Question 1

Graph the solution set.
-$$\begin{array} { l } 
x + 2 y \leq 0 \
x - y \geq - 6
\end{array}$$

Accepted Answer

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

Question 2

Solve the problem.
-The sum of the squares of two positive integers is 106 and the difference of the squares of the numbers is 56. Find the numbers.

Accepted Answer

A)  The numbers are 8 and 4. 
B)  The numbers are 11 and 7. 
C)  The numbers are 10 and 6. 
D)  The numbers are 9 and 5. 
A)  The numbers are 8 and 4. 
B)  The numbers are 11 and 7. 
C)  The numbers are 10 and 6. 
D)  The numbers are 9 and 5.

Question 3

Choose the one alternative that best completes the statement or answers the question.
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
-$\frac { 2 x ^ { 2 } - 7 x + 2 } { 4 x ^ { 3 } + 64 x }$

Accepted Answer

A)  $\frac { A } { 4 x } + \frac { B } { x ^ { 2 } + 16 }$ 
B)  $\frac { A } { 4 x } + \frac { B } { x + 4 } + \frac { C } { x - 4 }$ 
C)  $\frac { A } { 4 x } + \frac { B x + \mathrm { C } } { x + 4 } + \frac { D x + E } { x - 4 }$ 
D)  $\frac { A } { 4 x } + \frac { B x + \mathrm { C } } { x ^ { 2 } + 16 }$ 
A)  $\frac { A } { 4 x } + \frac { B } { x ^ { 2 } + 16 }$ 
B)  $\frac { A } { 4 x } + \frac { B } { x + 4 } + \frac { C } { x - 4 }$ 
C)  $\frac { A } { 4 x } + \frac { B x + \mathrm { C } } { x + 4 } + \frac { D x + E } { x - 4 }$ 
D)  $\frac { A } { 4 x } + \frac { B x + \mathrm { C } } { x ^ { 2 } + 16 }$

Question 4

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$$\begin{array} { l } 
2 x + 2 y + 5 z = - 19 \
2 x + 2 y + 3 z = - 13 \
6 x + 6 y + 11 z = - 44
\end{array}$$

Accepted Answer

A)  No solution; inconsistent 
B)  Infinitely many solutions; dependent 
C)  $\{ ( 1,2 , - 5 ) \}$ 
D)  $\{ ( 1,1 , - 4 ) \}$ 
A)  No solution; inconsistent 
B)  Infinitely many solutions; dependent 
C)  $\{ ( 1,2 , - 5 ) \}$ 
D)  $\{ ( 1,1 , - 4 ) \}$

Question 5

Find the partial fraction decomposition.
-$\frac { - 2 x ^ { 3 } - 5 x ^ { 2 } - 8 x - 15 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

Accepted Answer

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

Question 6

Choose the one alternative that best completes the statement or answers the question.
Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
-$$\frac { x ^ { 2 } + 2 x + 4 } { ( x + 2 ) \left( x ^ { 2 } - 5 x + 9 \right) }$$

Accepted Answer

A)  $\frac { A } { x + 2 } + \frac { B x + C } { x ^ { 2 } - 5 x + 9 }$ 
B)  $\frac { A x } { x + 2 } + \frac { B x } { x ^ { 2 } - 5 x + 9 }$ 
C)  $\frac { A x + B } { x + 2 } + \frac { C x + D } { x ^ { 2 } - 5 x + 9 }$ 
D)  $\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } - 5 x + 9 }$ 
A)  $\frac { A } { x + 2 } + \frac { B x + C } { x ^ { 2 } - 5 x + 9 }$ 
B)  $\frac { A x } { x + 2 } + \frac { B x } { x ^ { 2 } - 5 x + 9 }$ 
C)  $\frac { A x + B } { x + 2 } + \frac { C x + D } { x ^ { 2 } - 5 x + 9 }$ 
D)  $\frac { A } { x + 2 } + \frac { B } { x ^ { 2 } - 5 x + 9 }$

Question 7

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$$\begin{aligned}
- 6 x - 3 y + 7 z & = - 7 \
- x + 2 y - 7 z & = - 10 \
- 3 x + 2 y - 8 z & = - 16
\end{aligned}$$

Accepted Answer

A)  $\{ ( 9,3,8 ) \}$ 
B)  $\{ ( 2 , - 4 , - 1 ) \}$ 
C)  $\{ ( 2,3,2 ) \}$ 
D)  $\{ ( 2,10,4 ) \}$ 
A)  $\{ ( 9,3,8 ) \}$ 
B)  $\{ ( 2 , - 4 , - 1 ) \}$ 
C)  $\{ ( 2,3,2 ) \}$ 
D)  $\{ ( 2,10,4 ) \}$

Question 8

Solve the system by using any method.
-$$\begin{array} { l } 
\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 256 } = 1 \
x ^ { 2 } + y = 16
\end{array}$$

Accepted Answer

A)  $\{ ( - 4,0 ) , ( 0,16 ) , ( 4,0 ) \}$ 
B)  $\{ ( 0 , - 16 ) \}$ 
C)  $\{ ( - 4,0 ) , ( 0 , - 16 ) , ( 4,0 ) \}$ 
D)  $\{ ( 0,16 ) \}$ 
A)  $\{ ( - 4,0 ) , ( 0,16 ) , ( 4,0 ) \}$ 
B)  $\{ ( 0 , - 16 ) \}$ 
C)  $\{ ( - 4,0 ) , ( 0 , - 16 ) , ( 4,0 ) \}$ 
D)  $\{ ( 0,16 ) \}$

Question 9

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The graph of a linear equation in two variables is a line in a two-dimensional coordinate system.The graph of a linear equation in three variables is a________ in a three-dimensional coordinate system.

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$\begin{array} { r } 
\frac { 1 } { 5 } x + \frac { 1 } { 3 } y = \frac { 17 } { 15 } \
\frac { 8 } { 9 } x + \frac { 8 } { 9 } y = \frac { 8 } { 9 }
\end{array}$$

Accepted Answer

A)  $\{ ( - 6,7 ) \}$ 
B)  $\{ ( - 1,4 ) \}$ 
C)  $\{ ( - 11,10 ) \}$ 
D)  $\{ ( - 14,15 ) \}$ 
A)  $\{ ( - 6,7 ) \}$ 
B)  $\{ ( - 1,4 ) \}$ 
C)  $\{ ( - 11,10 ) \}$ 
D)  $\{ ( - 14,15 ) \}$

Question 11

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
y \leq - x ^ { 2 } + 3 \
y \leq - x + 2 \
y > - 4
\end{array}$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D)  The solution set is {  } . 
A) 
  
B) 
  
C) 
  
D)  The solution set is {  } .

Question 12

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
y  4 \
x < 2
\end{array}$$

Accepted Answer

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

Question 13

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$$\begin{aligned}
2 x + 3 y + 5 z & = - 23 \
- 4 x - 2 y + 4 z & = 9 \
- 6 x - y + 13 z & = - 5
\end{aligned}$$

Accepted Answer

A)  $\{ ( - 1 , - 2 , - 3 ) \}$ 
B)  $\{ ( - 1 , - 3 , - 2 ) \}$ 
C)  No solution; inconsistent 
D)  Infinitely many solutions; dependent 
A)  $\{ ( - 1 , - 2 , - 3 ) \}$ 
B)  $\{ ( - 1 , - 3 , - 2 ) \}$ 
C)  No solution; inconsistent 
D)  Infinitely many solutions; dependent

Question 14

Solve the system by using any method.
-$$\begin{array} { l } 
y = - x ^ { 2 } - 8 x - 14 \
y = x ^ { 2 } + 4 x + 2
\end{array}$$

Accepted Answer

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

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-When setting up a partial fraction decomposition, if a fraction has a linear denominator, then the
numerator should be (constant/linear). That is, should the numerator be set up as A or Ax + B?

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \leq 9$$

Accepted Answer

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

Question 17

Graph the solution set.
-$$\begin{array} { l } 
6 x - 5 y > 15 \
x + 3 y < - 9
\end{array}$$

Accepted Answer

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

Question 18

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$\begin{array} { l } 
9 x - 7 y = 47 \
y = - \frac { 3 } { 2 } x + 10
\end{array}$$

Accepted Answer

A) { } ; The system is inconsistent. 
B)  $\left\{ \left( \frac { 74 } { 39 } , \frac { 93 } { 13 } \right) \right\}$ 
C)  $\{ ( 6,1 ) \}$ 
D)  $\left\{ ( x , y ) \mid y = - \frac { 3 } { 2 } x + 10 \right\}$; The equations are dependent. 
A) { } ; The system is inconsistent. 
B)  $\left\{ \left( \frac { 74 } { 39 } , \frac { 93 } { 13 } \right) \right\}$ 
C)  $\{ ( 6,1 ) \}$ 
D)  $\left\{ ( x , y ) \mid y = - \frac { 3 } { 2 } x + 10 \right\}$; The equations are dependent.

Question 19

Solve the system. If there is more than one solution, write the general solution.
-$$\begin{array} { l } 
2 x + 2 y - 3 z = 3 \
- 5 x - 2 y + 5 z = 14 \
- 8 x - 2 y + 7 z = 31
\end{array}$$

Accepted Answer

A)  No solution; inconsistent 
B)  $\{ ( - 3 , - 3 , - 5 ) \}$ 
C)  $\left\{ \left[ x , \frac { 5 } { 4 } x + \frac { 57 } { 4 } , \frac { 3 } { 2 } x + \frac { 17 } { 2 } \mid x \right. \right.$ is any real number $\left. \} \right\}$ 
D)  $\{ ( - 3 , - 4 , - 4 ) \}$ 
A)  No solution; inconsistent 
B)  $\{ ( - 3 , - 3 , - 5 ) \}$ 
C)  $\left\{ \left[ x , \frac { 5 } { 4 } x + \frac { 57 } { 4 } , \frac { 3 } { 2 } x + \frac { 17 } { 2 } \mid x \right. \right.$ is any real number $\left. \} \right\}$ 
D)  $\{ ( - 3 , - 4 , - 4 ) \}$

Question 20

Solve the problem.
-A rectangular plot of land has a 40-yd diagonal and an area of $768 \mathrm { yd } ^ { 2 }$ . Find the dimensions of the plot of land.

Accepted Answer

A)  The plot of land is 4 yd by 192 yd. 
B)  The plot of land is 8 yd by 32 yd. 
C)  The plot of land is 8 yd by 96 yd. 
D)  The plot of land is 24 yd by 32 yd. 
A)  The plot of land is 4 yd by 192 yd. 
B)  The plot of land is 8 yd by 32 yd. 
C)  The plot of land is 8 yd by 96 yd. 
D)  The plot of land is 24 yd by 32 yd.

Graph the solution set. - x+2y\leq0 x-y\geq-6

Solve the problem. -The sum of the squares of two positive integers is 106 and the difference of the squares of the numbers is 56. Find the numbers.

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { 2 x ^ { 2 } - 7 x + 2 } { 4 x ^ { 3 } + 64 x }$

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+2y+5z=-19 2x+2y+3z=-13 6x+6y+11z=-44

Find the partial fraction decomposition. - $\frac { - 2 x ^ { 3 } - 5 x ^ { 2 } - 8 x - 15 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { x ^ { 2 } + 2 x + 4 } { ( x + 2 ) \left( x ^ { 2 } - 5 x + 9 \right) }$

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - -6x-3y+7z =-7 -x+2y-7z =-10 -3x+2y-8z =-16

Solve the system by using any method. - +=1 +y=16

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - x+y= x+y=

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y\leq-+3 y\leq-x+2 y>-4

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y< y>4 x<2

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+3y+5z =-23 -4x-2y+4z =9 -6x-y+13z =-5

Solve the system by using any method. - y=--8x-14 y=+4x+2

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \leq 9$

Graph the solution set. - 6x-5y>15 x+3y<-9

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 9x-7y=47 y=-x+10

Solve the system. If there is more than one solution, write the general solution. - 2x+2y-3z=3 -5x-2y+5z=14 -8x-2y+7z=31

Solve the problem. -A rectangular plot of land has a 40-yd diagonal and an area of $768 \mathrm { yd } ^ { 2 }$ . Find the dimensions of the plot of land.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 5: Systems of Equations and Inequalities

Graph the solution set. - x+2y\leq0 x-y\geq-6

Solve the problem. -The sum of the squares of two positive integers is 106 and the difference of the squares of the numbers is 56. Find the numbers.

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - 2x2−7x+24x3+64x\frac { 2 x ^ { 2 } - 7 x + 2 } { 4 x ^ { 3 } + 64 x }4x3+64x2x2−7x+2​

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+2y+5z=-19 2x+2y+3z=-13 6x+6y+11z=-44

Find the partial fraction decomposition. - −2x3−5x2−8x−15x4+6x2+9\frac { - 2 x ^ { 3 } - 5 x ^ { 2 } - 8 x - 15 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }x4+6x2+9−2x3−5x2−8x−15​

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - -6x-3y+7z =-7 -x+2y-7z =-10 -3x+2y-8z =-16

Solve the system by using any method. - +=1 +y=16

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - x+y= x+y=

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y\leq-+3 y\leq-x+2 y>-4

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y< y>4 x<2

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent. - 2x+3y+5z =-23 -4x-2y+4z =9 -6x-y+13z =-5

Solve the system by using any method. - y=--8x-14 y=+4x+2

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - (x+1)2+(y−2)2≤9( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \leq 9(x+1)2+(y−2)2≤9

Graph the solution set. - 6x-5y>15 x+3y<-9

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - 9x-7y=47 y=-x+10

Solve the system. If there is more than one solution, write the general solution. - 2x+2y-3z=3 -5x-2y+5z=14 -8x-2y+7z=31

Solve the problem. -A rectangular plot of land has a 40-yd diagonal and an area of 768yd2768 \mathrm { yd } ^ { 2 }768yd2 . Find the dimensions of the plot of land.

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on. - $\frac { 2 x ^ { 2 } - 7 x + 2 } { 4 x ^ { 3 } + 64 x }$

Find the partial fraction decomposition. - $\frac { - 2 x ^ { 3 } - 5 x ^ { 2 } - 8 x - 15 } { x ^ { 4 } + 6 x ^ { 2 } + 9 }$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $( x + 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } \leq 9$

Solve the problem. -A rectangular plot of land has a 40-yd diagonal and an area of $768 \mathrm { yd } ^ { 2 }$ . Find the dimensions of the plot of land.