Question 1

Solve Linear Systems by Substitution
-$$\begin{aligned}
\mathrm { y } & = 3 \mathrm { x } - 1 \
4 \mathrm { y } + 16 \mathrm { x } & = 80
\end{aligned}$$

Accepted Answer

A)  $\{ ( 3,8 ) \}$ 
B)  $\{ ( 8,3 ) \}$ 
C)  $\{ ( - 3,8 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( 3,8 ) \}$ 
B)  $\{ ( 8,3 ) \}$ 
C)  $\{ ( - 3,8 ) \}$ 
D)  $\varnothing$

Question 2

Use Mathematical Models Involving Linear Inequalities
-A person with no more than $1000 to invest plans to place the money in two investments, telecommunications and pharmaceuticals. The telecommunications investment is to be no more than 3 times the pharmaceuticals investment. Write a system of inequalities to describe the situation. Let x = amount to be invested in telecommunications and y = amount to be invested in pharmaceuticals.

Accepted Answer

A)  $x + y \leq 1000$
$x \leq 3 y$
$x \geq 0$
$y \geq 0$ 
B)  $x + y = 1000$
$x \leq 3 y$
$x \geq 0$
$\mathrm { y } \geq 0$ 
C)  $x + y = 1000$
$y \geq 3 x$
$x \geq 0$
$y \geq 0$ 
D)  $x + y \leq 1000$
$3 x \leq y$
$x \geq 0$
$y \geq 0$ 
A)  $x + y \leq 1000$
$x \leq 3 y$
$x \geq 0$
$y \geq 0$ 
B)  $x + y = 1000$
$x \leq 3 y$
$x \geq 0$
$\mathrm { y } \geq 0$ 
C)  $x + y = 1000$
$y \geq 3 x$
$x \geq 0$
$y \geq 0$ 
D)  $x + y \leq 1000$
$3 x \leq y$
$x \geq 0$
$y \geq 0$

Question 3

Solve Problems Using Systems of Linear Equations
-You invested $\$ 28,800$ and started a business selling vases. Supplies cost $\$ 18$ per vase and you are selling each vase for $\$ 34$. Determine the number of vases, $x$, that must be produced and sold to break even.

Accepted Answer

A)  1800 units 
B)  1801 units 
C)  1802 units 
D)  577 units 
A)  1800 units 
B)  1801 units 
C)  1802 units 
D)  577 units

Question 4

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
y = x ^ { 2 } + 4 \
y = - x ^ { 2 } + 6
\end{array}$$

Accepted Answer

A)  $\{ ( 1,5 ) , ( - 1,5 ) \}$ 
B)  $\{ ( 1,5 ) , ( 1 , - 5 ) , ( - 1,5 ) , ( - 1 , - 5 ) \}$ 
C)  $\{ ( 5,1 ) , ( 5 , - 1 ) \}$ 
D)  $\{ ( 1,5 ) , ( 1 , - 5 ) \}$ 
A)  $\{ ( 1,5 ) , ( - 1,5 ) \}$ 
B)  $\{ ( 1,5 ) , ( 1 , - 5 ) , ( - 1,5 ) , ( - 1 , - 5 ) \}$ 
C)  $\{ ( 5,1 ) , ( 5 , - 1 ) \}$ 
D)  $\{ ( 1,5 ) , ( 1 , - 5 ) \}$

Question 5

Write the partial fraction decomposition of the rational expression.
-$$\frac { 6 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }$$

Accepted Answer

A)  $\frac { 19 } { x } + \frac { - 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
B)  $\frac { 19 } { x } + \frac { 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
C)  $\frac { 19 } { x } + \frac { - 6 } { x + 1 } + \frac { 7 } { x - 1 }$ 
D)  $\frac { 19 } { x } + \frac { - 7 } { x + 1 } + \frac { 6 } { x - 1 }$ 
A)  $\frac { 19 } { x } + \frac { - 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
B)  $\frac { 19 } { x } + \frac { 6 } { x + 1 } + \frac { - 7 } { x - 1 }$ 
C)  $\frac { 19 } { x } + \frac { - 6 } { x + 1 } + \frac { 7 } { x - 1 }$ 
D)  $\frac { 19 } { x } + \frac { - 7 } { x + 1 } + \frac { 6 } { x - 1 }$

Question 6

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l } 
y = 18 - 5 x \
5 x + y = 28
\end{array}$$

Accepted Answer

A)  $\{ ( 12,13 ) \}$ 
B)  $\{ ( 15,3 ) \}$ 
C)  $\{ ( x , y ) \mid 5 x + y = 18 \}$ 
D)  $\varnothing$ ) 
A)  $\{ ( 12,13 ) \}$ 
B)  $\{ ( 15,3 ) \}$ 
C)  $\{ ( x , y ) \mid 5 x + y = 18 \}$ 
D)  $\varnothing$ )

Question 7

Solve Nonlinear Systems By Addition
-$$\begin{array} { l } 
2 x ^ { 2 } + x y - y ^ { 2 } = 3 \
x ^ { 2 } + 2 x y + y ^ { 2 } = 3
\end{array}$$

Accepted Answer

A)  $\left\{ \left( \frac { 2 \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) , \left( - \frac { 2 \sqrt { 3 } } { 3 } , - \frac { \sqrt { 3 } } { 3 } \right) \right\}$ 
B)  $\left\{ \left( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { \sqrt { 3 } } { 3 } \right) , \left( - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) \right\}$ 
C)  $\left\{ \left( \frac { - 2 } { 3 } , \frac { 1 } { 3 } \right) , \left( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { 1 } { 3 } \right) \right\}$ 
D)  $\left\{ \left( \frac { - 2 } { 3 } , - \frac { 1 } { 3 } \right) , \left( \frac { 2 \sqrt { 3 } } { 3 } , \frac { 1 } { 3 } \right) \right\}$ 
A)  $\left\{ \left( \frac { 2 \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) , \left( - \frac { 2 \sqrt { 3 } } { 3 } , - \frac { \sqrt { 3 } } { 3 } \right) \right\}$ 
B)  $\left\{ \left( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { \sqrt { 3 } } { 3 } \right) , \left( - \frac { 2 \sqrt { 3 } } { 3 } , \frac { \sqrt { 3 } } { 3 } \right) \right\}$ 
C)  $\left\{ \left( \frac { - 2 } { 3 } , \frac { 1 } { 3 } \right) , \left( \frac { 2 \sqrt { 3 } } { 3 } , - \frac { 1 } { 3 } \right) \right\}$ 
D)  $\left\{ \left( \frac { - 2 } { 3 } , - \frac { 1 } { 3 } \right) , \left( \frac { 2 \sqrt { 3 } } { 3 } , \frac { 1 } { 3 } \right) \right\}$

Question 8

Use Mathematical Models Involving Linear Inequalities
-Benjamin never has more than 23 hours free during the week. He is trying to make a weekly plan for dividing his free time between reading and working out. He wants to spend at least 8 hours per week reading. Write a system of inequalities to describe the situation. Let $x$ represent the number of hours for reading and $y$ represent the number of hours for working out.

Accepted Answer

A)  $x + y \leq 23$
$x \geq 8$
$y \geq 0$ 
B)  $x + y \leq 23$
$x \geq 8 y$
$x \geq 0$
$y \geq 0$ 
C)  $x + y \leq 23$
$y \geq 8$
$x \geq 0$ 
D)  $x + y \leq 23$
$x \leq 8 y$
$x \geq 0$
$y \geq 0$ 
A)  $x + y \leq 23$
$x \geq 8$
$y \geq 0$ 
B)  $x + y \leq 23$
$x \geq 8 y$
$x \geq 0$
$y \geq 0$ 
C)  $x + y \leq 23$
$y \geq 8$
$x \geq 0$ 
D)  $x + y \leq 23$
$x \leq 8 y$
$x \geq 0$
$y \geq 0$

Question 9

Solve Nonlinear Systems By Substitution
-$$\begin{array} { l } 
x + y = 5 \
y = x ^ { 2 } - 6 x + 9
\end{array}$$

Accepted Answer

A)  $\{ ( 4,1 ) , ( 1,4 ) \}$ 
B)  $\{ ( - 4,9 ) , ( - 1,6 ) \}$ 
C)  $\{ ( 3,2 ) \}$ 
D)  $\{ ( 4,9 ) , ( 1,4 ) \}$ 
A)  $\{ ( 4,1 ) , ( 1,4 ) \}$ 
B)  $\{ ( - 4,9 ) , ( - 1,6 ) \}$ 
C)  $\{ ( 3,2 ) \}$ 
D)  $\{ ( 4,9 ) , ( 1,4 ) \}$

Question 10

Solve Problems Using Systems of Nonlinear Equations
-The sum of the squares of two numbers is 82 . The sum of the two numbers is $- 8$. Find the two numbers.

Accepted Answer

A)  $- 9$ and 1 
B)  $- 9$ and $1 ; - 1$ and 9 
C)  $- 1$ and 9 
D)  $- 9$ and $- 1 ; 1$ and 9 
A)  $- 9$ and 1 
B)  $- 9$ and $1 ; - 1$ and 9 
C)  $- 1$ and 9 
D)  $- 9$ and $- 1 ; 1$ and 9

Question 11

Solve Nonlinear Systems By Addition
-$$x ^ { 2 } + y ^ { 2 } = 145$$
$x ^ { 2 } - y ^ { 2 } = - 17$

Accepted Answer

A)  $\{ ( 8,9 ) , ( - 8,9 ) , ( 8 , - 9 ) , ( - 8 , - 9 ) \}$ 
B)  $\{ ( 8,9 ) , ( 9,8 ) , ( - 8 , - 9 ) , ( - 9 , - 8 ) \}$ 
C)  $\{ ( 8 , - 9 ) , ( 8,9 ) \}$ 
D)  $\{ ( - 8 , - 9 ) , ( - 9 , - 8 ) \}$ 
A)  $\{ ( 8,9 ) , ( - 8,9 ) , ( 8 , - 9 ) , ( - 8 , - 9 ) \}$ 
B)  $\{ ( 8,9 ) , ( 9,8 ) , ( - 8 , - 9 ) , ( - 9 , - 8 ) \}$ 
C)  $\{ ( 8 , - 9 ) , ( 8,9 ) \}$ 
D)  $\{ ( - 8 , - 9 ) , ( - 9 , - 8 ) \}$

Question 12

Solve Problems Using Systems of Nonlinear Equations
-The sum of two squares of two numbers is 29 , and the difference of their squares is 21 . Find the numbers.

Accepted Answer

A)  5 and $2 ; - 5$ and $2 ; 5$ and $- 2 ; - 5$ and $- 2$ 
B)  5 and 2 
C)  5 and $2 ; - 5$ and $- 2$ 
D)  5 and $2 ; - 5$ and $2 ; 5$ and $- 2$ 
A)  5 and $2 ; - 5$ and $2 ; 5$ and $- 2 ; - 5$ and $- 2$ 
B)  5 and 2 
C)  5 and $2 ; - 5$ and $- 2$ 
D)  5 and $2 ; - 5$ and $2 ; 5$ and $- 2$

Question 13

Solve Problems Using Systems in Three Variables
-A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 5 bags of potato chips, and 2 soft drinks for $\$ 10.75$. The price of a hot dog is $\$ 1.25$ more than the price of a bag of potato chips. The cost of a soft drink is $\$ 2.50$ less than the price of two hot dogs. Find the cost of each item.

Accepted Answer

A)  $\$ 2.00$ for a hot dog; $\$ 0.75$ for a bag of potato chips; $\$ 1.50$ for a soft drink 
B)  $\$ 0.75$ for a hot dog; $\$ 2.00$ for a bag of potato chips; $\$ 1.50$ for a soft drink 
C)  $\$ 2.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips; $\$ 0.75$ for a soft drink 
D)  $\$ 2.25$ for a hot dog; $\$ 1.00$ for a bag of potato chips; $\$ 1.50$ for a soft drink 
A)  $\$ 2.00$ for a hot dog; $\$ 0.75$ for a bag of potato chips; $\$ 1.50$ for a soft drink 
B)  $\$ 0.75$ for a hot dog; $\$ 2.00$ for a bag of potato chips; $\$ 1.50$ for a soft drink 
C)  $\$ 2.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips; $\$ 0.75$ for a soft drink 
D)  $\$ 2.25$ for a hot dog; $\$ 1.00$ for a bag of potato chips; $\$ 1.50$ for a soft drink

Question 14

Solve Linear Systems by Addition
-$$\begin{array} { c } 
x - 6 y = - 35 \
- 4 x - 7 y = - 15
\end{array}$$

Accepted Answer

A)  $\{ ( - 5,5 ) \}$ 
B)  $\{ ( - 6,6 ) \}$ 
C)  $\{ ( 5,6 ) \}$ 
D)  $\varnothing$ 
A)  $\{ ( - 5,5 ) \}$ 
B)  $\{ ( - 6,6 ) \}$ 
C)  $\{ ( 5,6 ) \}$ 
D)  $\varnothing$

Question 15

Use Linear Programming to Solve Problems
-Objective Function: $z = - x - 7 y$
Find maximum.

Accepted Answer

A)  maximum: $- 18$ 
B)  maximum: $- 24$ 
C)  maximum: $- 37$ 
D)  maximum: $- 30$ 
A)  maximum: $- 18$ 
B)  maximum: $- 24$ 
C)  maximum: $- 37$ 
D)  maximum: $- 30$

Question 16

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution
-$$\begin{array} { l } 
3 x + y = 11 \
9 x + 3 y = 33
\end{array}$$

Accepted Answer

A)  $\{ ( 0,11 ) \}$ 
B)  $\{ ( 5 , - 4 ) \}$ 
C)  $\{ ( x , y ) \mid 3 x + y = 11 \}$ 
D)  $\varnothing$ ) 
A)  $\{ ( 0,11 ) \}$ 
B)  $\{ ( 5 , - 4 ) \}$ 
C)  $\{ ( x , y ) \mid 3 x + y = 11 \}$ 
D)  $\varnothing$ )

Question 17

Use Linear Programming to Solve Problems
-A doctor has told a sick patient to take vitamin pills. The patient needs at least 45 units of vitamin A, at least 11 units of vitamin $B$, and at least 37 units of vitamin $\mathrm { C }$. The red vitamin pills cost 10 \$ each and contain 6 units of $A , 1$ unit of $B$, and 2 units of $C$. The blue vitamin pills cost $20 c$ each and contain 4 units of $A , 1$ unit of $B$, and 5 units of $C$. How many pills should the patient take each day to minimize costs?

Accepted Answer

A)  6 red and 5 blue 
B)  5 red and 6 blue 
C)  11 red and 0 blue 
D)  7 red and 4 blue 
A)  6 red and 5 blue 
B)  5 red and 6 blue 
C)  11 red and 0 blue 
D)  7 red and 4 blue

Question 18

Solve Problems Using Systems in Three Variables
-Find the values of $a , b$, and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 2,4 ) , ( - 1 , - 4 )$, and $( 4,16 )$.

Accepted Answer

A)  $\mathrm { a } = 2 ; \mathrm { b } = - 2 ; \mathrm { c } = - 8$ 
B)  $\mathrm { a } = 2 ; \mathrm { b } = - 8 ; \mathrm { c } = - 2$ 
C)  $a = - 2 ; b = - 2 ; c = - 8$ 
D)  $\mathrm { a } = - 2 ; \mathrm { b } = - 8 ; \mathrm { c } = - 2$ 
A)  $\mathrm { a } = 2 ; \mathrm { b } = - 2 ; \mathrm { c } = - 8$ 
B)  $\mathrm { a } = 2 ; \mathrm { b } = - 8 ; \mathrm { c } = - 2$ 
C)  $a = - 2 ; b = - 2 ; c = - 8$ 
D)  $\mathrm { a } = - 2 ; \mathrm { b } = - 8 ; \mathrm { c } = - 2$

Question 19

Use Linear Programming to Solve Problems
-Objective Function: $z = x + 8 y + 7$
Find minimum.

Accepted Answer

A)  minimum: 27 
B)  minimum: 49 
C)  minimum: 35 
D)  no minimum 
A)  minimum: 27 
B)  minimum: 49 
C)  minimum: 35 
D)  no minimum

Question 20

Solve Problems Using Systems in Three Variables
-Ms. Adams received a bonus check for $12,000. She decided to divide the money among three different investments. With some of the money, she purchased a municipal bond paying 5.8% simple interest. She invested twice the amount she paid for the municipal bond in a certificate of deposit paying 4.1% simple interest. Ms. Adams placed the balance of the money in a money market account paying 3.1% simple interest. If Ms. Adams' total interest for one year was $428.40, how much was placed in each account?

Accepted Answer

A)  municipal bond: $1200 
B)  municipal bond: $700 certificate of deposit: $2400 certificate of deposit: $1400
Money market: $8400 money market: $9900 
C)  municipal bond: $1700 
D)  municipal bond: $950 certificate of deposit: $3400 certificate of deposit: $1900
Money market: $6900 money market: $9150 
A)  municipal bond: $1200 
B)  municipal bond: $700 certificate of deposit: $2400 certificate of deposit: $1400
Money market: $8400 money market: $9900 
C)  municipal bond: $1700 
D)  municipal bond: $950 certificate of deposit: $3400 certificate of deposit: $1900
Money market: $6900 money market: $9150

Solve Linear Systems by Substitution - =3-1 4+16 =80

Solve Problems Using Systems of Linear Equations -You invested $\$ 28,800$ and started a business selling vases. Supplies cost $\$ 18$ per vase and you are selling each vase for $\$ 34$ . Determine the number of vases, $x$ , that must be produced and sold to break even.

Solve Nonlinear Systems By Addition - y=+4 y=-+6

Write the partial fraction decomposition of the rational expression. - $\frac { 6 x ^ { 2 } - x - 19 } { x ( x + 1 ) ( x - 1 ) }$

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - y=18-5x 5x+y=28

Solve Nonlinear Systems By Addition - 2+xy-=3 +2xy+=3

Solve Nonlinear Systems By Substitution - x+y=5 y=-6x+9

Solve Problems Using Systems of Nonlinear Equations -The sum of the squares of two numbers is 82 . The sum of the two numbers is $- 8$ . Find the two numbers.

Solve Nonlinear Systems By Addition - $x ^ { 2 } + y ^ { 2 } = 145$ $x ^ { 2 } - y ^ { 2 } = - 17$

Solve Problems Using Systems of Nonlinear Equations -The sum of two squares of two numbers is 29 , and the difference of their squares is 21 . Find the numbers.

Solve Linear Systems by Addition - x-6y=-35 -4x-7y=-15

Use Linear Programming to Solve Problems -Objective Function: $z = - x - 7 y$ Find maximum.

Identify Systems That Do Not Have Exactly One Ordered-Pair Solution - 3x+y=11 9x+3y=33

Solve Problems Using Systems in Three Variables -Find the values of $a , b$ , and $c$ such that the graph of the quadratic equation $y = a x ^ { 2 } + b x + c$ passes through the points $( - 2,4 ) , ( - 1 , - 4 )$ , and $( 4,16 )$ .

Use Linear Programming to Solve Problems -Objective Function: $z = x + 8 y + 7$ Find minimum.

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

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Exam 8: Systems of Equations and Inequalities