Question 1

Graph the solution set of the system of inequalities.
-$\begin{array}{l}
y \geq-x^{2}-6 x-4 \
y \geq x^{2}+6 x+4
\end{array}$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 2

Graph the solution set of the system of inequalities.
-$$\begin{array} { c } 
3 x - 2 y \leq 6 \
x - 1 \geq 0
\end{array}$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 3

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
$\begin{array} { l } 
y = e ^ { x + 3 } \
x ^ { 2 } - 4 y ^ { 2 } = 11
\end{array}$

Accepted Answer

A)  {(2.75,1.28)} 
B)  {(-3.52,0.59)} 
C)  {(1.04,-0.14),(3.52,-1.69)} 
D)  {(2.75,-1.28)}

Question 4

Solve the linear programming problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$, has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane $\mathrm { P } _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $P _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Accepted Answer

A)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
B)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
C)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
D)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes

Question 5

Graph the inequality.
-$-2 x-5 y \leq-10$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 6

Find the dimension of the matrix.
-$$\left[ \begin{array} { l l } 
5 & 0 \
0 & 5
\end{array} \right]$$

Accepted Answer

A)  $2 \times 2$ 
B)  $5 \times 5$ 
C)  5 
D)  4

Question 7

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-$$\begin{array} { l } 
y = \log ( x + 7 ) \
y = x ^ { 3 }
\end{array}$$

Accepted Answer

A)  $\{ ( 2.07,0.69 ) \}$ 
B)  $\{ ( - 1.83,1.64 ) , ( 1.68,2.16 ) \}$ 
C)  $\{ ( - 2.50,1.49 ) \}$ 
D)  $\{ ( 0.97,0.90 ) \}$

Question 8

Michael's bank contains only nickels, dimes, and quarters. There are 67 coins in all, valued at $5.25. The number of nickels is 1 short of being three times the sum of the number of dimes and quarters. How many dimes are in
The bank?

Accepted Answer

A)  7 dimes 
B)  10 dimes 
C)  50 dimes 
D)  15 dimes

Question 9

Find the inverse, if it exists, for the matrix.
-$$\left[ \begin{array} { r r } 
- 3 & 4 \
6 & - 4
\end{array} \right]$$

Accepted Answer

A) 
$\left[ \begin{array} { l } \frac { 1 } { 3 } \frac { 1 } { 3 } \ \frac { 1 } { 2 } \frac { 1 } { 4 } \end{array} \right]$ 
B) 
$\left[ \begin{array} { l l } \frac { 1 } { 2 } & \frac { 1 } { 4 } \ \frac { 1 } { 3 } & \frac { 1 } { 3 } \end{array} \right]$ 
C) 
$\left[\begin{array}{ll}
\frac{1}{4} & \frac{1}{3} \
\frac{1}{2} & \frac{1}{3}
\end{array}\right]$ 
D) 
$\left[\begin{array}{c}
\frac{1}{3}-\frac{1}{3} \
-\frac{1}{2}-\frac{1}{4}
\end{array}\right]$

Question 10

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product
can be calculated.
-$A$ is $1 \times 3 ; B$ is $3 \times 1$.

Accepted Answer

A)  $\mathrm { AB }$ cannot be calculated; $\mathrm { BA }$ is $3 \times 3$. 
B)  $\mathrm { AB }$ is $3 \times 3$; $\mathrm { BA }$ is $1 \times 1$. 
C)  $\mathrm { AB }$ is $1 \times 1$; BA cannot be calculated. 
D)  $\mathrm { AB }$ is $1 \times 1$; $\mathrm { BA }$ is $3 \times 3$.

Question 11

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set.
$\begin{aligned}
x - y & + 5 z = 4 \
3 x & + z = 0 \
x + 4 y & + z = - 16
\end{aligned}$

Accepted Answer

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

Question 12

Solve the linear programming problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane $\mathrm { P } _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $\mathrm { P } _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Accepted Answer

A)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
B)  $5 \mathrm { P } _ { 1 }$ planes and $22 \mathrm { P } _ { 2 }$ planes 
C)  $13 P _ { 1 }$ planes and $9 P _ { 2 }$ planes 
D)  $14 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes

Question 13

Use a graphing calculator to find the value of the determinant.
-$$\left| \begin{array} { r r r } 
- 0.3 & 5.3 & - 4 \
- 0.6 & 7.9 & - 3.1 \
- 9.8 & 6.1 & 4.6
\end{array} \right|$$

Accepted Answer

A)  $- 135.973$ 
B)  $172.705$ 
C)  $- 320.582$ 
D)  $- 487.257$

Question 14

Find the inverse, if it exists, for the matrix.
-$\left[ \begin{array} { l l l } 1 & 0 & 8 \ 1 & 2 & 3 \ 2 & 5 & 3 \end{array} \right]$

Accepted Answer

A)  The inverse does not exist. 
B) 
$$\left[ \begin{array} { l l l } 
1 & 1 & 2 \
0 & 2 & 5 \
8 & 3 & 3
\end{array} \right]$$ 
C) 
$$\left[ \begin{array} { r r r } 
- 1 & 0 & - 8 \
- 1 & - 2 & - 3 \
- 2 & - 5 & - 3
\end{array} \right]$$ 
D)

$$\left[ \begin{array} { r r r } 
9 & - 40 & 16 \
- 3 & 13 & - 5 \
- 1 & 5 & - 2
\end{array} \right]$$

Question 15

The sum of a student's three scores is 223. If the first is 11 points more than the second, and the sum of the first two is 43 more than twice the third, what was the first score?

Accepted Answer

A)  60 points 
B)  76 points 
C)  87 points 
D)  49 points

Question 16

A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 80 red wires.
How many of each type of cable were made?

Accepted Answer

A)  20 A; 15 B; 15 C 
B)  15 A; 16 B; 15 C 
C)  48 A; 20 B; 12 C 
D)  15 A; 20 B; 15 C

Question 17

Find the values of the variables for which the statement is true, if possible.
-$$\left[ \begin{array} { l l } 
0 & 0 \
\mathrm { a } & \mathrm { b }
\end{array} \right] = \left[ \begin{array} { r r } 
0 & \mathrm { q } \
5 & - 7
\end{array} \right]$$

Accepted Answer

A)  $a = 0 ; b = 0 ; q = 0$ 
B)  $a = 5 ; b = - 7 ; q = 0$ 
C)  $a = - 5 ; b = 7 ; q = 0$ 
D)  $a = - 7 ; b = 5 ; q = 0$

Question 18

Find the equation of the circle, written in the form $x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0$ passing through the points  (10,3),(5,-2) , and  (8,7) .

Accepted Answer

A)  $x ^ { 2 } + y ^ { 2 } - 5 x - 3 y + 9 = 0$ 
B)  $x ^ { 2 } + y ^ { 2 } + 10 x + 6 y + 9 = 0$ 
C)  $x ^ { 2 } + y ^ { 2 } - 10 x - 6 y - 2 = 0$ 
D)  $x ^ { 2 } + y ^ { 2 } - 10 x - 6 y + 9 = 0$

Question 19

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

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 20

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)  {(-1.84,-1.52),(1.50,-1.86)} 
C)  {(-1.50,-1.86),(1.84,-1.52)} 
D)  {(-1.50,1.86),(1.84,1.52)}

Exam 6: Systems and Matrices

Graph the solution set of the system of inequalities. - $\begin{array}{l}y \geq-x^{2}-6 x-4 \\y \geq x^{2}+6 x+4\end{array}$ $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2}-6 x-4 \\ y \geq x^{2}+6 x+4 \end{array} A) B) C) D)$

Graph the solution set of the system of inequalities. - $\begin{array} { c } 3 x - 2 y \leq 6 \\x - 1 \geq 0\end{array}$ $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \leq 6 \\ x - 1 \geq 0 \end{array} A) B) C) D)$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. $\begin{array} { l } y = e ^ { x + 3 } \\x ^ { 2 } - 4 y ^ { 2 } = 11\end{array}$

Graph the inequality. - $-2 x-5 y \leq-10$ $Graph the inequality. - -2 x-5 y \leq-10 A) B) C) D)$

Find the dimension of the matrix. - $\left[ \begin{array} { l l } 5 & 0 \\0 & 5\end{array} \right]$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - $\begin{array} { l } y = \log ( x + 7 ) \\y = x ^ { 3 }\end{array}$

Michael's bank contains only nickels, dimes, and quarters. There are 67 coins in all, valued at $5.25. The number of nickels is 1 short of being three times the sum of the number of dimes and quarters. How many dimes are in The bank?

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } - 3 & 4 \\6 & - 4\end{array} \right]$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $1 \times 3 ; B$ is $3 \times 1$ .

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. $\begin{aligned}x - y & + 5 z = 4 \\3 x & + z = 0 \\x + 4 y & + z = - 16\end{aligned}$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } - 0.3 & 5.3 & - 4 \\- 0.6 & 7.9 & - 3.1 \\- 9.8 & 6.1 & 4.6\end{array} \right|$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

The sum of a student's three scores is 223. If the first is 11 points more than the second, and the sum of the first two is 43 more than twice the third, what was the first score?

A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 80 red wires. How many of each type of cable were made?

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { r r } 0 & \mathrm { q } \\5 & - 7\end{array} \right]$

Find the equation of the circle, written in the form $x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0$ passing through the points (10,3) ,(5,-2) , and (8,7) .

Graph the solution set of the system of inequalities. - $\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}$ $Graph the solution set of the system of inequalities. - \begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array} A) B) C) D)$

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

Exam 6: Systems and Matrices

Graph the solution set of the system of inequalities. - y≥−x2−6x−4y≥x2+6x+4\begin{array}{l}y \geq-x^{2}-6 x-4 \\y \geq x^{2}+6 x+4\end{array}y≥−x2−6x−4y≥x2+6x+4​

Graph the solution set of the system of inequalities. - 3x−2y≤6x−1≥0\begin{array} { c } 3 x - 2 y \leq 6 \\x - 1 \geq 0\end{array}3x−2y≤6x−1≥0​

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. y=ex+3x2−4y2=11\begin{array} { l } y = e ^ { x + 3 } \\x ^ { 2 } - 4 y ^ { 2 } = 11\end{array}y=ex+3x2−4y2=11​

Graph the inequality. - −2x−5y≤−10-2 x-5 y \leq-10−2x−5y≤−10

Find the dimension of the matrix. - [5005]\left[ \begin{array} { l l } 5 & 0 \\0 & 5\end{array} \right][50​05​]

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - y=log⁡(x+7) y=x3\begin{array} { l } y = \log ( x + 7 ) \\y = x ^ { 3 }\end{array}y=log(x+7) y=x3​

Michael's bank contains only nickels, dimes, and quarters. There are 67 coins in all, valued at $5.25. The number of nickels is 1 short of being three times the sum of the number of dimes and quarters. How many dimes are in The bank?

Find the inverse, if it exists, for the matrix. - [−346−4]\left[ \begin{array} { r r } - 3 & 4 \\6 & - 4\end{array} \right][−36​4−4​]

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - AAA is 1×3;B1 \times 3 ; B1×3;B is 3×13 \times 13×1 .

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x−y+5z=43x+z=0x+4y+z=−16\begin{aligned}x - y & + 5 z = 4 \\3 x & + z = 0 \\x + 4 y & + z = - 16\end{aligned}x−y3xx+4y​+5z=4+z=0+z=−16​

Use a graphing calculator to find the value of the determinant. - ∣−0.35.3−4−0.67.9−3.1−9.86.14.6∣\left| \begin{array} { r r r } - 0.3 & 5.3 & - 4 \\- 0.6 & 7.9 & - 3.1 \\- 9.8 & 6.1 & 4.6\end{array} \right|​−0.3−0.6−9.8​5.37.96.1​−4−3.14.6​​

Find the inverse, if it exists, for the matrix. - [108123253]\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]​112​025​833​​

The sum of a student's three scores is 223. If the first is 11 points more than the second, and the sum of the first two is 43 more than twice the third, what was the first score?

A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 95 black, 100 white and 80 red wires. How many of each type of cable were made?

Find the values of the variables for which the statement is true, if possible. - [00ab]=[0q5−7]\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { r r } 0 & \mathrm { q } \\5 & - 7\end{array} \right][0a​0b​]=[05​q−7​]

Find the equation of the circle, written in the form x2+y2+ax+by+c=0x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0x2+y2+ax+by+c=0 passing through the points (10,3) ,(5,-2) , and (8,7) .

Graph the solution set of the system of inequalities. - 2x+3y≥6x−y≥3y≤2\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}2x+3y≥6x−y≥3y≤2​

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. y=2x+94x2+y2=5.7\begin{array} { l } y = \sqrt [ 4 ] { 2 x + 9 } \\x ^ { 2 } + y ^ { 2 } = 5.7\end{array}y=42x+9​x2+y2=5.7​

Graph the solution set of the system of inequalities. - $\begin{array}{l}y \geq-x^{2}-6 x-4 \\y \geq x^{2}+6 x+4\end{array}$ $Graph the solution set of the system of inequalities. - \begin{array}{l} y \geq-x^{2}-6 x-4 \\ y \geq x^{2}+6 x+4 \end{array} A) B) C) D)$

Graph the solution set of the system of inequalities. - $\begin{array} { c } 3 x - 2 y \leq 6 \\x - 1 \geq 0\end{array}$ $Graph the solution set of the system of inequalities. - \begin{array} { c } 3 x - 2 y \leq 6 \\ x - 1 \geq 0 \end{array} A) B) C) D)$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. $\begin{array} { l } y = e ^ { x + 3 } \\x ^ { 2 } - 4 y ^ { 2 } = 11\end{array}$

Graph the inequality. - $-2 x-5 y \leq-10$ $Graph the inequality. - -2 x-5 y \leq-10 A) B) C) D)$

Find the dimension of the matrix. - $\left[ \begin{array} { l l } 5 & 0 \\0 & 5\end{array} \right]$

Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth. - $\begin{array} { l } y = \log ( x + 7 ) \\y = x ^ { 3 }\end{array}$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { r r } - 3 & 4 \\6 & - 4\end{array} \right]$

The sizes of two matrices are given. Find the size of the product AB and the size of the product BA, if the given product can be calculated. - $A$ is $1 \times 3 ; B$ is $3 \times 1$ .

Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. $\begin{aligned}x - y & + 5 z = 4 \\3 x & + z = 0 \\x + 4 y & + z = - 16\end{aligned}$

Use a graphing calculator to find the value of the determinant. - $\left| \begin{array} { r r r } - 0.3 & 5.3 & - 4 \\- 0.6 & 7.9 & - 3.1 \\- 9.8 & 6.1 & 4.6\end{array} \right|$

Find the inverse, if it exists, for the matrix. - $\left[ \begin{array} { l l l } 1 & 0 & 8 \\ 1 & 2 & 3 \\ 2 & 5 & 3 \end{array} \right]$

Find the values of the variables for which the statement is true, if possible. - $\left[ \begin{array} { l l } 0 & 0 \\\mathrm { a } & \mathrm { b }\end{array} \right] = \left[ \begin{array} { r r } 0 & \mathrm { q } \\5 & - 7\end{array} \right]$

Find the equation of the circle, written in the form $x ^ { 2 } + y ^ { 2 } + a x + b y + c = 0$ passing through the points (10,3) ,(5,-2) , and (8,7) .

Graph the solution set of the system of inequalities. - $\begin{array}{r}2 x+3 y \geq 6 \\x-y \geq 3 \\y \leq 2\end{array}$ $Graph the solution set of the system of inequalities. - \begin{array}{r} 2 x+3 y \geq 6 \\ x-y \geq 3 \\ y \leq 2 \end{array} A) B) C) D)$

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