question 6

Solve Linear Systems by Addition
-$$\begin{array} { l } 
2 x + 15 y = - 91 \
9 x + 3 y = 42
\end{array}$$

Accepted Answer

A)  $\{ ( 7 , - 7 ) \}$ 
B)  $\{ ( - 7,7 ) \}$ 
C)  $\{ ( 9 , - 9 ) \}$ 
D)  $\{ ( - 3,7 ) \}$ 
A)  $\{ ( 7 , - 7 ) \}$ 
B)  $\{ ( - 7,7 ) \}$ 
C)  $\{ ( 9 , - 9 ) \}$ 
D)  $\{ ( - 3,7 ) \}$

Question 7

Solve Problems Using Systems in Three Variables
-The sum of three numbers is 12. If the second number is subtracted from the sum of the first and third numbers, the result is 2. If the third number is subtracted from the sum of the first and second numbers, the result is 4. Find the three numbers. [Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]

Accepted Answer

A)  $x = 3 , y = 5 , z = 4$ 
B)  $x = 4 , y = 5 , z = 3$ 
C)  $x = 4 , y = 6 , z = 2$ 
D)  $x = 1 , y = 7 , z = 4$ 
A)  $x = 3 , y = 5 , z = 4$ 
B)  $x = 4 , y = 5 , z = 3$ 
C)  $x = 4 , y = 6 , z = 2$ 
D)  $x = 1 , y = 7 , z = 4$

Question 8

Graph the inequality.
-$$2 x + 5 y \leq 10$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Solve Problems Using Systems of Linear Equations
-An-Mei owns a business making and selling jackets. She has a fixed cost of $\$ 4500$. It costs $\$ 85$ to produce each jacket. The selling price is $\$ 115$ per jacket. Let $x$ represent the number of jackets produced and sold and write the cost function, $C$, and revenue function, $R$.

Accepted Answer

A)  $C ( x ) = 85 x + 4500$
$R ( x ) = 115 x$ 
B)  $C ( x ) = 85 + 115 x$
$R ( x ) = 4500 x$ 
C)  $C ( x ) = 85 + 4500 x$
$R ( x ) = 115$ 
D)  $C ( x ) = 85 x + 4500 x$
$R ( x ) = 115 x$ 
A)  $C ( x ) = 85 x + 4500$
$R ( x ) = 115 x$ 
B)  $C ( x ) = 85 + 115 x$
$R ( x ) = 4500 x$ 
C)  $C ( x ) = 85 + 4500 x$
$R ( x ) = 115$ 
D)  $C ( x ) = 85 x + 4500 x$
$R ( x ) = 115 x$

Question 10

Solve Problems Using Systems of Nonlinear Equations
-In a 1-mile race, the winner crosses the finish line 11 feet ahead of the second-place runner and 27 feet ahead of the third-place runner. Assuming that each runner maintains a constant speed throughout the race, by how many feet does the second-place runner beat the third-place runner? ( 5280 feet in 1 mile.)

Accepted Answer

A)  $16.03 \mathrm { ft }$ 
B)  $- 11.06 \mathrm { ft }$ 
C)  $- 16.08 \mathrm { ft }$ 
D)  $5.01 \mathrm { ft }$ 
A)  $16.03 \mathrm { ft }$ 
B)  $- 11.06 \mathrm { ft }$ 
C)  $- 16.08 \mathrm { ft }$ 
D)  $5.01 \mathrm { ft }$

Question 11

Solve Problems Using Systems of Linear Equations
-Is there a profit when 910 binoculars are produced?

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 12

Solve Systems of Linear Equations in Three Variables
-$$\begin{array} { c } 
x - y + 5 z = - 2 \
5 x \quad + z = 0 \
x + 5 y + z = 10
\end{array}$$

Accepted Answer

A)  $\{ ( 0,2,0 ) \}$ 
B)  $\{ ( 0,0,2 ) \}$ 
C)  $\{ ( 2,0,0 ) \}$ 
D)  $\{ ( 0,2 , - 2 ) \}$ 
A)  $\{ ( 0,2,0 ) \}$ 
B)  $\{ ( 0,0,2 ) \}$ 
C)  $\{ ( 2,0,0 ) \}$ 
D)  $\{ ( 0,2 , - 2 ) \}$

Question 13

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l } 
8 x - 3 y = 3 \
- 16 x + 6 y = - 9
\end{array}$$

Accepted Answer

A)  $\left\{ \left( \frac { 4 } { 3 } , - \frac { 1 } { 2 } \right) \right\}$ 
B)  $\{ ( 2,3 ) \}$ 
C)  $\{ ( x , y ) \mid 8 x - 3 y = 3 \}$ 
D)  $\varnothing$ 
A)  $\left\{ \left( \frac { 4 } { 3 } , - \frac { 1 } { 2 } \right) \right\}$ 
B)  $\{ ( 2,3 ) \}$ 
C)  $\{ ( x , y ) \mid 8 x - 3 y = 3 \}$ 
D)  $\varnothing$

Question 14

Solve Problems Using Systems of Linear Equations
-Jarod is having a problem with rabbits getting into his vegetable garden, so he decides to fence it in. The length of the garden is 11 feet more than 5 times the width. He needs 70 feet of fencing to do the job. Find the length and width of the garden.

Accepted Answer

A)  length: 31 feet; width: 4 feet 
B)  length: $60 \frac { 1 } { 6 }$ feet; width: $9 \frac { 5 } { 6 }$ feet 
C)  length: 36 feet; width: 5 feet 
D)  length: 26 feet; width: 3 feet 
A)  length: 31 feet; width: 4 feet 
B)  length: $60 \frac { 1 } { 6 }$ feet; width: $9 \frac { 5 } { 6 }$ feet 
C)  length: 36 feet; width: 5 feet 
D)  length: 26 feet; width: 3 feet

Question 15

Use Mathematical Models Involving Linear Inequalities
-A woman works out by running and swimming. When she runs, she burns 7 calories per minute. When she swims, she burns 10 calories per minute. She wants to burn at least 490 calories in her workout.
Graph an inequality that describes the situation. Let $x$ represent the number of minutes running and $y$ the number of minutes swimming. Because $x$ and $y$ must be positive, limit the graph to quadrant I only.

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

Use Linear Programming to Solve Problems
-Two kinds of crated cargo, $A$ and $B$, are to be shipped by truck. The weight and volume of each type are given in the following table:

The shipping company charges $\$ 75$ per crate for cargo $\mathrm { A }$ and $\$ 100$ per crate for cargo $\mathrm { B }$. The truck has a maximum load limit of 7,200 pounds and 1,000 cubic feet. How many of each type of cargo should be shipped to maximize profit for the shipping company?

Accepted Answer

A)  18 crates of cargo A and 10 crates of cargo B 
B)  20 crates of cargo $\mathrm { A }$ and 0 crates of cargo $\mathrm { B }$ 
C)  0 crates of cargo $\mathrm { A }$ and 20 crates of cargo $\mathrm { B }$ 
D)  10 crates of cargo $A$ and 18 crates of cargo $B$ 
A)  18 crates of cargo A and 10 crates of cargo B 
B)  20 crates of cargo $\mathrm { A }$ and 0 crates of cargo $\mathrm { B }$ 
C)  0 crates of cargo $\mathrm { A }$ and 20 crates of cargo $\mathrm { B }$ 
D)  10 crates of cargo $A$ and 18 crates of cargo $B$

Question 17

Solve Problems Using Systems of Nonlinear Equations
-The area of a rectangular piece of cardboard shown is 780 square inches. The cardboard is used to make an open box by cutting a 5-inch square from each corner and turning up the sides. If the box is to have a volume of 1450 cubic inches, find the dimensions of the cardboard that must be used.

Accepted Answer

A)  20 inches by 39 inches 
B)  25 inches by 44 inches 
C)  15 inches by 34 inches 
D)  10 inches by 24 inches 
A)  20 inches by 39 inches 
B)  25 inches by 44 inches 
C)  15 inches by 34 inches 
D)  10 inches by 24 inches

Question 18

Use Linear Programming to Solve Problems
-$$\begin{array} { l l } 
\text { Objective Function } & \mathrm { z } = 8 \mathrm { x } - 17 \mathrm { y } \
\text { Constraints } & 0 \leq x \leq 5 \
& 0 \leq y \leq 8 \
& 4 x + 5 y \leq 30 \
& 4 x + 3 y \leq 20
\end{array}$$

Accepted Answer

A)  Maximum: 40; at $( 5,0 )$ 
B)  Maximum: 0 ; at $( 0,0 )$ 
C)  Maximum: $- 75$; at $( 1.25,5 )$ 
D)  Maximum: $- 102$; at $( 0,6 )$ 
A)  Maximum: 40; at $( 5,0 )$ 
B)  Maximum: 0 ; at $( 0,0 )$ 
C)  Maximum: $- 75$; at $( 1.25,5 )$ 
D)  Maximum: $- 102$; at $( 0,6 )$

Question 19

Write the partial fraction decomposition of the rational expression.
-$\frac { 50 - 7 x } { x ( x - 5 ) ^ { 2 } }$

Accepted Answer

A)  $\frac { 2 } { x } + \frac { - 2 } { x - 5 } + \frac { 3 } { ( x - 5 ) ^ { 2 } }$ 
B)  $\frac { 2 } { x } + \frac { 3 } { x - 5 } + \frac { - 2 } { ( x - 5 ) ^ { 2 } }$ 
C)  $\frac { 2 } { x } + \frac { - 2 } { x - 5 } + \frac { 6 } { ( x - 5 ) ^ { 2 } }$ 
D)  $\frac { - 2 } { x } + \frac { 2 } { x - 5 } + \frac { 3 } { ( x - 5 ) ^ { 2 } }$ 
A)  $\frac { 2 } { x } + \frac { - 2 } { x - 5 } + \frac { 3 } { ( x - 5 ) ^ { 2 } }$ 
B)  $\frac { 2 } { x } + \frac { 3 } { x - 5 } + \frac { - 2 } { ( x - 5 ) ^ { 2 } }$ 
C)  $\frac { 2 } { x } + \frac { - 2 } { x - 5 } + \frac { 6 } { ( x - 5 ) ^ { 2 } }$ 
D)  $\frac { - 2 } { x } + \frac { 2 } { x - 5 } + \frac { 3 } { ( x - 5 ) ^ { 2 } }$

Question 20

Graph the inequality.
-$y<-4 x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - $\frac { x } { 3 } + \frac { y } { 3 } = 0$ $x - y = - 8$

Graph a Nonlinear Inequality in Two Variables - $y \geq \log ( x - 2 )$ $Graph a Nonlinear Inequality in Two Variables - y \geq \log ( x - 2 )$

Write the partial fraction decomposition of the rational expression. - $\frac { - 4 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$

Solve Problems Using Systems of Nonlinear Equations -A right triangle has an area of 36 square inches. The square of the hypotenuse is 145 . Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Solve Nonlinear Systems By Substitution - y=(x+5+1 2x-y+10=0

Solve Linear Systems by Addition - 2x+15y=-91 9x+3y=42

Graph the inequality. - $2 x + 5 y \leq 10$ $Graph the inequality. - 2 x + 5 y \leq 10$

Solve Problems Using Systems of Linear Equations -Is there a profit when 910 binoculars are produced?

Solve Systems of Linear Equations in Three Variables - x-y+5z=-2 5x+z=0 x+5y+z=10

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - 8x-3y=3 -16x+6y=-9

Use Linear Programming to Solve Problems - Objective Function =8-17 Constraints 0\leqx\leq5 0\leqy\leq8 4x+5y\leq30 4x+3y\leq20

Write the partial fraction decomposition of the rational expression. - $\frac { 50 - 7 x } { x ( x - 5 ) ^ { 2 } }$

Graph the inequality. - $y<-4 x$

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 8: Systems of Equations and Inequalities

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - x3+y3=0\frac { x } { 3 } + \frac { y } { 3 } = 03x​+3y​=0 x−y=−8x - y = - 8x−y=−8

Graph a Nonlinear Inequality in Two Variables - y≥log⁡(x−2)y \geq \log ( x - 2 )y≥log(x−2)

Write the partial fraction decomposition of the rational expression. - −4x2−13x−12(x+2)(x+1)2\frac { - 4 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }(x+2)(x+1)2−4x2−13x−12​

Solve Problems Using Systems of Nonlinear Equations -A right triangle has an area of 36 square inches. The square of the hypotenuse is 145 . Find the lengths of the legs of the triangle. Round your answer to the nearest inch.

Solve Nonlinear Systems By Substitution - y=(x+5+1 2x-y+10=0

Solve Linear Systems by Addition - 2x+15y=-91 9x+3y=42

Graph the inequality. - 2x+5y≤102 x + 5 y \leq 102x+5y≤10

Solve Problems Using Systems of Linear Equations -Is there a profit when 910 binoculars are produced?

Solve Systems of Linear Equations in Three Variables - x-y+5z=-2 5x+z=0 x+5y+z=10

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - 8x-3y=3 -16x+6y=-9

Use Linear Programming to Solve Problems - Objective Function =8-17 Constraints 0\leqx\leq5 0\leqy\leq8 4x+5y\leq30 4x+3y\leq20

Write the partial fraction decomposition of the rational expression. - 50−7xx(x−5)2\frac { 50 - 7 x } { x ( x - 5 ) ^ { 2 } }x(x−5)250−7x​

Graph the inequality. - y<−4xy<-4 xy<−4x

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - $\frac { x } { 3 } + \frac { y } { 3 } = 0$ $x - y = - 8$

Graph a Nonlinear Inequality in Two Variables - $y \geq \log ( x - 2 )$ $Graph a Nonlinear Inequality in Two Variables - y \geq \log ( x - 2 )$

Write the partial fraction decomposition of the rational expression. - $\frac { - 4 x ^ { 2 } - 13 x - 12 } { ( x + 2 ) ( x + 1 ) ^ { 2 } }$

Graph the inequality. - $2 x + 5 y \leq 10$ $Graph the inequality. - 2 x + 5 y \leq 10$

Write the partial fraction decomposition of the rational expression. - $\frac { 50 - 7 x } { x ( x - 5 ) ^ { 2 } }$

Graph the inequality. - $y<-4 x$