Question 1

Use the elimination method to solve the system.
-$$\left\{ \begin{array} { l } 
x + y = - 8 \
x - y = 12
\end{array} \right.$$

Accepted Answer

A)  $x = 5 , y = 14$ 
B)  $x = 8 , y = - 10$ 
C)  $x = 2 , y = - 10$ 
D)  $x = 9 , y = 5$ 
A)  $x = 5 , y = 14$ 
B)  $x = 8 , y = - 10$ 
C)  $x = 2 , y = - 10$ 
D)  $x = 9 , y = 5$

Question 2

Graph the inequality.
-$y \leq-8$

Accepted Answer

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

Question 3

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
4 & 0 \
- 1 & - 1
\end{array} \right]$$

Accepted Answer

A)  $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ - \frac { 1 } { 4 } & - 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - 1 & 0 \ - \frac { 1 } { 4 } & \frac { 1 } { 4 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ \frac { 1 } { 4 } & - 1 \end{array} \right]$ 
D)  No inverse 
A)  $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ - \frac { 1 } { 4 } & - 1 \end{array} \right]$ 
B)  $\left[ \begin{array} { c c } - 1 & 0 \ - \frac { 1 } { 4 } & \frac { 1 } { 4 } \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } \frac { 1 } { 4 } & 0 \ \frac { 1 } { 4 } & - 1 \end{array} \right]$ 
D)  No inverse

Question 4

Write the word or phrase that best completes each statement or answers the question.
Show that the matrix has no inverse.
-$A=\left[\begin{array}{rr}
14 & -6 \
-7 & 3
\end{array}\right]$

Accepted Answer

@#IMG-DLM& The matrix @#LAT-DLM& is sufficiently r

Question 5

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

Accepted Answer

A)  $y \geq 0 , x \geq 0 , x \leq 9$, and $y + x \leq 7$ 
B)  $y \geq 0 , x \geq 0 , x \leq 7$, and $y + x \geq 9$ 
C)  $x \leq 7$, and $y + x \leq 9$ 
D)  $y \geq 0 , x \geq 0 , x \leq 7$, and $y + x \leq 9$ 
A)  $y \geq 0 , x \geq 0 , x \leq 9$, and $y + x \leq 7$ 
B)  $y \geq 0 , x \geq 0 , x \leq 7$, and $y + x \geq 9$ 
C)  $x \leq 7$, and $y + x \leq 9$ 
D)  $y \geq 0 , x \geq 0 , x \leq 7$, and $y + x \leq 9$

Question 6

Solve the system of equations by using substitution.
-$$\left\{ \begin{array} { l } 
5 x + 3 y = 80 \
2 x + y = 30
\end{array} \right.$$

Accepted Answer

A)  $x = 0 , y = 0$ 
B)  $x = 10 , y = 10$ 
C)  $x = 0 , y = 10$ 
D)  $x = 10 , y = 0$ 
A)  $x = 0 , y = 0$ 
B)  $x = 10 , y = 10$ 
C)  $x = 0 , y = 10$ 
D)  $x = 10 , y = 0$

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Choose the one alternative that best completes the statement or answers the question.
-$$\frac { 3 x - 2 } { x ^ { 3 } - 1 }$$

Accepted Answer

A)  $\frac { 3 } { x - 1 } + \frac { - 3 ( x - 7 ) } { x ^ { 2 } + x + 1 }$ 
B)  $\frac { \frac { 1 } { 3 } } { x - 1 } + \frac { - \frac { 1 } { 3 } x + \frac { 7 } { 3 } } { \left( x ^ { 2 } + x + 1 \right) }$ 
C)  $\frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { \frac { 1 } { 2 } } { x - 1 } + \frac { \frac { 5 } { 2 } } { x + 1 }$ 
A)  $\frac { 3 } { x - 1 } + \frac { - 3 ( x - 7 ) } { x ^ { 2 } + x + 1 }$ 
B)  $\frac { \frac { 1 } { 3 } } { x - 1 } + \frac { - \frac { 1 } { 3 } x + \frac { 7 } { 3 } } { \left( x ^ { 2 } + x + 1 \right) }$ 
C)  $\frac { 3 } { ( x - 1 ) ^ { 2 } } + \frac { 1 } { ( x - 1 ) ^ { 3 } }$ 
D)  $\frac { \frac { 1 } { 2 } } { x - 1 } + \frac { \frac { 5 } { 2 } } { x + 1 }$

Question 10

Choose the one alternative that best completes the statement or answers the question.
-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 $\mathrm { P } _ { 2 }$ 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)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
B)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
C)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes 
D)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes 
A)  $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes 
B)  $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes 
C)  $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes 
D)  $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes

Question 11

Choose the one alternative that best completes the statement or answers the question.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation h = -16t2 + 600 where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. A second person, in the same building but on a lower floor that is 408 feet from the ground, drops a
White ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation
H = -16(t - 3)2 + 408 where h is measured in feet and t is the number of seconds since the yellow ball was
Dropped. Find the time that the balls are the same distance above the ground and find this distance.

Accepted Answer

A)  2.5 sec; 500 ft 
B)  3.5 sec; 404 ft 
C)  3 sec; 456 ft 
D)  4 sec; 344 ft 
A)  2.5 sec; 500 ft 
B)  3.5 sec; 404 ft 
C)  3 sec; 456 ft 
D)  4 sec; 344 ft

Question 12

2x + 3y ≥6
-$y > x ^ { 2 }$
$7 x + 6 y \leq 42$

Accepted Answer

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

Question 13

Choose the one alternative that best completes the statement or answers the question.
Find the value of the determinant.
-$$\left| \begin{array} { r r } 
- 6 & - 4 \
- 8 & 8
\end{array} \right|$$

Accepted Answer

A)  80 
B)  88 
C)  $- 16$ 
D)  $- 80$ 
A)  80 
B)  88 
C)  $- 16$ 
D)  $- 80$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-Let $\mathrm { A } = \left[ \begin{array} { r r } - 2 & 3 \ 3 & 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } - 2 & 0 \ - 1 & 3 \end{array} \right]$. Find $\mathrm { AB }$.

Accepted Answer

A)  $\left[ \begin{array} { r r } 9 & 1 \ 6 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 1 & 9 \ - 8 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 4 & 0 \ - 3 & 6 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 4 & - 6 \ - 4 & 3 \end{array} \right]$ 
A)  $\left[ \begin{array} { r r } 9 & 1 \ 6 & - 8 \end{array} \right]$ 
B)  $\left[ \begin{array} { r r } 1 & 9 \ - 8 & 6 \end{array} \right]$ 
C)  $\left[ \begin{array} { r r } 4 & 0 \ - 3 & 6 \end{array} \right]$ 
D)  $\left[ \begin{array} { r r } 4 & - 6 \ - 4 & 3 \end{array} \right]$

Question 15

Graph the inequality.
-$y \leq x^{2}+5$

Accepted Answer

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

Question 16

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

Accepted Answer

A)  12 
B)  -6 
C)  $- 12$ 
D)  6 
A)  12 
B)  -6 
C)  $- 12$ 
D)  6

Question 17

Use the elimination method to solve the system.
-$\left\{ \begin{array} { c } 3 x + 48 y = 48 \ 3 x - 6 y = - 6 \ \end{array} \right.$

Accepted Answer

A)  x = 0 , y = 1 
B)  $x = 1 , y = 1$ 
C)  $x = 0 , y = 0$ 
D)  $x = 1 , y = 0$ 
A)  x = 0 , y = 1 
B)  $x = 1 , y = 1$ 
C)  $x = 0 , y = 0$ 
D)  $x = 1 , y = 0$

Question 18

Write the partial fraction decomposition of the rational expression.
-$$\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$$

Accepted Answer

A)  $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$ 
B)  $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } - \frac { 2 } { x + 11 }$ 
C)  $- \frac { 8 } { x + 8 } - \frac { 2 } { x + 2 } - \frac { 2 } { x + 11 }$ 
D)  $- \frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$ 
A)  $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$ 
B)  $\frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } - \frac { 2 } { x + 11 }$ 
C)  $- \frac { 8 } { x + 8 } - \frac { 2 } { x + 2 } - \frac { 2 } { x + 11 }$ 
D)  $- \frac { 8 } { x + 8 } + \frac { 2 } { x + 2 } + \frac { 2 } { x + 11 }$

Question 19

Solve the problem.
-The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 560 people paid admission, the total receipts were $7,390. How many who paid were
Senior citizens?

Accepted Answer

A)  282 senior citizens 
B)  115 senior citizens 
C)  205 senior citizens 
D)  372 senior citizens 
A)  282 senior citizens 
B)  115 senior citizens 
C)  205 senior citizens 
D)  372 senior citizens

Question 20

Find the inverse of the matrix.
-$$\left[ \begin{array} { r r } 
- 1 & 6 \
0 & 2
\end{array} \right]$$

Accepted Answer

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

Use the elimination method to solve the system. - $\left\{ \begin{array} { l } x + y = - 8 \\x - y = 12\end{array} \right.$

Graph the inequality. - $y \leq-8$ $Graph the inequality. - y \leq-8$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 4 & 0 \\- 1 & - 1\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Show that the matrix has no inverse. - $A=\left[\begin{array}{rr}14 & -6 \\-7 & 3\end{array}\right]$

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

Solve the system of equations by using substitution. - $\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.$

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

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

Choose the one alternative that best completes the statement or answers the question. - $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

2x + 3y ≥6 - $y > x ^ { 2 }$ $7 x + 6 y \leq 42$ $2x + 3y ≥6 - y > x ^ { 2 } 7 x + 6 y \leq 42$

Choose the one alternative that best completes the statement or answers the question. Find the value of the determinant. - $\left| \begin{array} { r r } - 6 & - 4 \\- 8 & 8\end{array} \right|$

Choose the one alternative that best completes the statement or answers the question. -Let $\mathrm { A } = \left[ \begin{array} { r r } - 2 & 3 \\ 3 & 2 \end{array} \right]$ and $\mathrm { B } = \left[ \begin{array} { l l } - 2 & 0 \\ - 1 & 3 \end{array} \right]$ . Find $\mathrm { AB }$ .

Graph the inequality. - $y \leq x^{2}+5$ $Graph the inequality. - y \leq x^{2}+5$

Use the elimination method to solve the system. - $\left\{ \begin{array} { c } 3 x + 48 y = 48 \\ 3 x - 6 y = - 6 \\ \end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$

Solve the problem. -The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 560 people paid admission, the total receipts were $7,390. How many who paid were Senior citizens?

Find the inverse of the matrix. - $\left[ \begin{array} { r r } - 1 & 6 \\0 & 2\end{array} \right]$

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

Use the elimination method to solve the system. - {x+y=−8x−y=12\left\{ \begin{array} { l } x + y = - 8 \\x - y = 12\end{array} \right.{x+y=−8x−y=12​

Graph the inequality. - y≤−8y \leq-8y≤−8

Find the inverse of the matrix. - [40−1−1]\left[ \begin{array} { r r } 4 & 0 \\- 1 & - 1\end{array} \right][4−1​0−1​]

Write the word or phrase that best completes each statement or answers the question. Show that the matrix has no inverse. - A=[14−6−73]A=\left[\begin{array}{rr}14 & -6 \\-7 & 3\end{array}\right]A=[14−7​−63​]

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

Solve the system of equations by using substitution. - {5x+3y=802x+y=30\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.{5x+3y=802x+y=30​

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​

2x + 3y ≥6 - {2x+3y≥6x−y≥3y≤2\left\{ \begin{aligned}2 x + 3 y & \geq 6 \\x - y & \geq 3 \\y & \leq 2\end{aligned} \right.⎩⎨⎧​2x+3yx−yy​≥6≥3≤2​

Choose the one alternative that best completes the statement or answers the question. - 3x−2x3−1\frac { 3 x - 2 } { x ^ { 3 } - 1 }x3−13x−2​

2x + 3y ≥6 - y>x2y > x ^ { 2 }y>x2 7x+6y≤427 x + 6 y \leq 427x+6y≤42

Choose the one alternative that best completes the statement or answers the question. Find the value of the determinant. - ∣−6−4−88∣\left| \begin{array} { r r } - 6 & - 4 \\- 8 & 8\end{array} \right|​−6−8​−48​​

Graph the inequality. - y≤x2+5y \leq x^{2}+5y≤x2+5

Use the elimination method to solve the system. - {3x+48y=483x−6y=−6\left\{ \begin{array} { c } 3 x + 48 y = 48 \\ 3 x - 6 y = - 6 \\ \end{array} \right.{3x+48y=483x−6y=−6​

Write the partial fraction decomposition of the rational expression. - 12x2+162x+384(x+8)(x+2)(x+11)\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }(x+8)(x+2)(x+11)12x2+162x+384​

Solve the problem. -The Family Fine Arts Center charges $20 per adult and $10 per senior citizen for its performances. On a recent weekend evening when 560 people paid admission, the total receipts were $7,390. How many who paid were Senior citizens?

Find the inverse of the matrix. - [−1602]\left[ \begin{array} { r r } - 1 & 6 \\0 & 2\end{array} \right][−10​62​]

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

Use the elimination method to solve the system. - $\left\{ \begin{array} { l } x + y = - 8 \\x - y = 12\end{array} \right.$

Graph the inequality. - $y \leq-8$ $Graph the inequality. - y \leq-8$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } 4 & 0 \\- 1 & - 1\end{array} \right]$

Write the word or phrase that best completes each statement or answers the question. Show that the matrix has no inverse. - $A=\left[\begin{array}{rr}14 & -6 \\-7 & 3\end{array}\right]$

Solve the system of equations by using substitution. - $\left\{ \begin{array} { l } 5 x + 3 y = 80 \\2 x + y = 30\end{array} \right.$

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

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

Choose the one alternative that best completes the statement or answers the question. - $\frac { 3 x - 2 } { x ^ { 3 } - 1 }$

2x + 3y ≥6 - $y > x ^ { 2 }$ $7 x + 6 y \leq 42$ $2x + 3y ≥6 - y > x ^ { 2 } 7 x + 6 y \leq 42$

Choose the one alternative that best completes the statement or answers the question. Find the value of the determinant. - $\left| \begin{array} { r r } - 6 & - 4 \\- 8 & 8\end{array} \right|$

Graph the inequality. - $y \leq x^{2}+5$ $Graph the inequality. - y \leq x^{2}+5$

Use the elimination method to solve the system. - $\left\{ \begin{array} { c } 3 x + 48 y = 48 \\ 3 x - 6 y = - 6 \\ \end{array} \right.$

Write the partial fraction decomposition of the rational expression. - $\frac { 12 x ^ { 2 } + 162 x + 384 } { ( x + 8 ) ( x + 2 ) ( x + 11 ) }$

Find the inverse of the matrix. - $\left[ \begin{array} { r r } - 1 & 6 \\0 & 2\end{array} \right]$