Question 1

Write the augmented matrix for the system.
-$$\left\{ \begin{array} { c } 
- 2 x + 6 y = 8 \
5 y = 20
\end{array} \right.$$

Accepted Answer

A)  $\left[ \begin{array} { r r | r } 8 & 6 & - 2 \ 20 & 0 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 5 & 0 & 20 \ - 2 & 6 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 0 & 5 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 5 & 20 & 0 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r | r } 8 & 6 & - 2 \ 20 & 0 & 5 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 5 & 0 & 20 \ - 2 & 6 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 0 & 5 & 20 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } - 2 & 6 & 8 \ 5 & 20 & 0 \end{array} \right]$

Question 2

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region.  
-$z = x + 7 y + 9$ Find minimum.

Accepted Answer

A)  Minimum 34 
B)  No Minimum 
C)  Minimum 46 
D)  Minimum 27 
A)  Minimum 34 
B)  No Minimum 
C)  Minimum 46 
D)  Minimum 27

Question 3

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the
systems of equations. Are the points of intersection solutions to the system of equations (Y/N)?
-

$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 25 \
2 y + x = 5
\end{array}$$

Accepted Answer

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

Question 4

Write the word or phrase that best completes each statement or answers the question.
Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$\begin{array} { l } 
x ^ { 2 } + 8 y ^ { 2 } = 25 \
- 7 x ^ { 2 } - 5 y ^ { 2 } = 100
\end{array}$

Accepted Answer

Either method may be used. Elimination m

Question 5

2x + 3y ≥6
-$\begin{array}{c}
2 x+3 y \geq 6 \
x-y \leq 3 \
x \geq 1
\end{array}$

Accepted Answer

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

Question 6

Perform the indicated operation, whenever possible.
-$$\left[ \begin{array} { r r } 
- 1 & 0 \
6 & 2
\end{array} \right] - \left[ \begin{array} { r r } 
- 1 & 6 \
3 & 1
\end{array} \right]$$

Accepted Answer

A)  $[ - 2 ]$ 
B)  $\left[ \begin{array} { r r } 0 & - 6 \ 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 6 \ 9 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & 6 \ - 3 & - 1 \end{array} \right]$ 
A)  $[ - 2 ]$ 
B)  $\left[ \begin{array} { r r } 0 & - 6 \ 3 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } - 2 & 6 \ 9 & 3 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 0 & 6 \ - 3 & - 1 \end{array} \right]$

Question 7

Choose the one alternative that best completes the statement or answers the question.
-A man is planting a section of garden with tomatoes and cucumbers. The available area of the section is 130 square feet. He wants the area planted with tomatoes to be more than $20 \%$ of the area planted with cucumbers Write a system of inequalities to describe the situation. Let $x =$ amount to be planted in tomatoes and $y =$ amount to be planted in cucumbers.

Accepted Answer

A) $\begin{array}{l} x+y \leq 130 \ x>0.20 y \ x \geq 0 \ y \geq 0 \end{array}$ B) $\begin{array}{l} x+y \leq 130 \ x>20 y \ x \geq 0 \ y \geq 0 \end{array}$ C) $\begin{array}{l} x+y \leq 130 \ x<0.20 y \ x \geq 0 \ y \geq 0 \end{array}$ D) $\begin{array}{l} x+y=130 \ x \geq 0.20 y \ x \geq 0 \ y \geq 0 \end{array}$ A) $\begin{array}{l} x+y \leq 130 \ x>0.20 y \ x \geq 0 \ y \geq 0 \end{array}$ B) $\begin{array}{l} x+y \leq 130 \ x>20 y \ x \geq 0 \ y \geq 0 \end{array}$ C) $\begin{array}{l} x+y \leq 130 \ x<0.20 y \ x \geq 0 \ y \geq 0 \end{array}$ D) $\begin{array}{l} x+y=130 \ x \geq 0.20 y \ x \geq 0 \ y \geq 0 \end{array}$

Question 8

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
2 & 5 \
- 5 & - 3
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \ \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & \frac { 5 } { 19 } \ - \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l } \frac { 2 } { 19 } - \frac { 5 } { 19 } \ \frac { 5 } { 19 } - \frac { 3 } { 19 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } \frac { 5 } { 19 } & \frac { 2 } { 19 } \ - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \end{array} \right]$ 
A)  $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \ \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - \frac { 3 } { 19 } & \frac { 5 } { 19 } \ - \frac { 5 } { 19 } & \frac { 2 } { 19 } \end{array} \right]$ 
C)  $\left[ \begin{array} { l } \frac { 2 } { 19 } - \frac { 5 } { 19 } \ \frac { 5 } { 19 } - \frac { 3 } { 19 } \end{array} \right]$ 
D)  $\left[ \begin{array} { c c } \frac { 5 } { 19 } & \frac { 2 } { 19 } \ - \frac { 3 } { 19 } & - \frac { 5 } { 19 } \end{array} \right]$

Question 9

Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l } 
\mathrm { R } _ { 1 } = \frac { 1 } { 2 } \mathrm { r } 1 \
{ \left[ \begin{array} { r r | r } 
2 & - 2 & - 4 \
4 & 2 & - 5
\end{array} \right] }
\end{array}$$

Accepted Answer

A)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 2 \ 2 & 1 & - \frac { 5 } { 2 } \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 4 \ 4 & 2 & - 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 2 \ 5 & 1 & - 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 2 \ 4 & 2 & - 5 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 2 \ 2 & 1 & - \frac { 5 } { 2 } \end{array} \right]$ 
B)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 4 \ 4 & 2 & - 5 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 2 \ 5 & 1 & - 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r | r } 1 & - 1 & - 2 \ 4 & 2 & - 5 \end{array} \right]$

Question 10

Perform the indicated operation, whenever possible.
-Let $A = \left[ \begin{array} { r r r } - 4 & 6 & 7 \ 3 & - 5 & 12 \ 7 & - 11 & 14 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 6 & 10 & - 4 \ - 5 & 6 & - 8 \ 3 & 11 & 7 \end{array} \right]$. Find $A - B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 10 & - 4 & 3 \ - 2 & - 11 & 4 \ 4 & - 22 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 2 & 16 & 3 \ - 2 & 1 & 4 \ 10 & 0 & 21 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 10 & - 4 & 11 \ 8 & - 11 & 20 \ 4 & - 22 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 10 & 4 & - 11 \ - 8 & 11 & - 20 \ - 4 & 22 & - 7 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } - 10 & - 4 & 3 \ - 2 & - 11 & 4 \ 4 & - 22 & 7 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } 2 & 16 & 3 \ - 2 & 1 & 4 \ 10 & 0 & 21 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 10 & - 4 & 11 \ 8 & - 11 & 20 \ 4 & - 22 & 7 \end{array} \right]$ 
D)  $\left[ \begin{array} { c c c } 10 & 4 & - 11 \ - 8 & 11 & - 20 \ - 4 & 22 & - 7 \end{array} \right]$

Question 11

Write the word or phrase that best completes each statement or answers the question.
-Melody has $45,000 to invest and wishes to receive an annual income of $4290 from this money. She has chosen
investments that pay 5%, 8%, and 12% simple interest. Melody wants to have the amount invested at 12% to be
double the amount invested at 8%. How much should she invest at each rate?

Accepted Answer

$9000 at 5

Question 12

Solve the system of equations using substitution.
-$$\left\{ \begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 39 \
x - y = 3
\end{array} \right.$$

Accepted Answer

A)  $x = - 8 , y = 5$ 
B)  $x = 8 , y = - 5$ 
C)  $x = - 8 , y = - 5$ 
D)  $x = 8 , y = 5$ 
A)  $x = - 8 , y = 5$ 
B)  $x = 8 , y = - 5$ 
C)  $x = - 8 , y = - 5$ 
D)  $x = 8 , y = 5$

Question 13

Choose the one alternative that best completes the statement or answers the question.
-$$\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$$

Accepted Answer

A)  $\frac { x } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
B)  $\frac { 2 x + 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x - 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
C)  $\frac { x + 1 } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
D)  $\frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
A)  $\frac { x } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
B)  $\frac { 2 x + 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x - 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
C)  $\frac { x + 1 } { x ^ { 2 } + 5 } + \frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$ 
D)  $\frac { 2 x - 2 } { \left( x ^ { 2 } + 5 \right) ^ { 2 } } + \frac { 5 x + 1 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

Question 14

Write a system of linear inequalities that has the given graph.
-

Accepted Answer

A) 
$$\left\{ \begin{array} { r } 
y \geq 0 \
x \geq 0 \
x \leq 6 \
y \leq 9 \
x + y \geq 3
\end{array} \right.$$ 
B) 
$$\left\{ \begin{array} { r } 
y \geq 0 \
x \geq 0 \
x \leq 9 \
x + y \geq 3
\end{array} \right.$$ 
C) 
$\left\{\begin{array}{r}
x \leq 6 \
y \leq 9 \
x+y \geq 3
\end{array}\right.$ 
D) 
$$\left\{ \begin{array} { r } 
y \geq 0 \
x \geq 0 \
y \leq 9 \
x + y \geq 3
\end{array} \right.$$ 
A) 
$$\left\{ \begin{array} { r } 
y \geq 0 \
x \geq 0 \
x \leq 6 \
y \leq 9 \
x + y \geq 3
\end{array} \right.$$ 
B) 
$$\left\{ \begin{array} { r } 
y \geq 0 \
x \geq 0 \
x \leq 9 \
x + y \geq 3
\end{array} \right.$$ 
C) 
$\left\{\begin{array}{r}
x \leq 6 \
y \leq 9 \
x+y \geq 3
\end{array}\right.$ 
D) 
$$\left\{ \begin{array} { r } 
y \geq 0 \
x \geq 0 \
y \leq 9 \
x + y \geq 3
\end{array} \right.$$

Question 15

Choose the one alternative that best completes the statement or answers the question.
-$$\left\{ \begin{array} { l } 
2 x ^ { 2 } + y ^ { 2 } = 17 \
3 x ^ { 2 } - 2 y ^ { 2 } = - 6
\end{array} \right.$$

Accepted Answer

A)  $x = 1 , y = 3 ; x = 1 , y = - 3 ; x = - 1 , y = 3 ; x = - 1 , y = - 3$ 
B)  $x = 2 , y = 3 ; x = 2 , y = - 3 ; x = - 2 , y = 3 ; x = - 2 , y = - 3$ 
C)  $x = 2 , y = - 3 ; x = - 2 , y = 3$ 
D)  $x = 1 , y = 3 ; x = - 1 , y = - 3$ 
A)  $x = 1 , y = 3 ; x = 1 , y = - 3 ; x = - 1 , y = 3 ; x = - 1 , y = - 3$ 
B)  $x = 2 , y = 3 ; x = 2 , y = - 3 ; x = - 2 , y = 3 ; x = - 2 , y = - 3$ 
C)  $x = 2 , y = - 3 ; x = - 2 , y = 3$ 
D)  $x = 1 , y = 3 ; x = - 1 , y = - 3$

Question 16

Write the partial fraction decomposition of the rational expression.
-$$\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$$

Accepted Answer

A)  $\frac { 5 } { x - 2 } + \frac { - 4 } { x - 3 }$ 
B)  $\frac { 5 } { x - 2 } + \frac { 4 } { x - 3 }$ 
C)  $\frac { - 4 } { x - 2 } + \frac { 5 } { x - 3 }$ 
D)  $\frac { 4 } { x - 2 } + \frac { - 5 } { x - 3 }$ 
A)  $\frac { 5 } { x - 2 } + \frac { - 4 } { x - 3 }$ 
B)  $\frac { 5 } { x - 2 } + \frac { 4 } { x - 3 }$ 
C)  $\frac { - 4 } { x - 2 } + \frac { 5 } { x - 3 }$ 
D)  $\frac { 4 } { x - 2 } + \frac { - 5 } { x - 3 }$

Question 17

Solve the system.
-$$\left\{ \begin{array} { c } 
x + 5 y = 4 \
3 x + 15 y = 12
\end{array} \right.$$

Accepted Answer

A)  $( 0,0 )$ 
B)  $( - 3,0 )$ 
C)  inconsistent (no solution) 
D)  $y = - \frac { x } { 5 } + \frac { 4 } { 5 }$, where $x$ is any real number 
A)  $( 0,0 )$ 
B)  $( - 3,0 )$ 
C)  inconsistent (no solution) 
D)  $y = - \frac { x } { 5 } + \frac { 4 } { 5 }$, where $x$ is any real number

Question 18

Solve the problem.
-A flat rectangular piece of aluminum has a perimeter of 68 inches. The length is 14 inches longer than the width. Find the width.

Accepted Answer

A)  28 inches 
B)  26 inches 
C)  8 inches 
D)  18 inches 
A)  28 inches 
B)  26 inches 
C)  8 inches 
D)  18 inches

Question 19

2x + 3y ≥6
-$$\left\{ \begin{array} { l } 
x ^ { 2 } + y ^ { 2 } \leq 100 \
- 7 x + 3 y \leq - 21
\end{array} \right.$$

Accepted Answer

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

Question 20

2x + 3y ≥6
-$$\begin{aligned}
2 x + 3 y & \geq 6 \
x - y & \geq 3 \
y & \leq 2
\end{aligned}$$

Accepted Answer

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

Write the augmented matrix for the system. - $\left\{ \begin{array} { c } - 2 x + 6 y = 8 \\5 y = 20\end{array} \right.$

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region. - $z = x + 7 y + 9$ Find minimum.

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - +8=25 -7-5=100

2x + 3y ≥6 - 2x+3y\geq6 x-y\leq3 x\geq1 $2x + 3y ≥6 - \begin{array}{c} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ x \geq 1 \end{array}$

Perform the indicated operation, whenever possible. - $\left[ \begin{array} { r r } - 1 & 0 \\6 & 2\end{array} \right] - \left[ \begin{array} { r r } - 1 & 6 \\3 & 1\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 2 & 5 \\- 5 & - 3\end{array} \right]$

Perform the row operation(s) on the given augmented matrix. - =1 2 -2 -4 4 2 -5

Perform the indicated operation, whenever possible. -Let $A = \left[ \begin{array} { r r r } - 4 & 6 & 7 \\ 3 & - 5 & 12 \\ 7 & - 11 & 14 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } 6 & 10 & - 4 \\ - 5 & 6 & - 8 \\ 3 & 11 & 7 \end{array} \right]$ . Find $A - B$ .

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.$

Choose the one alternative that best completes the statement or answers the question. - $\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

Write a system of linear inequalities that has the given graph. -

Choose the one alternative that best completes the statement or answers the question. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$

Solve the system. - $\left\{ \begin{array} { c } x + 5 y = 4 \\3 x + 15 y = 12\end{array} \right.$

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 68 inches. The length is 14 inches longer than the width. Find the width.

2x + 3y ≥6 - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 100 \\- 7 x + 3 y \leq - 21\end{array} \right.$ $2x + 3y ≥6 - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 100 \\ - 7 x + 3 y \leq - 21 \end{array} \right.$

2x + 3y ≥6 - 2x+3y \geq6 x-y \geq3 y \leq2 $2x + 3y ≥6 - \begin{aligned} 2 x + 3 y & \geq 6 \\ x - y & \geq 3 \\ y & \leq 2 \end{aligned}$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 10: Systems of Equations and Inequalities

Write the augmented matrix for the system. - {−2x+6y=85y=20\left\{ \begin{array} { c } - 2 x + 6 y = 8 \\5 y = 20\end{array} \right.{−2x+6y=85y=20​

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region. - z=x+7y+9z = x + 7 y + 9z=x+7y+9 Find minimum.

The graph of two equations along with the points of intersection are given. Substitute the points of intersection into the systems of equations. Are the points of intersection solutions to the system of equations (Y/N)? - +=25 2y+x=5

Write the word or phrase that best completes each statement or answers the question. Which method should be used to solve the system? Explain your answer, including a description of the first step. - +8=25 -7-5=100

2x + 3y ≥6 - 2x+3y\geq6 x-y\leq3 x\geq1

Perform the indicated operation, whenever possible. - [−1062]−[−1631]\left[ \begin{array} { r r } - 1 & 0 \\6 & 2\end{array} \right] - \left[ \begin{array} { r r } - 1 & 6 \\3 & 1\end{array} \right][−16​02​]−[−13​61​]

Find the inverse of the matrix. - [25−5−3]\left[ \begin{array} { r r } 2 & 5 \\- 5 & - 3\end{array} \right][2−5​5−3​]

Perform the row operation(s) on the given augmented matrix. - =1 2 -2 -4 4 2 -5

Solve the system of equations using substitution. - {x2−y2=39x−y=3\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.{x2−y2=39x−y=3​

Choose the one alternative that best completes the statement or answers the question. - 2x3−2x2+15x−9(x2+5)3\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }(x2+5)32x3−2x2+15x−9​

Write a system of linear inequalities that has the given graph. -

Choose the one alternative that best completes the statement or answers the question. - {2x2+y2=173x2−2y2=−6\left\{ \begin{array} { l } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.{2x2+y2=173x2−2y2=−6​

Write the partial fraction decomposition of the rational expression. - x−7(x−2)(x−3)\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }(x−2)(x−3)x−7​

Solve the system. - {x+5y=43x+15y=12\left\{ \begin{array} { c } x + 5 y = 4 \\3 x + 15 y = 12\end{array} \right.{x+5y=43x+15y=12​

Solve the problem. -A flat rectangular piece of aluminum has a perimeter of 68 inches. The length is 14 inches longer than the width. Find the width.

2x + 3y ≥6 - {x2+y2≤100−7x+3y≤−21\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 100 \\- 7 x + 3 y \leq - 21\end{array} \right.{x2+y2≤100−7x+3y≤−21​

2x + 3y ≥6 - 2x+3y \geq6 x-y \geq3 y \leq2

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Write the augmented matrix for the system. - $\left\{ \begin{array} { c } - 2 x + 6 y = 8 \\5 y = 20\end{array} \right.$

Find the maximum or minimum value of the objective function, subject to the constraints graphed in this feasible region. - $z = x + 7 y + 9$ Find minimum.

2x + 3y ≥6 - 2x+3y\geq6 x-y\leq3 x\geq1 $2x + 3y ≥6 - \begin{array}{c} 2 x+3 y \geq 6 \\ x-y \leq 3 \\ x \geq 1 \end{array}$

Perform the indicated operation, whenever possible. - $\left[ \begin{array} { r r } - 1 & 0 \\6 & 2\end{array} \right] - \left[ \begin{array} { r r } - 1 & 6 \\3 & 1\end{array} \right]$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 2 & 5 \\- 5 & - 3\end{array} \right]$

Solve the system of equations using substitution. - $\left\{ \begin{array} { l } x ^ { 2 } - y ^ { 2 } = 39 \\x - y = 3\end{array} \right.$

Choose the one alternative that best completes the statement or answers the question. - $\frac { 2 x ^ { 3 } - 2 x ^ { 2 } + 15 x - 9 } { \left( x ^ { 2 } + 5 \right) ^ { 3 } }$

Choose the one alternative that best completes the statement or answers the question. - $\left\{ \begin{array} { l } 2 x ^ { 2 } + y ^ { 2 } = 17 \\3 x ^ { 2 } - 2 y ^ { 2 } = - 6\end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { x - 7 } { ( x - 2 ) ( x - 3 ) }$

Solve the system. - $\left\{ \begin{array} { c } x + 5 y = 4 \\3 x + 15 y = 12\end{array} \right.$

2x + 3y ≥6 - $\left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 100 \\- 7 x + 3 y \leq - 21\end{array} \right.$ $2x + 3y ≥6 - \left\{ \begin{array} { l } x ^ { 2 } + y ^ { 2 } \leq 100 \\ - 7 x + 3 y \leq - 21 \end{array} \right.$

2x + 3y ≥6 - 2x+3y \geq6 x-y \geq3 y \leq2 $2x + 3y ≥6 - \begin{aligned} 2 x + 3 y & \geq 6 \\ x - y & \geq 3 \\ y & \leq 2 \end{aligned}$