Question 1

Write the partial fraction decomposition of the rational expression.
-$$\frac { 100 - 15 x } { x ^ { 3 } - 10 x ^ { 2 } + 25 x }$$

Accepted Answer

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

Question 2

Write the partial fraction decomposition of the rational expression.
-$$\frac { 13 x + 8 } { x ^ { 2 } - 2 x - 8 }$$

Accepted Answer

A)  $\frac { 10 } { x - 4 } + \frac { - 3 } { x + 2 }$ 
B)  $\frac { 11 } { x - 4 } + \frac { 2 } { x + 2 }$ 
C)  $\frac { 10 } { x - 4 } + \frac { 3 } { x + 2 }$ 
D)  $\frac { 10 } { x + 4 } + \frac { 3 } { x - 2 }$ 
A)  $\frac { 10 } { x - 4 } + \frac { - 3 } { x + 2 }$ 
B)  $\frac { 11 } { x - 4 } + \frac { 2 } { x + 2 }$ 
C)  $\frac { 10 } { x - 4 } + \frac { 3 } { x + 2 }$ 
D)  $\frac { 10 } { x + 4 } + \frac { 3 } { x - 2 }$

Question 3

Solve the system of equations by substitution.
-(4, 2) 2x + y = 6 3x + 2y = 8

Accepted Answer

A) not a solution 
B) solution 
A) not a solution 
B) solution

Question 4

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-$$\begin{array} { l } 
\frac { 1 } { 2 } x + \frac { 1 } { 3 } y = 4 \
\frac { 1 } { 4 } x + \frac { 1 } { 6 } y = 2
\end{array}$$

Accepted Answer

A)  $( 0,12 )$ 
B)  $\left( - 1 , \frac { 15 } { 2 } \right)$ 
C)  $\left( x , - \frac { 3 } { 2 } x + 12 \right)$ or $\left( - \frac { 2 } { 3 } y + 8 , y \right)$ 
D)  no solution 
A)  $( 0,12 )$ 
B)  $\left( - 1 , \frac { 15 } { 2 } \right)$ 
C)  $\left( x , - \frac { 3 } { 2 } x + 12 \right)$ or $\left( - \frac { 2 } { 3 } y + 8 , y \right)$ 
D)  no solution

Question 5

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
3 y - x = 10 \
x ^ { 2 } + y ^ { 2 } - 100 = 0
\end{array}$$

Accepted Answer

A)  $\left( 0 , \frac { 10 } { 3 } \right) , \left( 6 , \frac { 16 } { 3 } \right)$ 
B)  $( 10,0 ) , ( - 10,0 ) , ( 8,6 )$ 
C)  $( - 10,0 ) , ( 8,6 )$ 
D)  $\left( 0 , \frac { 10 } { 3 } \right) , \left( 0 , - \frac { 10 } { 3 } \right) , \left( 6 , \frac { 16 } { 3 } \right)$ 
A)  $\left( 0 , \frac { 10 } { 3 } \right) , \left( 6 , \frac { 16 } { 3 } \right)$ 
B)  $( 10,0 ) , ( - 10,0 ) , ( 8,6 )$ 
C)  $( - 10,0 ) , ( 8,6 )$ 
D)  $\left( 0 , \frac { 10 } { 3 } \right) , \left( 0 , - \frac { 10 } { 3 } \right) , \left( 6 , \frac { 16 } { 3 } \right)$

Question 6

Determine the real solutions to the system of nonlinear equations.
-$$6 x ^ { 2 } + 8 y ^ { 2 } = 128$$
$$y = x + 4$$

Accepted Answer

A)  $( 0,4 ) , \left( \frac { 32 } { 7 } , \frac { 60 } { 7 } \right)$ 
B)  $( 0,4 ) , \left( - \frac { 32 } { 7 } , - \frac { 4 } { 7 } \right)$ 
C)  $( 0 , - 4 ) , \left( - \frac { 32 } { 7 } , - \frac { 4 } { 7 } \right)$ 
D)  $( 0 , - 4 ) , \left( \frac { 32 } { 7 } , \frac { 60 } { 7 } \right)$ 
A)  $( 0,4 ) , \left( \frac { 32 } { 7 } , \frac { 60 } { 7 } \right)$ 
B)  $( 0,4 ) , \left( - \frac { 32 } { 7 } , - \frac { 4 } { 7 } \right)$ 
C)  $( 0 , - 4 ) , \left( - \frac { 32 } { 7 } , - \frac { 4 } { 7 } \right)$ 
D)  $( 0 , - 4 ) , \left( \frac { 32 } { 7 } , \frac { 60 } { 7 } \right)$

Question 7

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers.
-The sum of two squares of two numbers is 29, and the difference of their squares is 21. Find the numbers.

Accepted Answer

A) 5 and 2; -5 and 2; 5 and -2 
B) 5 and 2 
C) 5 and 2; -5 and 2; 5 and -2; -5 and -2 
D) 5 and 2; -5 and -2 
A) 5 and 2; -5 and 2; 5 and -2 
B) 5 and 2 
C) 5 and 2; -5 and 2; 5 and -2; -5 and -2 
D) 5 and 2; -5 and -2

Question 8

Solve the system of equations by substitution.
-$$\begin{array} { r } 
2 x + 9 y = - 8 \
x + \frac { 1 } { 3 } y = \frac { 13 } { 3 }
\end{array}$$

Accepted Answer

A) (-5, 2) 
B) ( -5, -2) 
C) (5, 2) 
D) (5, -2) 
A) (-5, 2) 
B) ( -5, -2) 
C) (5, 2) 
D) (5, -2)

Question 9

Determine the real solutions to the system of nonlinear equations.
-$x y = 20$ $x + y = 9$

Accepted Answer

A)  $( 5,4 ) , ( 4,5 )$ 
B)  $( 6,3 ) , ( 3,6 )$ 
C)  $( 20,1 ) , ( 1,20 )$ 
D)  $( 10,2 ) , ( 2,10 )$ 
A)  $( 5,4 ) , ( 4,5 )$ 
B)  $( 6,3 ) , ( 3,6 )$ 
C)  $( 20,1 ) , ( 1,20 )$ 
D)  $( 10,2 ) , ( 2,10 )$

Question 10

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form.
-$$\begin{array} { r } 
x - y + 5 z = - 21 \
5 x + z = - 4 \
x + 2 y + z = - 2
\end{array}$$

Accepted Answer

A)  $( - 4,0,1 )$ 
B)  no solution 
C)  $( - 4,1,0 )$ 
D)  $( 0,1 , - 4 )$ 
A)  $( - 4,0,1 )$ 
B)  no solution 
C)  $( - 4,1,0 )$ 
D)  $( 0,1 , - 4 )$

Question 11

Solve the system of equations by elimination.
-3x - 5y = -12 6x + 8y = -24

Accepted Answer

A) (0, -4) 
B) (0, 4) 
C) (-4, 0) 
D) (4, 0) 
A) (0, -4) 
B) (0, 4) 
C) (-4, 0) 
D) (4, 0)

Question 12

Determine the real solutions to the system of nonlinear equations.
-$$\begin{array} { l } 
4 x ^ { 2 } - 4 y ^ { 2 } = 48 \
4 x ^ { 2 } + 2 y ^ { 2 } = 72
\end{array}$$

Accepted Answer

A)  $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$ 
B)  $( 4 , - 2 ) , ( 4,2 )$ 
C)  $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$ 
D)  $( - 4 , - 2 ) , ( - 2 , - 4 )$ 
A)  $( 4,2 ) , ( 2,4 ) , ( - 4 , - 2 ) , ( - 2 , - 4 )$ 
B)  $( 4 , - 2 ) , ( 4,2 )$ 
C)  $( 4,2 ) , ( - 4,2 ) , ( 4 , - 2 ) , ( - 4 , - 2 )$ 
D)  $( - 4 , - 2 ) , ( - 2 , - 4 )$

Question 13

Graph the system of inequalities.
-$\begin{array}{l}
y>x^{2} \
6 x+4 y \leq 24
\end{array}$

Accepted Answer

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

Question 14

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y.
-3x + y = 6 -6x - 2y = -12

Accepted Answer

A)  $( x , - 3 x + 6 )$ or $\left( - \frac { 1 } { 3 } y + 2 , y \right)$ 
B)  $( x , 3 x + 6 )$ or $\left( \frac { 1 } { 3 } y - 2 , y \right)$ 
C)  no solution 
D)  $\left( - \frac { 1 } { 3 } x + 2 , x \right)$ or $( y , - 3 y + 6 )$ 
A)  $( x , - 3 x + 6 )$ or $\left( - \frac { 1 } { 3 } y + 2 , y \right)$ 
B)  $( x , 3 x + 6 )$ or $\left( \frac { 1 } { 3 } y - 2 , y \right)$ 
C)  no solution 
D)  $\left( - \frac { 1 } { 3 } x + 2 , x \right)$ or $( y , - 3 y + 6 )$

Question 15

Write the partial fraction decomposition of the rational expression.
-$$\frac { 4 x ^ { 3 } + 18 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$$

Accepted Answer

A)  $\frac { 4 x + 1 } { x ^ { 2 } + 3 } + \frac { 6 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
B)  $\frac { 4 x } { x ^ { 2 } + 3 } + \frac { 6 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
C)  $\frac { 4 x } { x ^ { 2 } + 3 } + \frac { - 6 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
D)  $\frac { 4 x } { x ^ { 2 } + 3 } + \frac { 6 x + 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
A)  $\frac { 4 x + 1 } { x ^ { 2 } + 3 } + \frac { 6 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
B)  $\frac { 4 x } { x ^ { 2 } + 3 } + \frac { 6 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
C)  $\frac { 4 x } { x ^ { 2 } + 3 } + \frac { - 6 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$ 
D)  $\frac { 4 x } { x ^ { 2 } + 3 } + \frac { 6 x + 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Question 16

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered
triple involving variable z.
-$$\begin{array} { r } 
x + 3 y + 2 z = 11 \
4 y + 9 z = - 12 \
x + 7 y + 11 z = - 1
\end{array}$$

Accepted Answer

A)  $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } + 3 , \mathrm { z } \right)$ 
B)  $\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)$ 
C)  $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right)$ 
D)  $\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$ 
A)  $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } + 3 , \mathrm { z } \right)$ 
B)  $\left( \frac { 19 z } { 4 } + 20 , \frac { 9 z } { 4 } + 3 , z \right)$ 
C)  $\left( \frac { 19 \mathrm { z } } { 4 } + 20 , - \frac { 9 \mathrm { z } } { 4 } - 3 , \mathrm { z } \right)$ 
D)  $\left( - \frac { 19 z } { 4 } + 20 , - \frac { 9 z } { 4 } + 3 , z \right)$

Question 17

Graph the inequality.
-

Accepted Answer

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

Question 18

Solve the problem.
-The diagonal of the floor of a rectangular office cubicle is 2 feet longer than the length of the cubicle and 5 feet longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Accepted Answer

A) width: 9.7 feet, length: 22.4 feet 
B) width: 4 feet, length: 11 feet 
C) width: 3.9 feet, length: 9.7 feet 
D) width: 2 feet, length: 9 feet 
A) width: 9.7 feet, length: 22.4 feet 
B) width: 4 feet, length: 11 feet 
C) width: 3.9 feet, length: 9.7 feet 
D) width: 2 feet, length: 9 feet

Question 19

Graph the system of inequalities.
-$\begin{array}{l}
2 x+3 y \geq 6 \
x-y \leq 3 \
y \leq 2
\end{array}$

Accepted Answer

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

Question 20

Graph the system of inequalities.
-$\begin{array}{l}
x+y^{2} \leq 16 \
y-x^{2}>0
\end{array}$

Accepted Answer

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

Write the partial fraction decomposition of the rational expression. - $\frac { 100 - 15 x } { x ^ { 3 } - 10 x ^ { 2 } + 25 x }$

Write the partial fraction decomposition of the rational expression. - $\frac { 13 x + 8 } { x ^ { 2 } - 2 x - 8 }$

Solve the system of equations by substitution. -(4, 2) 2x + y = 6 3x + 2y = 8

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. - x+y=4 x+y=2

Determine the real solutions to the system of nonlinear equations. - 3y-x=10 +-100=0

Determine the real solutions to the system of nonlinear equations. - $6 x ^ { 2 } + 8 y ^ { 2 } = 128$ $y = x + 4$

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. -The sum of two squares of two numbers is 29, and the difference of their squares is 21. Find the numbers.

Solve the system of equations by substitution. - 2x+9y=-8 x+y=

Determine the real solutions to the system of nonlinear equations. - $x y = 20$ $x + y = 9$

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - x-y+5z=-21 5x+z=-4 x+2y+z=-2

Solve the system of equations by elimination. -3x - 5y = -12 6x + 8y = -24

Determine the real solutions to the system of nonlinear equations. - 4-4=48 4+2=72

Graph the system of inequalities. - y> 6x+4y\leq24 $Graph the system of inequalities. - \begin{array}{l} y>x^{2} \\ 6 x+4 y \leq 24 \end{array}$

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -3x + y = 6 -6x - 2y = -12

Write the partial fraction decomposition of the rational expression. - $\frac { 4 x ^ { 3 } + 18 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+3y+2z=11 4y+9z=-12 x+7y+11z=-1

Graph the inequality. -

Solve the problem. -The diagonal of the floor of a rectangular office cubicle is 2 feet longer than the length of the cubicle and 5 feet longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 y\leq2 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}$

Graph the system of inequalities. - x+\leq16 y->0 $Graph the system of inequalities. - \begin{array}{l} x+y^{2} \leq 16 \\ y-x^{2}>0 \end{array}$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

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Math Exercises: Sets, Intervals, Absolute Value, and Properties

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Exam 7: Systems of Equations and Inequalities

Write the partial fraction decomposition of the rational expression. - 100−15xx3−10x2+25x\frac { 100 - 15 x } { x ^ { 3 } - 10 x ^ { 2 } + 25 x }x3−10x2+25x100−15x​

Write the partial fraction decomposition of the rational expression. - 13x+8x2−2x−8\frac { 13 x + 8 } { x ^ { 2 } - 2 x - 8 }x2−2x−813x+8​

Solve the system of equations by substitution. -(4, 2) 2x + y = 6 3x + 2y = 8

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. - x+y=4 x+y=2

Determine the real solutions to the system of nonlinear equations. - 3y-x=10 +-100=0

Determine the real solutions to the system of nonlinear equations. - 6x2+8y2=1286 x ^ { 2 } + 8 y ^ { 2 } = 1286x2+8y2=128 y=x+4y = x + 4y=x+4

Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and find the numbers. -The sum of two squares of two numbers is 29, and the difference of their squares is 21. Find the numbers.

Solve the system of equations by substitution. - 2x+9y=-8 x+y=

Determine the real solutions to the system of nonlinear equations. - xy=20x y = 20xy=20 x+y=9x + y = 9x+y=9

Use Gaussian elimination to solve the linear system by finding an equivalent system in triangular form. - x-y+5z=-21 5x+z=-4 x+2y+z=-2

Solve the system of equations by elimination. -3x - 5y = -12 6x + 8y = -24

Determine the real solutions to the system of nonlinear equations. - 4-4=48 4+2=72

Graph the system of inequalities. - y> 6x+4y\leq24

Use the substitution method or the elimination method to solve the system. If the system has infinitely many solutions, express the ordered pair in terms of x or y. -3x + y = 6 -6x - 2y = -12

Write the partial fraction decomposition of the rational expression. - 4x3+18x−2(x2+3)2\frac { 4 x ^ { 3 } + 18 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }(x2+3)24x3+18x−2​

Use Gauss-Jordan elimination to solve the linear system and determine whether the system has a unique solution, no solution, or infinitely many solutions. If the system has infinitely many solutions, describe the solution as an ordered triple involving variable z. - x+3y+2z=11 4y+9z=-12 x+7y+11z=-1

Graph the inequality. -

Solve the problem. -The diagonal of the floor of a rectangular office cubicle is 2 feet longer than the length of the cubicle and 5 feet longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 y\leq2

Graph the system of inequalities. - x+\leq16 y->0

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Write the partial fraction decomposition of the rational expression. - $\frac { 100 - 15 x } { x ^ { 3 } - 10 x ^ { 2 } + 25 x }$

Write the partial fraction decomposition of the rational expression. - $\frac { 13 x + 8 } { x ^ { 2 } - 2 x - 8 }$

Determine the real solutions to the system of nonlinear equations. - $6 x ^ { 2 } + 8 y ^ { 2 } = 128$ $y = x + 4$

Determine the real solutions to the system of nonlinear equations. - $x y = 20$ $x + y = 9$

Graph the system of inequalities. - y> 6x+4y\leq24 $Graph the system of inequalities. - \begin{array}{l} y>x^{2} \\ 6 x+4 y \leq 24 \end{array}$

Write the partial fraction decomposition of the rational expression. - $\frac { 4 x ^ { 3 } + 18 x - 2 } { \left( x ^ { 2 } + 3 \right) ^ { 2 } }$

Graph the system of inequalities. - 2x+3y\geq6 x-y\leq3 y\leq2 $Graph the system of inequalities. - \begin{array}{l} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ y \leq 2 \end{array}$

Graph the system of inequalities. - x+\leq16 y->0 $Graph the system of inequalities. - \begin{array}{l} x+y^{2} \leq 16 \\ y-x^{2}>0 \end{array}$