Question 1

Write the partial fraction decomposition of the rational expression.
-$\frac { 8 x + 1 } { x ^ { 3 } - 1 }$

Accepted Answer

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

Question 2

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 4 \
4 x ^ { 2 } + 16 y ^ { 2 } = 64
\end{array}$$

Accepted Answer

A)  $\{ ( 0,2 ) , ( 0 , - 2 ) \}$ 
B)  $\{ ( 2,0 ) , ( - 2,0 ) \}$ 
C)  $\{ ( 0,4 ) , ( 0 , - 4 ) \}$ 
D)  $\{ ( 4,0 ) , ( - 4,0 ) \}$ 
A)  $\{ ( 0,2 ) , ( 0 , - 2 ) \}$ 
B)  $\{ ( 2,0 ) , ( - 2,0 ) \}$ 
C)  $\{ ( 0,4 ) , ( 0 , - 4 ) \}$ 
D)  $\{ ( 4,0 ) , ( - 4,0 ) \}$ A

Question 3

Write the word or phrase that best completes each statement or answers the question.
-An artist is creating a mosaic that cannot be larger than the space allotted which is 4 feet tall and 6 feet wide. The mosaic must be at least 3 feet tall and 5 feet wide. The tiles in the mosaic have words written on them and the artist wants the words to all be horizontal in the final mosaic. The word tiles come in two sizes: The smaller tiles are 4 inches tall and 4 inches wide, while the large tiles are 6 inches tall and 12 inches wide. If the small tiles cost $3.50 each and the larger tiles cost $4.50 each, how many of each should be used to minimize the cost? What is the minimum cost?

Accepted Answer

0 small tile, 6 large tiles; minimum cost $27

Question 4

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l } 
y = 15 - 4 x \
16 x + 4 y = 60
\end{array}$$

Accepted Answer

A)  $\{ ( 0,15 ) \}$ 
B)  $\{ ( 5 , - 5 ) \}$ 
C)  $\{ ( x , y ) \mid 4 x + y = 15 \}$ 
D)  $\varnothing$ ) 
A)  $\{ ( 0,15 ) \}$ 
B)  $\{ ( 5 , - 5 ) \}$ 
C)  $\{ ( x , y ) \mid 4 x + y = 15 \}$ 
D)  $\varnothing$ )

Question 5

Write the partial fraction decomposition of the rational expression.
-$\frac { x } { x ^ { 2 } - 9 x + 20 }$

Accepted Answer

A)  $\frac { - 4 } { x - 4 } + \frac { 5 } { x - 5 }$ 
B)  $\frac { 4 } { x - 4 } + \frac { - 5 } { x - 5 }$ 
C)  $\frac { - 5 } { x - 4 } + \frac { 4 } { x - 5 }$ 
D)  $\frac { - 4 } { x - 4 } + \frac { - 5 } { x - 5 }$ 
A)  $\frac { - 4 } { x - 4 } + \frac { 5 } { x - 5 }$ 
B)  $\frac { 4 } { x - 4 } + \frac { - 5 } { x - 5 }$ 
C)  $\frac { - 5 } { x - 4 } + \frac { 4 } { x - 5 }$ 
D)  $\frac { - 4 } { x - 4 } + \frac { - 5 } { x - 5 }$

Question 6

Use Linear Programming to Solve Problems
-Objective Function
$z = 6 x - 3 y$
Constraints
$x \geq 0$
$0 \leq y \leq 8$
$x - y \leq 6$
$x + 2 y \leq 18$

Accepted Answer

A)  Maximum: 48; at $( 10,4 )$ 
B)  Maximum: 36; at $( 6,0 )$ 
C)  Maximum: $- 12$; at $( 2,8 )$ 
D)  Maximum: $- 24$; at $( 0,8 )$ 
A)  Maximum: 48; at $( 10,4 )$ 
B)  Maximum: 36; at $( 6,0 )$ 
C)  Maximum: $- 12$; at $( 2,8 )$ 
D)  Maximum: $- 24$; at $( 0,8 )$

Question 7

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 65 \
( x - 1 ) ^ { 2 } + y ^ { 2 } = 64
\end{array}$$

Accepted Answer

A)  $\{ ( 1,8 ) , ( 1 , - 8 ) \}$ 
B)  $\{ ( 1,8 ) , ( 1 , - 8 ) , ( - 1,8 ) , ( - 1 , - 8 ) \}$ 
C)  $\{ ( 8,1 ) , ( 8 , - 1 ) \}$ 
D)  $\{ ( 8,1 ) , ( 8 , - 1 ) , ( - 8,1 ) , ( - 8 , - 1 ) \}$ 
A)  $\{ ( 1,8 ) , ( 1 , - 8 ) \}$ 
B)  $\{ ( 1,8 ) , ( 1 , - 8 ) , ( - 1,8 ) , ( - 1 , - 8 ) \}$ 
C)  $\{ ( 8,1 ) , ( 8 , - 1 ) \}$ 
D)  $\{ ( 8,1 ) , ( 8 , - 1 ) , ( - 8,1 ) , ( - 8 , - 1 ) \}$

Question 8

Solve Problems Using Systems of Nonlinear Equations
-The sum of two numbers is 14 and their product is 45 . Find the numbers.

Accepted Answer

A)  9 and 5 
B)  $- 9$ and $- 5$ 
C)  9 and $5 ; - 9$ and $- 5$ 
D)  9 and $- 5 ; - 9$ and 5 
A)  9 and 5 
B)  $- 9$ and $- 5$ 
C)  9 and $5 ; - 9$ and $- 5$ 
D)  9 and $- 5 ; - 9$ and 5

Question 9

Use Linear Programming to Solve Problems
-Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 6 hours to make a hat and 4 hours to make an afghan, and she has no more than 66 hours available. She has material for no more than 14 items and no more than 10 afghans. The bazaar will sell the hats for $\$ 21$ each and the afghans for $\$ 5$ each. How many of each should she make to maximize the income for the bazaar? What is the maximum income?

Accepted Answer

A)  5 hats and 9 afghans; $\$ 150$ 
B)  9 hats and 5 afghans; $\$ 214$ 
C)  10 hats and 4 afghans; $\$ 230$ 
D)  7 hats and 7 afghans; $\$ 182$ 
A)  5 hats and 9 afghans; $\$ 150$ 
B)  9 hats and 5 afghans; $\$ 214$ 
C)  10 hats and 4 afghans; $\$ 230$ 
D)  7 hats and 7 afghans; $\$ 182$

Question 10

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-

Accepted Answer

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

Question 11

Write the partial fraction decomposition of the rational expression.
-$$\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$$

Accepted Answer

A)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
B)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
C)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
D)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
A)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
B)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$ 
C)  $\frac { 1 } { x + 3 } - \frac { 1 } { x - 3 } - \frac { 7 } { x ^ { 2 } + 8 }$ 
D)  $\frac { 1 } { x + 3 } + \frac { 1 } { x - 3 } + \frac { 7 } { x ^ { 2 } + 8 }$

Question 12

Graph a Nonlinear Inequality in Two Variables
-$y>3^{x}$

Accepted Answer

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

Question 13

Solve Problems Using Systems of Linear Equations
-Steve invests in a circus production. The cost includes an overhead of $\$ 117,000$, plus production costs of $\$ 7000$ per performance. A sold-out performance brings in $\$ 16,000$. Determine the dollar amount coming in and going out at the break-even point.

Accepted Answer

A)  $\$ 208,000$ 
B)  $\$ 91,000$ 
C)  $\$ 13$ 
D)  $\$ 81,391$ 
A)  $\$ 208,000$ 
B)  $\$ 91,000$ 
C)  $\$ 13$ 
D)  $\$ 81,391$

Question 14

Solve Systems of Linear Equations in Three Variables
-$$\begin{array} { r } 
y + 4 z = 0 \
4 x + y - 2 z = 2 \
- 3 x - 3 z = - 9
\end{array}$$

Accepted Answer

A)  $\{ ( 2 , - 4,1 ) \}$ 
B)  $\{ ( 2 , - 8,2 ) \}$ 
C)  $\{ ( - 1 , - 3,4 ) \}$ 
D)  $\{ ( - 1,14,4 ) \}$ 
A)  $\{ ( 2 , - 4,1 ) \}$ 
B)  $\{ ( 2 , - 8,2 ) \}$ 
C)  $\{ ( - 1 , - 3,4 ) \}$ 
D)  $\{ ( - 1,14,4 ) \}$

Question 15

Graph the solution set of the system of inequalities or indicate that the system has no solution.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 100 \
- 3 x + 4 y \leq - 12
\end{array}$$

Accepted Answer

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

Question 16

Write the partial fraction decomposition of the rational expression.
-$\frac { 64 - 11 x } { x ^ { 3 } - 8 x ^ { 2 } + 16 x }$

Accepted Answer

A)  $\frac { 4 } { x } + \frac { - 4 } { x - 4 } + \frac { 5 } { ( x - 4 ) ^ { 2 } }$ 
B)  $\frac { 4 } { x } + \frac { 5 } { x - 4 } + \frac { - 4 } { ( x - 4 ) ^ { 2 } }$ 
C)  $\frac { 4 } { x } + \frac { - 4 } { x - 4 } + \frac { 10 } { ( x - 4 ) ^ { 2 } }$ 
D)  $\frac { - 4 } { x } + \frac { 4 } { x - 4 } + \frac { 5 } { ( x - 4 ) ^ { 2 } }$ 
A)  $\frac { 4 } { x } + \frac { - 4 } { x - 4 } + \frac { 5 } { ( x - 4 ) ^ { 2 } }$ 
B)  $\frac { 4 } { x } + \frac { 5 } { x - 4 } + \frac { - 4 } { ( x - 4 ) ^ { 2 } }$ 
C)  $\frac { 4 } { x } + \frac { - 4 } { x - 4 } + \frac { 10 } { ( x - 4 ) ^ { 2 } }$ 
D)  $\frac { - 4 } { x } + \frac { 4 } { x - 4 } + \frac { 5 } { ( x - 4 ) ^ { 2 } }$

Question 17

Graph the inequality.
-$$- 2 x - 3 y \leq 6$$

Accepted Answer

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

Question 18

Solve Problems Using Systems of Nonlinear Equations
-The area of a garden is 432 square feet, and the length of its diagonal is 30 feet. Find the dimensions of the garden.

Accepted Answer

A)  18 feet by 24 feet 
B)  3 feet by 144 feet 
C)  108 feet by 4 feet 
D)  12 feet by 36 feet 
A)  18 feet by 24 feet 
B)  3 feet by 144 feet 
C)  108 feet by 4 feet 
D)  12 feet by 36 feet

Question 19

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
- 5 x + y ^ { 2 } = 1
\end{array}$$

Accepted Answer

A)  $\{ ( 3,4 ) , ( 3 , - 4 ) \}$ 
B)  $\{ ( 3,4 ) \}$ 
C)  $\{ ( 3,4 ) , ( 3 , - 4 ) , ( - 8,4 ) , ( - 8 , - 4 ) \}$ 
D)  $\{ ( 3,4 ) , ( 3 , - 4 ) , ( - 3,4 ) , ( - 3 , - 4 ) \}$ 
A)  $\{ ( 3,4 ) , ( 3 , - 4 ) \}$ 
B)  $\{ ( 3,4 ) \}$ 
C)  $\{ ( 3,4 ) , ( 3 , - 4 ) , ( - 8,4 ) , ( - 8 , - 4 ) \}$ 
D)  $\{ ( 3,4 ) , ( 3 , - 4 ) , ( - 3,4 ) , ( - 3 , - 4 ) \}$

Question 20

Graph the inequality.
-$$\frac { x } { 4 } + \frac { y } { 2 } \leq 1$$

Accepted Answer

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

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x + 1 } { x ^ { 3 } - 1 }$

Solve Nonlinear Systems By Addition - +=4 4+16=64

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - y=15-4x 16x+4y=60

Write the partial fraction decomposition of the rational expression. - $\frac { x } { x ^ { 2 } - 9 x + 20 }$

Use Linear Programming to Solve Problems -Objective Function $z = 6 x - 3 y$ Constraints $x \geq 0$ $0 \leq y \leq 8$ $x - y \leq 6$ $x + 2 y \leq 18$

Solve Nonlinear Systems By Addition - +=65 (x-1+=64

Solve Problems Using Systems of Nonlinear Equations -The sum of two numbers is 14 and their product is 45 . Find the numbers.

Graph the solution set of the system of inequalities or indicate that the system has no solution. -

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

Graph a Nonlinear Inequality in Two Variables - $y>3^{x}$ $Graph a Nonlinear Inequality in Two Variables - y>3^{x}$

Solve Systems of Linear Equations in Three Variables - y+4z=0 4x+y-2z=2 -3x-3z=-9

Write the partial fraction decomposition of the rational expression. - $\frac { 64 - 11 x } { x ^ { 3 } - 8 x ^ { 2 } + 16 x }$

Graph the inequality. - $- 2 x - 3 y \leq 6$ $Graph the inequality. - - 2 x - 3 y \leq 6$

Solve Problems Using Systems of Nonlinear Equations -The area of a garden is 432 square feet, and the length of its diagonal is 30 feet. Find the dimensions of the garden.

Solve Nonlinear Systems By Addition - +=25 -5x+=1

Graph the inequality. - $\frac { x } { 4 } + \frac { y } { 2 } \leq 1$ $Graph the inequality. - \frac { x } { 4 } + \frac { y } { 2 } \leq 1$

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

Write the partial fraction decomposition of the rational expression. - 8x+1x3−1\frac { 8 x + 1 } { x ^ { 3 } - 1 }x3−18x+1​

Solve Nonlinear Systems By Addition - +=4 4+16=64

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - y=15-4x 16x+4y=60

Write the partial fraction decomposition of the rational expression. - xx2−9x+20\frac { x } { x ^ { 2 } - 9 x + 20 }x2−9x+20x​

Use Linear Programming to Solve Problems -Objective Function z=6x−3yz = 6 x - 3 yz=6x−3y Constraints x≥0x \geq 0x≥0 0≤y≤80 \leq y \leq 80≤y≤8 x−y≤6x - y \leq 6x−y≤6 x+2y≤18x + 2 y \leq 18x+2y≤18

Solve Nonlinear Systems By Addition - +=65 (x-1+=64

Solve Problems Using Systems of Nonlinear Equations -The sum of two numbers is 14 and their product is 45 . Find the numbers.

Graph the solution set of the system of inequalities or indicate that the system has no solution. -

Write the partial fraction decomposition of the rational expression. - x2−111x4−x2−72\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }x4−x2−72x2−111​

Graph a Nonlinear Inequality in Two Variables - y>3xy>3^{x}y>3x

Solve Systems of Linear Equations in Three Variables - y+4z=0 4x+y-2z=2 -3x-3z=-9

Graph the solution set of the system of inequalities or indicate that the system has no solution. - +\leq100 -3x+4y\leq-12

Write the partial fraction decomposition of the rational expression. - 64−11xx3−8x2+16x\frac { 64 - 11 x } { x ^ { 3 } - 8 x ^ { 2 } + 16 x }x3−8x2+16x64−11x​

Graph the inequality. - −2x−3y≤6- 2 x - 3 y \leq 6−2x−3y≤6

Solve Problems Using Systems of Nonlinear Equations -The area of a garden is 432 square feet, and the length of its diagonal is 30 feet. Find the dimensions of the garden.

Solve Nonlinear Systems By Addition - +=25 -5x+=1

Graph the inequality. - x4+y2≤1\frac { x } { 4 } + \frac { y } { 2 } \leq 14x​+2y​≤1

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

Write the partial fraction decomposition of the rational expression. - $\frac { 8 x + 1 } { x ^ { 3 } - 1 }$

Write the partial fraction decomposition of the rational expression. - $\frac { x } { x ^ { 2 } - 9 x + 20 }$

Use Linear Programming to Solve Problems -Objective Function $z = 6 x - 3 y$ Constraints $x \geq 0$ $0 \leq y \leq 8$ $x - y \leq 6$ $x + 2 y \leq 18$

Write the partial fraction decomposition of the rational expression. - $\frac { x ^ { 2 } - 111 } { x ^ { 4 } - x ^ { 2 } - 72 }$

Graph a Nonlinear Inequality in Two Variables - $y>3^{x}$ $Graph a Nonlinear Inequality in Two Variables - y>3^{x}$

Write the partial fraction decomposition of the rational expression. - $\frac { 64 - 11 x } { x ^ { 3 } - 8 x ^ { 2 } + 16 x }$

Graph the inequality. - $- 2 x - 3 y \leq 6$ $Graph the inequality. - - 2 x - 3 y \leq 6$

Graph the inequality. - $\frac { x } { 4 } + \frac { y } { 2 } \leq 1$ $Graph the inequality. - \frac { x } { 4 } + \frac { y } { 2 } \leq 1$