Question 1

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { l } 
x ^ { 2 } + y ^ { 2 } = 9 \
x - 9 y = 10
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 2

Use the properties of determinants to find the value of the second determinant, given the value of the first.
-$$\left| \begin{array} { c c c } 
x & y & z \
u & v & w \
1 & - 3 & - 3
\end{array} \right| = 66 \left| \begin{array} { r r r } 
x & y & z \
u & v & w \
- 2 & 6 & 6
\end{array} \right| = ?$$

Accepted Answer

A)  66 
B)  132 
C)  -66 
D)  -132 
A)  66 
B)  132 
C)  -66 
D)  -132

Question 3

Solve the system of equations.
-$$\left\{ \begin{aligned}
x + y + z & = 0 \
x - y + 4 z & = - 11 \
3 x + 3 y + 3 z & = 4
\end{aligned} \right.$$

Accepted Answer

A)  $x = - 3 , y = 1 , z = 2$ 
B)  $x = - 3 , y = 2 , z = 1$ 
C)  $x = 2 , y = 1 , z = - 3$ 
D)  inconsistent (no solution) 
A)  $x = - 3 , y = 1 , z = 2$ 
B)  $x = - 3 , y = 2 , z = 1$ 
C)  $x = 2 , y = 1 , z = - 3$ 
D)  inconsistent (no solution)

Question 4

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$$\begin{array} { l } 
x ^ { 2 } - y ^ { 2 } = 36 \
3 x - y = - 6
\end{array}$$

Accepted Answer

Substitution should be used, b

Question 5

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary.
-$$\left[ \begin{array} { r r r } 
- 16 & 3 & 28 \
5 & - 14 & 15 \
34 & 25 & 2
\end{array} \right]$$

Accepted Answer

A) $\left[\begin{array}{rrr}
-0.02 & 0.03 & 0.02 \
0.02 & -0.04 & 0.01 \
0.02 & 0.02 & 0.00
\end{array}\right]$

В)$\left[\begin{array}{rrr}
-0.02 & 0.03 & 0.02 \
0.02 & -0.04 & 0.02 \
0.02 & 0.02 & 0.01
\end{array}\right]$ 
C)  $\left[\begin{array}{rrr}
-0.01 & 0.03 & 0.02 \
0.02 & -0.03 & 0.01 \
0.02 & 0.02 & 0.01
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-0.01 & 0.02 & 0.01 \
0.02 & -0.03 & 0.01 \
0.02 & 0.02 & 0.01
\end{array}\right]$ 
A) $\left[\begin{array}{rrr}
-0.02 & 0.03 & 0.02 \
0.02 & -0.04 & 0.01 \
0.02 & 0.02 & 0.00
\end{array}\right]$

В)$\left[\begin{array}{rrr}
-0.02 & 0.03 & 0.02 \
0.02 & -0.04 & 0.02 \
0.02 & 0.02 & 0.01
\end{array}\right]$ 
C)  $\left[\begin{array}{rrr}
-0.01 & 0.03 & 0.02 \
0.02 & -0.03 & 0.01 \
0.02 & 0.02 & 0.01
\end{array}\right]$ 
D) $\left[\begin{array}{rrr}
-0.01 & 0.02 & 0.01 \
0.02 & -0.03 & 0.01 \
0.02 & 0.02 & 0.01
\end{array}\right]$

Question 6

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

A)

Accepted Answer

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

Question 7

Find the value(s) of the function, subject to the system of inequalities.
-Find the maximum and minimum of $$z = 18 x + 24 y \text { subject to } x \geq 0 , y \geq 0,4 x + 5 y \leq 30,4 x + 3 y \leq 20 , x \leq 5 , y \leq 8$$

Accepted Answer

A)  -144; 0 
B)  -97.5; -144 
C)  90; 0 
D)  90; -144 
A)  -144; 0 
B)  -97.5; -144 
C)  90; 0 
D)  90; -144

Question 8

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

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 9

Verify that the values of the variables listed are solutions of the system of equations.
-$$\begin{array} { l } 
\left\{ \begin{array} { c } 
x + y + z = 6 \
x - y + 4 z = 14 \
5 x + y + z = 26
\end{array} \right. \
x = 5 , y = - 1 , z = 2
\end{array}$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Question 10

Solve the problem.
-$$\text { Given that } \left| \begin{array} { l l l } 
x & y & z \
a & b & c \
2 & 4 & 5
\end{array} \right| = 3 \text {, find the value of the determinant } \left| \begin{array} { l l l } 
2 & 4 & 5 \
3 a & 3 b & 3 c \
x - 2 & y - 4 & z - 5
\end{array} \right|$$

Accepted Answer

A)  -9 
B)  0 
C)  9 
D)  6 
A)  -9 
B)  0 
C)  9 
D)  6

Question 11

Perform the row operation(s) on the given augmented matrix.
-$$\begin{array} { l } 
R _ { 2 } = - 2 r _ { 2 } + r \
{ \left[ \begin{array} { r r r | r } 
2 & 4 & 6 & - 8 \
1 & 2 & 3 & 6 \
4 & 6 & 7 & 1
\end{array} \right] }
\end{array}$$

Accepted Answer

A)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & 0 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & 6 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & - 20 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ 0 & 0 & 0 & 0 \ 4 & 6 & 7 & 1 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r | r } 2 & 4 & 6 & - 8 \ - 4 & - 8 & - 12 & 6 \ 4 & 6 & 7 & 1 \end{array} \right]$

Question 12

Perform the indicated operations and simplify.
-Let $A = \left[ \begin{array} { r r } 3 & - 4 \ - 2 & 5 \end{array} \right] , B = \left[ \begin{array} { r r r } 5 & - 2 & 8 \ 1 & 0 & - 3 \end{array} \right]$, and $C = \left[ \begin{array} { r r r } 7 & - 9 & 0 \ 3 & - 5 & 1 \ - 1 & 6 & 2 \end{array} \right]$. Find $A B + B C$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } 68 & 3 & 31 \ 8 & - 2 & - 5 \end{array} \right]$

В) $\left[ \begin{array} { l r r } 32 & 7 & 50 \ 5 & - 23 & - 37 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 10 & - 19 & 12 \ - 15 & 31 & - 25 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 32 & 19 & 40 \ - 15 & 31 & - 37 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } 68 & 3 & 31 \ 8 & - 2 & - 5 \end{array} \right]$

В) $\left[ \begin{array} { l r r } 32 & 7 & 50 \ 5 & - 23 & - 37 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 10 & - 19 & 12 \ - 15 & 31 & - 25 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } 32 & 19 & 40 \ - 15 & 31 & - 37 \end{array} \right]$

Question 13

Graph the inequality.
-$2 x+3 y \leq 6$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 14

Solve the problem.
-The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Accepted Answer

A)  width = 3.9 ft, length = 9.7 ft 
B)  width = 9.7 ft, length = 22.4 ft 
C)  width = 2 ft, length = 9 ft 
D)  width = 4 ft, length = 11 ft 
A)  width = 3.9 ft, length = 9.7 ft 
B)  width = 9.7 ft, length = 22.4 ft 
C)  width = 2 ft, length = 9 ft 
D)  width = 4 ft, length = 11 ft

Question 15

Solve the problem.
-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. A)
$\begin{array}{l}
x+y \leq 130 \
x>0.20 y \
x \geq 0 \
y \geq 0
\end{array}$

Accepted Answer

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) $\begin{array}{l} x+y=130 \ x \geq 0.20 y \ x \geq 0 \ y \geq 0 \end{array}$ 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 16

Graph the system of inequalities.
-$\left\{\begin{aligned}
4 x+3 y & \geq 12 \
x & \geq y
\end{aligned}\right.$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 17

Graph the system of inequalities.
-$\begin{array}{l}
y>x^{2} \
2 x+5 y \leq 10
\end{array}$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 18

Graph the system of inequalities.
-$\begin{array}{l}
y>x^{2} \
7 x+6 y \leq 42
\end{array}$

A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 19

Perform the indicated matrix operations.
-Let $A = \left[ \begin{array} { r r r } - 6 & - 6 & - 3 \ - 3 & 2 & - 8 \ 5 & - 2 & - 7 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 5 & - 5 & - 1 \ 7 & - 6 & 1 \ 1 & - 5 & - 2 \end{array} \right]$. Find $2 A - 2 B$.

Accepted Answer

A)  $\left[ \begin{array} { r r r } - 11 & 4 & 6 \ - 11 & - 4 & - 7 \ - 4 & - 7 & - 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 11 & - 11 & - 4 \ 4 & - 4 & - 7 \ 6 & - 7 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 17 & - 17 & - 7 \ 1 & - 2 & - 15 \ 11 & - 9 & - 16 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 2 & - 2 & - 4 \ - 20 & 16 & - 18 \ 8 & 6 & - 10 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r r } - 11 & 4 & 6 \ - 11 & - 4 & - 7 \ - 4 & - 7 & - 9 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r r } - 11 & - 11 & - 4 \ 4 & - 4 & - 7 \ 6 & - 7 & - 9 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r r } - 17 & - 17 & - 7 \ 1 & - 2 & - 15 \ 11 & - 9 & - 16 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r r } - 2 & - 2 & - 4 \ - 20 & 16 & - 18 \ 8 & 6 & - 10 \end{array} \right]$

Question 20

Verify that the values of the variables listed are solutions of the system of equations.
-$$\begin{array} { l } 
\left\{ \begin{array} { l } 
4 x + y = 13 \
2 x + 4 y = 24
\end{array} \right. \
x = 2 , y = 5
\end{array}$$

Accepted Answer

A)  not a solution 
B)  solution 
A)  not a solution 
B)  solution

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=9 x-9y=10

Use the properties of determinants to find the value of the second determinant, given the value of the first. - $\left| \begin{array} { c c c } x & y & z \\u & v & w \\1 & - 3 & - 3\end{array} \right| = 66 \left| \begin{array} { r r r } x & y & z \\u & v & w \\- 2 & 6 & 6\end{array} \right| = ?$

Solve the system of equations. - $\left\{ \begin{aligned}x + y + z & = 0 \\x - y + 4 z & = - 11 \\3 x + 3 y + 3 z & = 4\end{aligned} \right.$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=36 3x-y=-6

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r } - 16 & 3 & 28 \\5 & - 14 & 15 \\34 & 25 & 2\end{array} \right]$

Find the value(s) of the function, subject to the system of inequalities. -Find the maximum and minimum of $z = 18 x + 24 y \text { subject to } x \geq 0 , y \geq 0,4 x + 5 y \leq 30,4 x + 3 y \leq 20 , x \leq 5 , y \leq 8$

Verify that the values of the variables listed are solutions of the system of equations. - x+y+z=6 x-y+4z=14 5x+y+z=26 x=5,y=-1,z=2

Solve the problem. - $\text { Given that } \left| \begin{array} { l l l } x & y & z \\a & b & c \\2 & 4 & 5\end{array} \right| = 3 \text {, find the value of the determinant } \left| \begin{array} { l l l } 2 & 4 & 5 \\3 a & 3 b & 3 c \\x - 2 & y - 4 & z - 5\end{array} \right|$

Perform the row operation(s) on the given augmented matrix. - =-2+r 2 4 6 -8 1 2 3 6 4 6 7 1

Solve the problem. -The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Perform the indicated matrix operations. -Let $A = \left[ \begin{array} { r r r } - 6 & - 6 & - 3 \\ - 3 & 2 & - 8 \\ 5 & - 2 & - 7 \end{array} \right]$ and $B = \left[ \begin{array} { r r r } - 5 & - 5 & - 1 \\ 7 & - 6 & 1 \\ 1 & - 5 & - 2 \end{array} \right]$ . Find $2 A - 2 B$ .

Verify that the values of the variables listed are solutions of the system of equations. - 4x+y=13 2x+4y=24 x=2,y=5

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

Review

Filters

Exam 10: Systems of Equations and Inequalities

Which method should be used to solve the system? Explain your answer, including a description of the first step. - +=9 x-9y=10

Solve the system of equations. - {x+y+z=0x−y+4z=−113x+3y+3z=4\left\{ \begin{aligned}x + y + z & = 0 \\x - y + 4 z & = - 11 \\3 x + 3 y + 3 z & = 4\end{aligned} \right.⎩⎨⎧​x+y+zx−y+4z3x+3y+3z​=0=−11=4​

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -=36 3x-y=-6

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - [−163285−141534252]\left[ \begin{array} { r r r } - 16 & 3 & 28 \\5 & - 14 & 15 \\34 & 25 & 2\end{array} \right]​−16534​3−1425​28152​​

Graph the system of inequalities. - 2x+3y\leq6 x-y\geq3 x\geq1 A) B) C) D)

Graph the system of inequalities. - {2x+3y≤6x−y≤3\left\{\begin{array}{r}2 x+3 y \leq 6 \\x-y \leq 3\end{array}\right.{2x+3y≤6x−y≤3​ A) B) C) D)

Verify that the values of the variables listed are solutions of the system of equations. - x+y+z=6 x-y+4z=14 5x+y+z=26 x=5,y=-1,z=2

Perform the row operation(s) on the given augmented matrix. - =-2+r 2 4 6 -8 1 2 3 6 4 6 7 1

Graph the inequality. - 2x+3y≤62 x+3 y \leq 62x+3y≤6 A) B) C) D)

Solve the problem. -The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.

Graph the system of inequalities. - {4x+3y≥12x≥y\left\{\begin{aligned}4 x+3 y & \geq 12 \\x & \geq y\end{aligned}\right.{4x+3yx​≥12≥y​ A) B) C) D)

Graph the system of inequalities. - y> 2x+5y\leq10 A) B) C) D)

Graph the system of inequalities. - y> 7x+6y\leq42 A) B) C) D) 11ed85da_92d6_0e7e_a8cb_8df47af1905d_TB7697_11

Verify that the values of the variables listed are solutions of the system of equations. - 4x+y=13 2x+4y=24 x=2,y=5

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

Review

Filters

Solve the system of equations. - $\left\{ \begin{aligned}x + y + z & = 0 \\x - y + 4 z & = - 11 \\3 x + 3 y + 3 z & = 4\end{aligned} \right.$

Use a graphing utility to find the inverse of the matrix, if it exists. Round answers to two decimal places, if necessary. - $\left[ \begin{array} { r r r } - 16 & 3 & 28 \\5 & - 14 & 15 \\34 & 25 & 2\end{array} \right]$