Question 1

Graph the linear inequality.
-$x-y>-2$

Accepted Answer

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

Question 2

Solve the system by elimination.
-2x + y = 9 x - 2y = 2

Accepted Answer

A)  (6, 2) 
B)  (5, -1) 
C)  (3, 1) 
D)  (4, 1) 
A)  (6, 2) 
B)  (5, -1) 
C)  (3, 1) 
D)  (4, 1)

Question 3

Determine whether the matrices are inverses.
-$$\left[ \begin{array} { r r } 
10 & 1 \
- 1 & 0
\end{array} \right] , \left[ \begin{array} { r r } 
0 & 1 \
- 1 & 10
\end{array} \right]$$

B) $Y e s$

Accepted Answer

A) True 
 B)False

Question 4

Use Gaussian elimination to solve the system of equations.
-$$\begin{array} { l } 
9 x - 5 y = 54 \
3 x - 3 y = 18
\end{array}$$

Accepted Answer

A)  $( 6,0 )$ 
B)  No solution 
C)  $( 5,1 )$ 
D)  $( 6,1 )$ 
A)  $( 6,0 )$ 
B)  No solution 
C)  $( 5,1 )$ 
D)  $( 6,1 )$

Question 5

Write the augmented matrix for the system.
-

Accepted Answer

A)  $\text {  }\left[\begin{array}{lll}
3 & 0 & 9 \
7 & 8 & 8
\end{array}\right]$ 
B)  
$\left[ \begin{array} { r r r } 59 & 8 & 7 \ 9 & 0 & 3 \end{array} \right]$ 
C) 
 $\left[ \begin{array} { r r r } 7 & 8 & 59 \ 0 & 3 & 9 \end{array} \right]$ 
D)  
$\left[ \begin{array} { r r r } 7 & 8 & 59 \ 3 & 9 & 0 \end{array} \right]$ 
A)  $\text {  }\left[\begin{array}{lll}
3 & 0 & 9 \
7 & 8 & 8
\end{array}\right]$ 
B)  
$\left[ \begin{array} { r r r } 59 & 8 & 7 \ 9 & 0 & 3 \end{array} \right]$ 
C) 
 $\left[ \begin{array} { r r r } 7 & 8 & 59 \ 0 & 3 & 9 \end{array} \right]$ 
D)  
$\left[ \begin{array} { r r r } 7 & 8 & 59 \ 3 & 9 & 0 \end{array} \right]$

Question 6

Solve the problem.
-A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1170 tickets. Also, they have sold 80 more adult tickets than children's tickets. How
Many children's tickets have they sold?

Accepted Answer

A)  549 
B)  545 
C)  547 
D)  541 
A)  549 
B)  545 
C)  547 
D)  541

Question 7

Perform the indicated operation, if possible.
-$\left[ \begin{array} { r } 3 \ - 2 \ - 4 \end{array} \right] + \left[ \begin{array} { r } - 5 \ 5 \ 8 \end{array} \right]$

Accepted Answer

A) 
$\left[ \begin{array} { r r } 3 & - 5 \ - 2 & 5 \ - 4 & 8 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l l } - 2 & 3 & 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 2 \ 4 \ 5 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r } - 2 \ 3 \ 4 \end{array} \right]$ 
A) 
$\left[ \begin{array} { r r } 3 & - 5 \ - 2 & 5 \ - 4 & 8 \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l l } - 2 & 3 & 4 \end{array} \right]$ 
C) 
$\left[ \begin{array} { l } 2 \ 4 \ 5 \end{array} \right]$ 
D) 
$\left[ \begin{array} { r } - 2 \ 3 \ 4 \end{array} \right]$

Question 8

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 9

Decide whether the ordered pair is a solution of the given system.
-(1, -6) x + y = -5
X - y = 7

Accepted Answer

A) True 
 B)False

Question 10

Graph the system of inequalities. Shade the region that represents the solution set.
-$\begin{aligned}
y & \geq x^{2} \
x+y & \leq 2
\end{aligned}$

Accepted Answer

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

Question 11

Solve the system by elimination.
-6x - 4y = 40 -3x - 2y = -4

Accepted Answer

A)  No solution 
B)  (4, -3) 
C)  (3, -3) 
D)  (4, -4) 
A)  No solution 
B)  (4, -3) 
C)  (3, -3) 
D)  (4, -4)

Question 12

Decide whether the ordered pair is a solution of the given system.
-(4, 5) 4x + y = 11
2x + 4y = -12

Accepted Answer

A) True 
 B)False

Question 13

Write the system of equations associated with the augmented matrix. Do not solve.
-$\left[ \begin{array} { l l l l } 1 & 0 & 0 & - 1 \ 0 & 1 & 0 & - 1 \ 0 & 0 & 1 & - 9 \end{array} \right]$

Accepted Answer

A)  $x = 1$
$y = 1$
$z = 9$ 
B)  $x = - 1$
$y = - 1$
$z = - 9$ 
C)  $x = 8$
$y = 8$
$z = 0$ 
D)  $x = 0$
$y = - 2$
$z = - 10$ 
A)  $x = 1$
$y = 1$
$z = 9$ 
B)  $x = - 1$
$y = - 1$
$z = - 9$ 
C)  $x = 8$
$y = 8$
$z = 0$ 
D)  $x = 0$
$y = - 2$
$z = - 10$

Question 14

Determine the order of the matrix.
-$$\left[ \begin{array} { l l l l } 
3 & - 6 & 5 & 7
\end{array} \right]$$

Accepted Answer

A)  1 
B)  $4 \times 1$ 
C)  4 
D)  $1 \times 4$ 
A)  1 
B)  $4 \times 1$ 
C)  4 
D)  $1 \times 4$

Question 15

Solve the system of equations by finding the reduced row echelon form for the augmented matrix.
-$x + y - 2 z = 8$ $3 x + z = - 6$

Accepted Answer

A)  $\left( \frac { 1 } { 3 } z - 2 , - \frac { 7 } { 3 } z + 10 , z \right)$ 
B)  $\left( - 2 z + \frac { 1 } { 3 } , 10 z - \frac { 7 } { 3 } , z \right)$ 
C)  $\left( - \frac { 1 } { 3 } z - 2 , \frac { 7 } { 3 } z + 10 , z \right)$ 
D)  $\left( \frac { 1 } { 3 } z + 2 , - \frac { 7 } { 3 } z - 10 , z \right)$ 
A)  $\left( \frac { 1 } { 3 } z - 2 , - \frac { 7 } { 3 } z + 10 , z \right)$ 
B)  $\left( - 2 z + \frac { 1 } { 3 } , 10 z - \frac { 7 } { 3 } , z \right)$ 
C)  $\left( - \frac { 1 } { 3 } z - 2 , \frac { 7 } { 3 } z + 10 , z \right)$ 
D)  $\left( \frac { 1 } { 3 } z + 2 , - \frac { 7 } { 3 } z - 10 , z \right)$

Question 16

Solve the problem.
-A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost. The average monthly salary of a counselor is $\$ 2400$ and the average monthly salary of an aide is $\$ 1100$. The camp can accommodate up to 35 staff members and needs at least 20 to run properly. They must have at least 10 aides, and may have up to 3 aides for every 2 counselors. How many counselors and how many aides should the camp hire to minimize cost?

Accepted Answer

A)  13 counselors and 16 aides 
B)  8 counselors and 12 aides 
C)  19 counselors and 23 aides 
D)  13 counselors and 17 aides 
A)  13 counselors and 16 aides 
B)  8 counselors and 12 aides 
C)  19 counselors and 23 aides 
D)  13 counselors and 17 aides

Question 17

When using the substitution or elimination method to solve a system of two equations, you end up with an
equation stating 0 = 0. What does this indicate to you about the system of equations?

Accepted Answer

Answers may vary. One possibility: The s

Question 18

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix.
-

Accepted Answer

The answer of Determine which elementary row operation(s) applied to...

Question 19

Find the partial fraction decomposition.
-$\frac { 6 } { 4 x ^ { 2 } - 36 }$

Accepted Answer

A)  $\frac { 1 / 2 } { 2 x - 6 } + \frac { - 1 / 2 } { ( 2 x - 6 ) ^ { 2 } }$ 
B)  $\frac { 1 } { 2 x - 6 } + \frac { - 1 } { 2 x + 6 }$ 
C)  $\frac { 1 / 2 } { 2 x + 6 } + \frac { - 1 / 2 } { 2 x - 6 }$ 
D)  $\frac { 1 / 2 } { 2 x - 6 } + \frac { - 1 / 2 } { 2 x + 6 }$ 
A)  $\frac { 1 / 2 } { 2 x - 6 } + \frac { - 1 / 2 } { ( 2 x - 6 ) ^ { 2 } }$ 
B)  $\frac { 1 } { 2 x - 6 } + \frac { - 1 } { 2 x + 6 }$ 
C)  $\frac { 1 / 2 } { 2 x + 6 } + \frac { - 1 / 2 } { 2 x - 6 }$ 
D)  $\frac { 1 / 2 } { 2 x - 6 } + \frac { - 1 / 2 } { 2 x + 6 }$

Question 20

Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix.
$$\left[ \begin{array} { r r r r } 
1 & 17 & 11 & 13 \
0 & 0 & 0 & 0 \
0 & - 18 & 5 & 3
\end{array} \right]$$
What conclusion can you draw about the solutions of the system?

Accepted Answer

A)  There is not enough information to draw any conclusion about the solutions of the system. 
B)  The system has infinitely many solutions. 
C)  The system has exactly one solution. 
D)  The system has no solutions. 
A)  There is not enough information to draw any conclusion about the solutions of the system. 
B)  The system has infinitely many solutions. 
C)  The system has exactly one solution. 
D)  The system has no solutions.

Graph the linear inequality. - $x-y>-2$

Solve the system by elimination. -2x + y = 9 x - 2y = 2

Determine whether the matrices are inverses. - $\left[ \begin{array} { r r } 10 & 1 \\- 1 & 0\end{array} \right] , \left[ \begin{array} { r r } 0 & 1 \\- 1 & 10\end{array} \right]$ B) $Y e s$

Use Gaussian elimination to solve the system of equations. - 9x-5y=54 3x-3y=18

Write the augmented matrix for the system. -

Solve the problem. -A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1170 tickets. Also, they have sold 80 more adult tickets than children's tickets. How Many children's tickets have they sold?

Perform the indicated operation, if possible. - $\left[ \begin{array} { r } 3 \\ - 2 \\ - 4 \end{array} \right] + \left[ \begin{array} { r } - 5 \\ 5 \\ 8 \end{array} \right]$

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Decide whether the ordered pair is a solution of the given system. -(1, -6) x + y = -5 X - y = 7

Graph the system of inequalities. Shade the region that represents the solution set. - y \geq x+y \leq2 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{aligned} y & \geq x^{2} \\ x+y & \leq 2 \end{aligned}$

Solve the system by elimination. -6x - 4y = 40 -3x - 2y = -4

Decide whether the ordered pair is a solution of the given system. -(4, 5) 4x + y = 11 2x + 4y = -12

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { l l l l } 1 & 0 & 0 & - 1 \\ 0 & 1 & 0 & - 1 \\ 0 & 0 & 1 & - 9 \end{array} \right]$

Determine the order of the matrix. - $\left[ \begin{array} { l l l l } 3 & - 6 & 5 & 7\end{array} \right]$

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - $x + y - 2 z = 8$ $3 x + z = - 6$

When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Find the partial fraction decomposition. - $\frac { 6 } { 4 x ^ { 2 } - 36 }$

Suppose that you are solving a system of three linear equations by the row echelon method and obtain the follon augmented matrix. $\left[ \begin{array} { r r r r } 1 & 17 & 11 & 13 \\0 & 0 & 0 & 0 \\0 & - 18 & 5 & 3\end{array} \right]$ What conclusion can you draw about the solutions of the system?

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 7: Systems and Matrices

Graph the linear inequality. - x−y>−2x-y>-2x−y>−2

Solve the system by elimination. -2x + y = 9 x - 2y = 2

Determine whether the matrices are inverses. - [101−10],[01−110]\left[ \begin{array} { r r } 10 & 1 \\- 1 & 0\end{array} \right] , \left[ \begin{array} { r r } 0 & 1 \\- 1 & 10\end{array} \right][10−1​10​],[0−1​110​] B) YesY e sYes

Use Gaussian elimination to solve the system of equations. - 9x-5y=54 3x-3y=18

Write the augmented matrix for the system. -

Solve the problem. -A theatre sells two types of tickets to their plays; children's tickets and adult tickets. For today's performance they have sold a total of 1170 tickets. Also, they have sold 80 more adult tickets than children's tickets. How Many children's tickets have they sold?

Perform the indicated operation, if possible. - [3−2−4]+[−558]\left[ \begin{array} { r } 3 \\ - 2 \\ - 4 \end{array} \right] + \left[ \begin{array} { r } - 5 \\ 5 \\ 8 \end{array} \right]​3−2−4​​+​−558​​

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Decide whether the ordered pair is a solution of the given system. -(1, -6) x + y = -5 X - y = 7

Graph the system of inequalities. Shade the region that represents the solution set. - y \geq x+y \leq2

Solve the system by elimination. -6x - 4y = 40 -3x - 2y = -4

Decide whether the ordered pair is a solution of the given system. -(4, 5) 4x + y = 11 2x + 4y = -12

Write the system of equations associated with the augmented matrix. Do not solve. - [100−1010−1001−9]\left[ \begin{array} { l l l l } 1 & 0 & 0 & - 1 \\ 0 & 1 & 0 & - 1 \\ 0 & 0 & 1 & - 9 \end{array} \right]​100​010​001​−1−1−9​​

Determine the order of the matrix. - [3−657]\left[ \begin{array} { l l l l } 3 & - 6 & 5 & 7\end{array} \right][3​−6​5​7​]

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - x+y−2z=8x + y - 2 z = 8x+y−2z=8 3x+z=−63 x + z = - 63x+z=−6

When using the substitution or elimination method to solve a system of two equations, you end up with an equation stating 0 = 0. What does this indicate to you about the system of equations?

Determine which elementary row operation(s) applied to the first matrix will yield the second matrix. -

Find the partial fraction decomposition. - 64x2−36\frac { 6 } { 4 x ^ { 2 } - 36 }4x2−366​

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Graph the linear inequality. - $x-y>-2$

Determine whether the matrices are inverses. - $\left[ \begin{array} { r r } 10 & 1 \\- 1 & 0\end{array} \right] , \left[ \begin{array} { r r } 0 & 1 \\- 1 & 10\end{array} \right]$ B) $Y e s$

Perform the indicated operation, if possible. - $\left[ \begin{array} { r } 3 \\ - 2 \\ - 4 \end{array} \right] + \left[ \begin{array} { r } - 5 \\ 5 \\ 8 \end{array} \right]$

Graph the system of inequalities. Shade the region that represents the solution set. - y \geq x+y \leq2 $Graph the system of inequalities. Shade the region that represents the solution set. - \begin{aligned} y & \geq x^{2} \\ x+y & \leq 2 \end{aligned}$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { l l l l } 1 & 0 & 0 & - 1 \\ 0 & 1 & 0 & - 1 \\ 0 & 0 & 1 & - 9 \end{array} \right]$

Determine the order of the matrix. - $\left[ \begin{array} { l l l l } 3 & - 6 & 5 & 7\end{array} \right]$

Solve the system of equations by finding the reduced row echelon form for the augmented matrix. - $x + y - 2 z = 8$ $3 x + z = - 6$

Find the partial fraction decomposition. - $\frac { 6 } { 4 x ^ { 2 } - 36 }$