Question 1

Identify the ordered triple that is a solution to the system.
-2x - 4y - 6z = 16
--8x - 7y + 7z = -2 4x - 3y - 7z = -8

Accepted Answer

A)  (-5, 9, -7) 
B)  (-11, 3, -1) 
C)  (-5, 3, -3) 
D)  All three points are solutions to the system. 
A)  (-5, 9, -7) 
B)  (-11, 3, -1) 
C)  (-5, 3, -3) 
D)  All three points are solutions to the system. C

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A ________system of equations in two variables is a system in which one or more equations
in the system is nonlinear.

Accepted Answer

nonlinear

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The equation $x ^ { 2 } + y ^ { 2 } = 4$ is a circle centered atـــــــــ with radius ــــــــــThe solution set to the inequality $x ^ { 2 } + y ^ { 2 } < 4$ represents the set of points (inside/outside) the circle $x ^ { 2 } + y ^ { 2 } = 4$.

Accepted Answer

(0, 0); 2; inside

Question 4

Solve the system. If a system has one unique solution, write the solution set. Otherwise, determine the number of solutions to the system, and determine whether the system is inconsistent, or the equations are dependent.
-$\frac { x + 15 } { 12 } + \frac { y + 3 } { 4 } + \frac { z + 12 } { 4 } = 4\]
\[\frac { x + 6 } { 3 } + \frac { y + 11 } { 12 } - \frac { z + 10 } { 3 } = 0\]
\[\frac { x + 5 } { 2 } - \frac { y + 2 } { 3 } + \frac { z + 28 } { 12 } = 2$

Accepted Answer

A)  $\{ ( 0,1 , - 3 ) \}$ 
B)  $\{ ( - 3,1 , - 4 ) \}$ 
C)  $\{ ( - 3 , - 1 , - 8 ) \}$ 
D)  $\{ ( - 1,0 , - 4 ) \}$ 
A)  $\{ ( 0,1 , - 3 ) \}$ 
B)  $\{ ( - 3,1 , - 4 ) \}$ 
C)  $\{ ( - 3 , - 1 , - 8 ) \}$ 
D)  $\{ ( - 1,0 , - 4 ) \}$

Question 5

Solve the problem.
-The hypotenuse of a right triangle is $\sqrt { 89 } \text { in }$ . The sum of the lengths of the legs is 13 in. Find the lengths of the legs.

Accepted Answer

A)  The legs are 6 in. and 9 in. 
B)  The legs are 6 in. and 7 in. 
C)  The legs are 5 in. and 8 in. 
D)  The legs are 4 in. and 9 in. 
A)  The legs are 6 in. and 9 in. 
B)  The legs are 6 in. and 7 in. 
C)  The legs are 5 in. and 8 in. 
D)  The legs are 4 in. and 9 in.

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A solution to a nonlinear system of equations in two variables is an________ pair with real-valued coordinates that satisfies each equation in the system. Graphically, a solution is a point of________of the graphs of the equations.

Accepted Answer

ordered; i

Question 7

Solve the problem.
-A manufacturer produces two models of a gas grill.Grill A requires 0.9 hr for assembly and 0.5 hr for packaging. Grill B requires 1.2 hr for assembly and 0.8 hr for packaging. The production Information and profit for each grill are given in the table. The manufacturer has 1,152 hr of labor Available for assembly and 716 hr of labor available for packaging. $\begin{array} { l | c | c | c } 
& \text { Assembly } & \text { Packaging } & \text { Profit } \
\hline \text { Grill A } & 0.9 \mathrm { hr } & 0.5 \mathrm { hr } & 80 \
\text { Grill B } & 1.2 \mathrm { hr } & 0.8 \mathrm { hr } & 110
\end{array}$
a. Determine the number of grill A units and the number of grill B units that should be produced to Maximize profit assuming that all grills will be sold.
b. What is the maximum profit under these constraints?
c. If the profit on grill A units is 120 and the profit on grill B units is unchanged, how many of each Type of grill unit should the manufacturer produce to maximize profit?

Accepted Answer

A)  a. $\mathrm { A } = 0 , \mathrm {~B} = 895$
b. Profit $= 98,450$
c. 520 units of $A$ and 570 units of B 
B)  a. $A = 520 , B = 570$
b. Profit = 57,656
c. 1,280 units of A and 0 units of B 
C)  a. $\mathrm { A } = 520 , \mathrm {~B} = 570$
b. Profit $= 104,300$
c. 1,280 units of $\mathrm { A }$ and 0 units of $\mathrm { B }$ 
D)  $\mathbf { a } . \mathrm { A } = 1,280 , \mathrm {~B} = 0$
b. Profit $= 102,400$
c. 1,280 units of $\mathrm { A }$ and 0 units of $\mathrm { B }$ 
A)  a. $\mathrm { A } = 0 , \mathrm {~B} = 895$
b. Profit $= 98,450$
c. 520 units of $A$ and 570 units of B 
B)  a. $A = 520 , B = 570$
b. Profit = 57,656
c. 1,280 units of A and 0 units of B 
C)  a. $\mathrm { A } = 520 , \mathrm {~B} = 570$
b. Profit $= 104,300$
c. 1,280 units of $\mathrm { A }$ and 0 units of $\mathrm { B }$ 
D)  $\mathbf { a } . \mathrm { A } = 1,280 , \mathrm {~B} = 0$
b. Profit $= 102,400$
c. 1,280 units of $\mathrm { A }$ and 0 units of $\mathrm { B }$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$5 x + 3 y < 22 , ( 3,2 )$ 
A) No
B) Yes

Accepted Answer

B
Graph th

Question 9

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A diner makes a profit of $1.30 for a cup of coffee and $1.10 for a cup of tea. Write an objective function z = f(x, y) that represents the total profit for selling x cups of coffee and y cups of tea.

Accepted Answer

A)  $z = 0.20 ( x + y )$ 
B)  $z = 1.30 x + 1.10 y$ 
C)  $z = 1.10 x + 1.30 y$ 
D)  $z = 2.40 ( x + y )$ 
A)  $z = 0.20 ( x + y )$ 
B)  $z = 1.30 x + 1.10 y$ 
C)  $z = 1.10 x + 1.30 y$ 
D)  $z = 2.40 ( x + y )$

Question 10

Graph the solution set.
-$$\begin{array} { l } 
4 x - y > 4 \
x + y < 6
\end{array}$$

Accepted Answer

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

Question 11

Determine the values of x and y that produce the minimum value of the objective function on the given
feasible region.
-Minimize $z = 7 x + 3 y$

Accepted Answer

A)  $x = 0 , y = 0$ 
B)  $x = 25 , y = 0$ 
C)  $x = 15 , y = 20$ 
D)  $x = 0 , y = 65$ 
A)  $x = 0 , y = 0$ 
B)  $x = 25 , y = 0$ 
C)  $x = 15 , y = 20$ 
D)  $x = 0 , y = 65$

Question 12

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$$\begin{array} { l } 
| x | < 3 \
| y | < 4
\end{array}$$

Accepted Answer

A)  The solution set is {  } . 
B) 
  
C) 
  
D) 
  
A)  The solution set is {  } . 
B) 
  
C) 
  
D)

Question 13

Graph the solution set. If there is no solution, indicate that the solution set is the empty set.
-$y \leq \frac { 8 } { x }$ $y > 0$ $y < x$

Accepted Answer

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

Question 14

Solve the system by using any method. If a system does not have one unique solution, state whether the
system is inconsistent or whether the equations are dependent.
-$$y = \frac { 7 } { 8 } x + 3$$
$8 y - 7 x = 24$

Accepted Answer

A)  $\left\{ ( x , y ) \mid y = \frac { 7 } { 8 } x + 3 \right\} ;$ The equations are dependent. 
B)  \{ \} ; The system is inconsistent. 
C)  $\left\{ \left( \frac { 3 } { 7 } , \frac { 27 } { 8 } \right) \right\}$ 
D)  $\{ ( 0,3 ) \}$ 
A)  $\left\{ ( x , y ) \mid y = \frac { 7 } { 8 } x + 3 \right\} ;$ The equations are dependent. 
B)  \{ \} ; The system is inconsistent. 
C)  $\left\{ \left( \frac { 3 } { 7 } , \frac { 27 } { 8 } \right) \right\}$ 
D)  $\{ ( 0,3 ) \}$

Question 15

Solve the problem.
-A pharmacist wants to mix a $16 \%$ saline solution with a $26 \%$ saline solution to get $15 \mathrm {~L}$ of a $20 \%$ saline solution. How much of each solution should she use?

Accepted Answer

A)  $10 \mathrm {~L}$ of the $16 \%$ solution; $5 \mathrm {~L}$ of the $26 \%$ solution 
B)  $5 \mathrm {~L}$ of the $16 \%$ solution; $10 \mathrm {~L}$ of the $26 \%$ solution 
C)  $9 \mathrm {~L}$ of the $16 \%$ solution; $6 \mathrm {~L}$ of the $26 \%$ solution 
D)  $6 \mathrm {~L}$ of the $16 \%$ solution; $9 \mathrm {~L}$ of the $26 \%$ solution 
A)  $10 \mathrm {~L}$ of the $16 \%$ solution; $5 \mathrm {~L}$ of the $26 \%$ solution 
B)  $5 \mathrm {~L}$ of the $16 \%$ solution; $10 \mathrm {~L}$ of the $26 \%$ solution 
C)  $9 \mathrm {~L}$ of the $16 \%$ solution; $6 \mathrm {~L}$ of the $26 \%$ solution 
D)  $6 \mathrm {~L}$ of the $16 \%$ solution; $9 \mathrm {~L}$ of the $26 \%$ solution

Question 16

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$$- 2 + 3 ( x + y ) > 4 y - 2$$

Accepted Answer

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

Question 17

Solve the problem.
-Josie invested $13,000 in three different mutual funds. A fund containing large cap stocks made 5.7% return in 1 yr. A real estate fund lost 12.6% in 1 yr, and a bond fund made 3.5% in 1 yr. The
Amount invested in the large cap stock fund was twice the amount invested in the real estate fund. If
Josie had a net return of $162.50 across all investments, how much did she invest in the large cap
Fund?

Accepted Answer

A)  She invested $8,000 in the large cap fund. 
B)  She invested $5,000 in the large cap fund. 
C)  She invested $5,500 in the large cap fund. 
D)  She invested $2,500 in the large cap fund. 
A)  She invested $8,000 in the large cap fund. 
B)  She invested $5,000 in the large cap fund. 
C)  She invested $5,500 in the large cap fund. 
D)  She invested $2,500 in the large cap fund.

Question 18

Determine the values of x and y that produce the minimum value of the objective function on the given
feasible region.
-Minimize: $z = 4 x + 3 y$

Accepted Answer

A)  $x = 6 , y = 2$ 
B)  $x = 2 , y = 8$ 
C)  $x = 7 , y = 10$ 
D)  $x = 8 , y = 4$ 
A)  $x = 6 , y = 2$ 
B)  $x = 2 , y = 8$ 
C)  $x = 7 , y = 10$ 
D)  $x = 8 , y = 4$

Question 19

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution to the inequality.
-$- 2 x \leq 3 y$

Accepted Answer

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

Question 20

Choose the one alternative that best completes the statement or answers the question.
Determine whether the ordered pair is a solution of the system.
-$( 4,2 )$
$$\begin{array} { l } 
6 x - 2 y = 20 \
- 8 x + 3 y = - 26
\end{array}$$

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Identify the ordered triple that is a solution to the system. -2x - 4y - 6z = 16 --8x - 7y + 7z = -2 4x - 3y - 7z = -8

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A ________system of equations in two variables is a system in which one or more equations in the system is nonlinear.

Solve the problem. -The hypotenuse of a right triangle is $\sqrt { 89 } \text { in }$ . The sum of the lengths of the legs is 13 in. Find the lengths of the legs.

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $5 x + 3 y < 22 , ( 3,2 )$ A) No B) Yes

Graph the solution set. - 4x-y>4 x+y<6

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize $z = 7 x + 3 y$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - |x|<3 |y|<4

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $y \leq \frac { 8 } { x }$ $y > 0$ $y < x$

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - $y = \frac { 7 } { 8 } x + 3$ $8 y - 7 x = 24$

Solve the problem. -A pharmacist wants to mix a $16 \%$ saline solution with a $26 \%$ saline solution to get $15 \mathrm {~L}$ of a $20 \%$ saline solution. How much of each solution should she use?

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- 2 + 3 ( x + y ) > 4 y - 2$

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize: $z = 4 x + 3 y$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- 2 x \leq 3 y$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution of the system. - $( 4,2 )$ 6x-2y=20 -8x+3y=-26

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 5: Systems of Equations and Inequalities

Identify the ordered triple that is a solution to the system. -2x - 4y - 6z = 16 --8x - 7y + 7z = -2 4x - 3y - 7z = -8

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A ________system of equations in two variables is a system in which one or more equations in the system is nonlinear.

Solve the problem. -The hypotenuse of a right triangle is 89 in \sqrt { 89 } \text { in }89​ in . The sum of the lengths of the legs is 13 in. Find the lengths of the legs.

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - 5x+3y<22,(3,2)5 x + 3 y < 22 , ( 3,2 )5x+3y<22,(3,2) A) No B) Yes

Graph the solution set. - 4x-y>4 x+y<6

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize z=7x+3yz = 7 x + 3 yz=7x+3y

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - |x|<3 |y|<4

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - y≤8xy \leq \frac { 8 } { x }y≤x8​ y>0y > 0y>0 y<xy < xy<x

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - y=78x+3y = \frac { 7 } { 8 } x + 3y=87​x+3 8y−7x=248 y - 7 x = 248y−7x=24

Solve the problem. -A pharmacist wants to mix a 16%16 \%16% saline solution with a 26%26 \%26% saline solution to get 15 L15 \mathrm {~L}15 L of a 20%20 \%20% saline solution. How much of each solution should she use?

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - −2+3(x+y)>4y−2- 2 + 3 ( x + y ) > 4 y - 2−2+3(x+y)>4y−2

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize: z=4x+3yz = 4 x + 3 yz=4x+3y

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - −2x≤3y- 2 x \leq 3 y−2x≤3y

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution of the system. - (4,2)( 4,2 )(4,2) 6x-2y=20 -8x+3y=-26

Equations and Inequalities

Functions and Relations

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Solve the problem. -The hypotenuse of a right triangle is $\sqrt { 89 } \text { in }$ . The sum of the lengths of the legs is 13 in. Find the lengths of the legs.

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $5 x + 3 y < 22 , ( 3,2 )$ A) No B) Yes

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize $z = 7 x + 3 y$

Graph the solution set. If there is no solution, indicate that the solution set is the empty set. - $y \leq \frac { 8 } { x }$ $y > 0$ $y < x$

Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. - $y = \frac { 7 } { 8 } x + 3$ $8 y - 7 x = 24$

Solve the problem. -A pharmacist wants to mix a $16 \%$ saline solution with a $26 \%$ saline solution to get $15 \mathrm {~L}$ of a $20 \%$ saline solution. How much of each solution should she use?

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- 2 + 3 ( x + y ) > 4 y - 2$

Determine the values of x and y that produce the minimum value of the objective function on the given feasible region. -Minimize: $z = 4 x + 3 y$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution to the inequality. - $- 2 x \leq 3 y$

Choose the one alternative that best completes the statement or answers the question. Determine whether the ordered pair is a solution of the system. - $( 4,2 )$ 6x-2y=20 -8x+3y=-26