Question 1

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants.
-$$\begin{array} { l } 
a x + y = b \
x + b y = a
\end{array}$$

Accepted Answer

A)  $\left\{ \left[ \frac { a ^ { 2 } - b } { a b - 1 } , \frac { b ^ { 2 } - a } { a b - 1 } \right) \right\}$ 
B)  $\left\{ \left\{ \frac { a ^ { 2 } + b } { a b - 1 } , \frac { b ^ { 2 } + a } { a b - 1 } \right) \right\}$ 
C)  $\left\{ \left[ \frac { b ^ { 2 } - a } { a b - 1 } , \frac { a ^ { 2 } - b } { a b - 1 } \right) \right\}$ 
D)  $\left\{ \left( \frac { a b - 1 } { b ^ { 2 } - a } , \frac { a b - 1 } { a ^ { 2 } - b } \right) \right\}$ 
A)  $\left\{ \left[ \frac { a ^ { 2 } - b } { a b - 1 } , \frac { b ^ { 2 } - a } { a b - 1 } \right) \right\}$ 
B)  $\left\{ \left\{ \frac { a ^ { 2 } + b } { a b - 1 } , \frac { b ^ { 2 } + a } { a b - 1 } \right) \right\}$ 
C)  $\left\{ \left[ \frac { b ^ { 2 } - a } { a b - 1 } , \frac { a ^ { 2 } - b } { a b - 1 } \right) \right\}$ 
D)  $\left\{ \left( \frac { a b - 1 } { b ^ { 2 } - a } , \frac { a b - 1 } { a ^ { 2 } - b } \right) \right\}$

Question 2

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form.
-

Accepted Answer

A)  $x + y \leq 2$
 $2 x + y \geq 5$ 
B)  $x - y \geq 2$
$2 x + y \leq 5$ 
C)  $x + y \geq 2$
$2 x + y \leq 5$ 
D)  $x - y \leq 2$  
$2 x + y \geq 5$ 
A)  $x + y \leq 2$
 $2 x + y \geq 5$ 
B)  $x - y \geq 2$
$2 x + y \leq 5$ 
C)  $x + y \geq 2$
$2 x + y \leq 5$ 
D)  $x - y \leq 2$  
$2 x + y \geq 5$

Question 3

Evaluate the determinant.
-$$\left| \begin{array} { l l l l } 
0 & 0 & 0 & 9 \
7 & 7 & 4 & 7 \
3 & 3 & 3 & 3 \
5 & 6 & 2 & 2
\end{array} \right|$$

Accepted Answer

A)  $- 27$ 
B)  $- 18$ 
C)  81 
D)  $- 81$ 
A)  $- 27$ 
B)  $- 18$ 
C)  81 
D)  $- 81$

Question 4

Write the system of equations associated with the augmented matrix. Do not solve.
-$$\left[ \begin{array} { l l l | l } 
1 & 0 & 0 & 7 \
0 & 1 & 0 & 1 \
0 & 0 & 1 & 5
\end{array} \right]$$

Accepted Answer

A)  $x = - 7$
$y = - 1$
 $z = - 5$ 
B)  $x = 0$
$y = 8$
$\mathrm { z } = 12$ 
C)  $x = 7$
$y = 1$
$z = 5$ 
D)  $x = 2$
$y = - 4$
$z = 0$ 
A)  $x = - 7$
$y = - 1$
 $z = - 5$ 
B)  $x = 0$
$y = 8$
$\mathrm { z } = 12$ 
C)  $x = 7$
$y = 1$
$z = 5$ 
D)  $x = 2$
$y = - 4$
$z = 0$

Question 5

Write the augmented matrix for the system. Do not
-$$\begin{array} { l } 
4 x + 6 y = 26 \
8 x + 5 y = 31
\end{array}$$

Accepted Answer

A) 
$$\left[ \begin{array} { l l | l } 
4 & 8 & 26 \
6 & 5 & 31
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { l l | l } 
26 & 6 & 4 \
31 & 8 & 5
\end{array} \right]$$ 
C) 
$\left[ \begin{array} { l l | l } 4 & 6 & 31 \ 5 & 8 & 26 \end{array} \right]$ 
D)

$$\left[ \begin{array} { l l | l } 
4 & 6 & 26 \
8 & 5 & 31
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { l l | l } 
4 & 8 & 26 \
6 & 5 & 31
\end{array} \right]$$ 
B) 
$$\left[ \begin{array} { l l | l } 
26 & 6 & 4 \
31 & 8 & 5
\end{array} \right]$$ 
C) 
$\left[ \begin{array} { l l | l } 4 & 6 & 31 \ 5 & 8 & 26 \end{array} \right]$ 
D)

$$\left[ \begin{array} { l l | l } 
4 & 6 & 26 \
8 & 5 & 31
\end{array} \right]$$

Question 6

Perform the operation or operations when possible.
-$$\left[ \begin{array} { l l } 
2 & 4
\end{array} \right] + \left[ \begin{array} { l } 
1 \
5
\end{array} \right]$$

Accepted Answer

A) 
$$\left[ \begin{array} { l } 
3 \
9
\end{array} \right]$$ 
B)

$$\left[ \begin{array} { l l } 
2 & 1 \
4 & 5
\end{array} \right]$$ 
C) 
[ $\left. \begin{array} { l l } 3 & 9 \end{array} \right]$ 
D)  They cannot be added. 
A) 
$$\left[ \begin{array} { l } 
3 \
9
\end{array} \right]$$ 
B)

$$\left[ \begin{array} { l l } 
2 & 1 \
4 & 5
\end{array} \right]$$ 
C) 
[ $\left. \begin{array} { l l } 3 & 9 \end{array} \right]$ 
D)  They cannot be added.

Question 7

Evaluate the determinant.
-$$\left| \begin{array} { l l l l } 
5 & 6 & 7 & 9 \
2 & 1 & 8 & 9 \
1 & 0 & 0 & 6 \
8 & 3 & 2 & 2
\end{array} \right|$$

Accepted Answer

A)  $- 1451$ 
B)  42 
C)  $- 4$ 
D)  $- 9$ 
A)  $- 1451$ 
B)  42 
C)  $- 4$ 
D)  $- 9$

Question 8

Find the matrix product when possible.
-Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \ 0 & 1 & 1 \ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \ 0 & - 1 & 0 \ - 1 & 1 & 0 \end{array} \right]$, find $A B$ and $B A$.

Accepted Answer

A) 
$\mathrm{AB}=\left[\begin{array}{crl}
0 & 2 & 1 \
0 & -1 & -1 \
0 & 2 & 1
\end{array}\right] ; \mathrm{BA}=\left[\begin{array}{rrr}
0 & 1 & 0 \
-1 & 0 & 0 \
2 & -2 & 0
\end{array}\right]$ 
B) 
$$\mathrm { AB } = \left[ \begin{array} { r r r } 
0 & - 1 & 0 \
0 & - 1 & 0 \
1 & 0 & 0
\end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 
0 & - 1 & 0 \
0 & - 1 & 0 \
1 & 0 & 0
\end{array} \right]$$ 
C) 
$$\mathrm { AB } = \left[ \begin{array} { r r r } 
0 & - 1 & 0 \
- 1 & 2 & 0 \
2 & - 2 & 0
\end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 
0 & 0 & - 1 \
0 & 1 & 1 \
0 & 0 & - 1
\end{array} \right]$$ 
D)

$$A B = \left[ \begin{array} { r r r } 
0 & 1 & 0 \
- 1 & 0 & 0 \
2 & - 2 & 0
\end{array} \right] ; B A = \left[ \begin{array} { c r l } 
0 & 2 & 1 \
0 & - 1 & - 1 \
0 & 2 & 1
\end{array} \right]$$ 
A) 
$\mathrm{AB}=\left[\begin{array}{crl}
0 & 2 & 1 \
0 & -1 & -1 \
0 & 2 & 1
\end{array}\right] ; \mathrm{BA}=\left[\begin{array}{rrr}
0 & 1 & 0 \
-1 & 0 & 0 \
2 & -2 & 0
\end{array}\right]$ 
B) 
$$\mathrm { AB } = \left[ \begin{array} { r r r } 
0 & - 1 & 0 \
0 & - 1 & 0 \
1 & 0 & 0
\end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { r r r } 
0 & - 1 & 0 \
0 & - 1 & 0 \
1 & 0 & 0
\end{array} \right]$$ 
C) 
$$\mathrm { AB } = \left[ \begin{array} { r r r } 
0 & - 1 & 0 \
- 1 & 2 & 0 \
2 & - 2 & 0
\end{array} \right] ; \mathrm { BA } = \left[ \begin{array} { c c c } 
0 & 0 & - 1 \
0 & 1 & 1 \
0 & 0 & - 1
\end{array} \right]$$ 
D)

$$A B = \left[ \begin{array} { r r r } 
0 & 1 & 0 \
- 1 & 0 & 0 \
2 & - 2 & 0
\end{array} \right] ; B A = \left[ \begin{array} { c r l } 
0 & 2 & 1 \
0 & - 1 & - 1 \
0 & 2 & 1
\end{array} \right]$$

Question 9

Solve the problem.
-The perimeter of a rectangle is $34 \mathrm {~cm}$. The length is $7 \mathrm {~cm}$ longer than the width. What are the length and width of the rectangle?

Accepted Answer

A)  Length: $13 \mathrm {~cm}$; width: $6 \mathrm {~cm}$ 
B)  Length: $12 \mathrm {~cm}$; width: $5 \mathrm {~cm}$ 
C)  Length: $7 \mathrm {~cm}$; width: $5 \mathrm {~cm}$ 
D)  Length: $17 \mathrm {~cm}$; width: $10 \mathrm {~cm}$ 
A)  Length: $13 \mathrm {~cm}$; width: $6 \mathrm {~cm}$ 
B)  Length: $12 \mathrm {~cm}$; width: $5 \mathrm {~cm}$ 
C)  Length: $7 \mathrm {~cm}$; width: $5 \mathrm {~cm}$ 
D)  Length: $17 \mathrm {~cm}$; width: $10 \mathrm {~cm}$

Question 10

Find the matrix product when possible.
-Momma's ice cream shop sells three types of ice cream: soft-serve, chunky, and nonfat. Location I sells 10 gal of soft-serve, 100 gal of chunky, and $30 \mathrm { gal }$ of nonfat ice cream each day. Location II sells $14 \mathrm { gal }$ of soft-serve and Location III sells $60 \mathrm { gal }$ of soft-serve each day. Daily sales of chunky ice cream are $90 \mathrm { gal }$ at Location II and $120 \mathrm { gal }$ at Location III. At Location II, $17 \mathrm { gal }$ of nonfat are sold each day, and 40 gal of nonfat are sold each day at Location III. Write a $3 \times 3$ matrix that shows the sales figures for the three locations, with the rows representing the three locations.

Accepted Answer

A) 
$$\left[ \begin{array} { r r c } 
10 & 100 & 30 \
14 & 90 & 17 \
60 & 40 & 120
\end{array} \right]$$ 
B)

$$\left[ \begin{array} { c c r } 
10 & 14 & 60 \
100 & 90 & 120 \
30 & 17 & 40
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
10 & 100 & 30 \
14 & 90 & 17 \
60 & 120 & 40
\end{array} \right]$$ 
D)

$$\left[ \begin{array} { r r r } 
10 & 90 & 30 \
14 & 100 & 17 \
60 & 120 & 40
\end{array} \right]$$ 
A) 
$$\left[ \begin{array} { r r c } 
10 & 100 & 30 \
14 & 90 & 17 \
60 & 40 & 120
\end{array} \right]$$ 
B)

$$\left[ \begin{array} { c c r } 
10 & 14 & 60 \
100 & 90 & 120 \
30 & 17 & 40
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
10 & 100 & 30 \
14 & 90 & 17 \
60 & 120 & 40
\end{array} \right]$$ 
D)

$$\left[ \begin{array} { r r r } 
10 & 90 & 30 \
14 & 100 & 17 \
60 & 120 & 40
\end{array} \right]$$

Question 11

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
-$$\begin{array} { c } 
x + y + z = - 3 \
x - y + 5 z = - 13 \
3 x + y + z = 5
\end{array}$$

Accepted Answer

A)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
B)  $\{ ( - 4,4 , - 3 ) \}$ 
C)  $\{ ( - 4 , - 3,4 ) \}$ 
D)  $\{ ( 4 , - 3 , - 4 ) \}$ 
A)  Cramer's rule does not apply since $D = 0 ; \varnothing$ 
B)  $\{ ( - 4,4 , - 3 ) \}$ 
C)  $\{ ( - 4 , - 3,4 ) \}$ 
D)  $\{ ( 4 , - 3 , - 4 ) \}$

Question 12

Solve the problem using matrices.
-A chemist has prepared two acid solutions, one of which is $6 \%$ acid by volume, another $10 \%$ acid. How many cubic centimeters of each should the chemist mix together to obtain $50 \mathrm {~cm} ^ { 3 }$ of a solution that is $7.84 \%$ acid.

Accepted Answer

A)  No solution 
B)  $27 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 23 \mathrm {~cm} ^ { 3 }$ of $10 \%$ 
C)  $3.92 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 46.08 \mathrm {~cm} ^ { 3 }$ of $10 \%$ 
D)  $50 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 50 \mathrm {~cm} ^ { 3 }$ of $10 \%$ 
A)  No solution 
B)  $27 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 23 \mathrm {~cm} ^ { 3 }$ of $10 \%$ 
C)  $3.92 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 46.08 \mathrm {~cm} ^ { 3 }$ of $10 \%$ 
D)  $50 \mathrm {~cm} ^ { 3 }$ of $6 \% ; 50 \mathrm {~cm} ^ { 3 }$ of $10 \%$

Question 13

Solve the problem.
-The following table shows the number of dog collars, in thousands, produced by Allied Pet Products in the three years considered. For a function of the form $f ( x ) = a x ^ { 2 } + b x + c$ that fits this datc what is the value of $\mathrm { c }$ ?
$\begin{array}{c|c}
\text { Year } & \begin{array}{c}
\text { Number of dog collars } \
\text { (in thousands) }
\end{array} \
\hline 0 & 20 \
\hline 6 & 14 \
\hline 18 & 23.6
\end{array}$

Accepted Answer

A)  12.8 
B)  14 
C)  20 
D)  23.6 
A)  12.8 
B)  14 
C)  20 
D)  23.6

Question 14

Provide an appropriate response.
-Let $\mathrm { A } = \left[ \begin{array} { l l } \mathrm { c } & 0 \ 0 & \mathrm {~b} \end{array} \right]$, where $\mathrm { c }$ and $\mathrm { b }$ are nonzero constants. Find $\mathrm { A } ^ { - 1 }$.

Accepted Answer

A) 
$$\left[ \begin{array} { l l } 
\frac { 1 } { c } & 0 \
0 & \frac { 1 } { b }
\end{array} \right]$$ 
B) 
$\left[\begin{array}{ll}
0 & \mathrm{c} \
\mathrm{b} & 0
\end{array}\right]$ 
C) 
$\left[\begin{array}{l}
\frac{1}{c} 1 \
1 \frac{1}{b}
\end{array}\right]$ 
D)

$\left[\begin{array}{ll}
\mathrm{c} & 0 \
0 & \mathrm{~b}
\end{array}\right]$ 
A) 
$$\left[ \begin{array} { l l } 
\frac { 1 } { c } & 0 \
0 & \frac { 1 } { b }
\end{array} \right]$$ 
B) 
$\left[\begin{array}{ll}
0 & \mathrm{c} \
\mathrm{b} & 0
\end{array}\right]$ 
C) 
$\left[\begin{array}{l}
\frac{1}{c} 1 \
1 \frac{1}{b}
\end{array}\right]$ 
D)

$\left[\begin{array}{ll}
\mathrm{c} & 0 \
0 & \mathrm{~b}
\end{array}\right]$

Question 15

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
y = \sqrt [ 4 ] { 2 x + 9 } \
x ^ { 2 } + y ^ { 2 } = 5.7
\end{array}$$

Accepted Answer

A)  $\{ ( - 1.84 , - 1.52 ) , ( 1.50 , - 1.86 ) \}$ 
B)  $\{ ( - 1.50,1.86 ) , ( 1.84,1.52 ) \}$ 
C)  $\{ ( - 1.84,1.52 ) , ( 1.50,1.86 ) \}$ 
D)  $\{ ( - 1.50 , - 1.86 ) , ( 1.84 , - 1.52 ) \}$ 
A)  $\{ ( - 1.84 , - 1.52 ) , ( 1.50 , - 1.86 ) \}$ 
B)  $\{ ( - 1.50,1.86 ) , ( 1.84,1.52 ) \}$ 
C)  $\{ ( - 1.84,1.52 ) , ( 1.50,1.86 ) \}$ 
D)  $\{ ( - 1.50 , - 1.86 ) , ( 1.84 , - 1.52 ) \}$

Question 16

Solve the problem.
-Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points $( - 2,4 ) , ( 0 , - 2 )$, and $( 3,1 )$

Accepted Answer

A)  $y = \frac { 2 } { 15 } x ^ { 2 } + 1 x - 5$ 
B)  $y = - \frac { 7 } { 5 } x ^ { 2 } + \frac { 4 } { 5 } x - 2$ 
C)  $y = \frac { 4 } { 5 } x ^ { 2 } - \frac { 7 } { 5 } x - 2$ 
D)  $y = \frac { 7 } { 15 } x ^ { 2 } - \frac { 14 } { 5 } x - \frac { 2 } { 3 }$ 
A)  $y = \frac { 2 } { 15 } x ^ { 2 } + 1 x - 5$ 
B)  $y = - \frac { 7 } { 5 } x ^ { 2 } + \frac { 4 } { 5 } x - 2$ 
C)  $y = \frac { 4 } { 5 } x ^ { 2 } - \frac { 7 } { 5 } x - 2$ 
D)  $y = \frac { 7 } { 15 } x ^ { 2 } - \frac { 14 } { 5 } x - \frac { 2 } { 3 }$

Question 17

Find the value of the determinant.
-$$\left| \begin{array} { l l } 
- 7 & 4 \
0 & 6
\end{array} \right|$$

Accepted Answer

A)  $- 28$ 
B)  42 
C)  $- 46$ 
D)  $- 42$ 
A)  $- 28$ 
B)  42 
C)  $- 46$ 
D)  $- 42$

Question 18

Solve the problem.
-Twice the water flow in the hot-water pipe is the same as three times the flow in the cold-water pipe. The combined flow is $1200 \mathrm {~L} / \mathrm { hr }$. What is the flow in each pipe?

Accepted Answer

A)  $400 \mathrm {~L} / \mathrm { hr }$ hot; $600 \mathrm {~L} / \mathrm { hr }$ cold 
B)  $480 \mathrm {~L} / \mathrm { hr }$ hot; $720 \mathrm {~L} / \mathrm { hr }$ cold 
C)  $600 \mathrm {~L} / \mathrm { hr }$ hot; $400 \mathrm {~L} / \mathrm { hr }$ cold 
D)  $720 \mathrm {~L} / \mathrm { hr }$ hot; $480 \mathrm {~L} / \mathrm { hr }$ cold 
A)  $400 \mathrm {~L} / \mathrm { hr }$ hot; $600 \mathrm {~L} / \mathrm { hr }$ cold 
B)  $480 \mathrm {~L} / \mathrm { hr }$ hot; $720 \mathrm {~L} / \mathrm { hr }$ cold 
C)  $600 \mathrm {~L} / \mathrm { hr }$ hot; $400 \mathrm {~L} / \mathrm { hr }$ cold 
D)  $720 \mathrm {~L} / \mathrm { hr }$ hot; $480 \mathrm {~L} / \mathrm { hr }$ cold

Question 19

Graph the solution set of the system of inequalities.
-$$\begin{array} { r } 
2 x + y \leq 4 \
x - 1 \geq 0
\end{array}$$

Accepted Answer

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

Question 20

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of
the concepts involved in graphing inequalities.
-

Accepted Answer

A)  $y \geq 3 x + 1$ 
B)  $y \leq - 3 x + 1$ 
C)  $y \geq - 3 x + 1$ 
D)  $y \leq 3 x + 1$ 
A)  $y \geq 3 x + 1$ 
B)  $y \leq - 3 x + 1$ 
C)  $y \geq - 3 x + 1$ 
D)  $y \leq 3 x + 1$

Solve the system for x and y using Cramer's rule. Assume a and b are nonzero constants. - ax+y=b x+by=a

Determine the system of inequalities illustrated in the graph. Write inequalities in standard form. -

Evaluate the determinant. - $\left| \begin{array} { l l l l } 0 & 0 & 0 & 9 \\7 & 7 & 4 & 7 \\3 & 3 & 3 & 3 \\5 & 6 & 2 & 2\end{array} \right|$

Write the system of equations associated with the augmented matrix. Do not solve. - $\left[ \begin{array} { l l l | l } 1 & 0 & 0 & 7 \\0 & 1 & 0 & 1 \\0 & 0 & 1 & 5\end{array} \right]$

Write the augmented matrix for the system. Do not - 4x+6y=26 8x+5y=31

Perform the operation or operations when possible. - $\left[ \begin{array} { l l } 2 & 4\end{array} \right] + \left[ \begin{array} { l } 1 \\5\end{array} \right]$

Evaluate the determinant. - $\left| \begin{array} { l l l l } 5 & 6 & 7 & 9 \\2 & 1 & 8 & 9 \\1 & 0 & 0 & 6 \\8 & 3 & 2 & 2\end{array} \right|$

Find the matrix product when possible. -Given $A = \left[ \begin{array} { r r r } 0 & - 1 & 0 \\ 0 & 1 & 1 \\ - 1 & 0 & - 1 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 1 & 1 & 0 \\ 0 & - 1 & 0 \\ - 1 & 1 & 0 \end{array} \right]$ , find $A B$ and $B A$ .

Solve the problem. -The perimeter of a rectangle is $34 \mathrm {~cm}$ . The length is $7 \mathrm {~cm}$ longer than the width. What are the length and width of the rectangle?

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. - x+y+z=-3 x-y+5z=-13 3x+y+z=5

Solve the problem using matrices. -A chemist has prepared two acid solutions, one of which is $6 \%$ acid by volume, another $10 \%$ acid. How many cubic centimeters of each should the chemist mix together to obtain $50 \mathrm {~cm} ^ { 3 }$ of a solution that is $7.84 \%$ acid.

Provide an appropriate response. -Let $\mathrm { A } = \left[ \begin{array} { l l } \mathrm { c } & 0 \\ 0 & \mathrm {~b} \end{array} \right]$ , where $\mathrm { c }$ and $\mathrm { b }$ are nonzero constants. Find $\mathrm { A } ^ { - 1 }$ .

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y= +=5.7

Solve the problem. -Find the equation of the parabola $y = a x ^ { 2 } + b x + c$ that passes through the points $( - 2,4 ) , ( 0 , - 2 )$ , and $( 3,1 )$

Find the value of the determinant. - $\left| \begin{array} { l l } - 7 & 4 \\0 & 6\end{array} \right|$

Solve the problem. -Twice the water flow in the hot-water pipe is the same as three times the flow in the cold-water pipe. The combined flow is $1200 \mathrm {~L} / \mathrm { hr }$ . What is the flow in each pipe?

Graph the solution set of the system of inequalities. - 2x+y\leq4 x-1\geq0 $Graph the solution set of the system of inequalities. - \begin{array} { r } 2 x + y \leq 4 \\ x - 1 \geq 0 \end{array}$

Determine the inequality which matches the calculator graph. Do not use your calculator. Instead, use your knowledge of the concepts involved in graphing inequalities. -

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Analytic Geometry

Further Topics in Algebra

Filters

Exam 10: Systems and Matrices