Deck 2: Linear Models, Equations, and Inequalities

Question 1

$$21 s + 40 = - 4 s$$

A) $\frac { 8 } { 5 }$
B) $- \frac { 8 } { 5 }$
C) $\frac { 40 } { 17 }$
D) $\frac { 5 } { 8 }$

Answer 1

B

Question 2

$$\frac { 1 } { 2 } y - \left( y - \frac { 1 } { 2 } \right) = \frac { 1 } { 32 } ( y + 5 )$$

A) $\frac { 11 } { 17 }$
B) $\frac { 11 } { 15 }$
C) $- \frac { 21 } { 17 }$
D) $- \frac { 11 } { 47 }$

Answer 2

A

Question 3

$$3 ( 2 z - 3 ) = 5 ( z + 4 )$$

A) 14
B) 11
C) 29
D) $- 11$

Answer 3

C

Question 4

$$\frac { 1 } { 5 } ( r + 6 ) = \frac { 1 } { 7 } ( r + 8 )$$

A) $- 1$
B) 2
C) $- 2$
D) 1

Question 5

$- 11.2 q = - 116.4 - 1.5 q$

A) $10.5$
В) $- 126$
C) $10.4$
D) 12

Question 6

$$9 x - ( 4 x - 1 ) = 2$$

A) $\frac { 1 } { 5 }$
B) $- \frac { 1 } { 13 }$
C) $\frac { 1 } { 13 }$
D) $- \frac { 1 } { 5 }$

Question 7

$$- 7.6 q + 1.4 = - 41.3 - 1.5 q$$

A) 7
B) $5.6$
C) $- 49$
D) $5.8$

Question 8

$$\frac { 6 x + 7 } { 7 } + \frac { 3 } { 7 } = - \frac { 4 x } { 7 }$$

A) - 1
B) $- \frac { 2 } { 5 }$
C) $- 5$
D) $\frac { 2 } { 5 }$

Question 9

$$13 ( 7 c - 4 ) = 5 c - 8$$

A) $\frac { 11 } { 48 }$
B) $\frac { 60 } { 43 }$
$C ) - \frac { 22 } { 43 }$
D) $\frac { 22 } { 43 }$

Question 10

$$4 ( y + 4 ) = 5 ( y - 6 )$$

A) $- 46$
B) 14
C) $- 14$
D) 46

Question 11

$$- \frac { 1 } { 2 } ( x - 6 ) - \frac { 1 } { 3 } ( x - 3 ) = x + 1$$

A) $- \frac { 30 } { 11 }$
B) $- \frac { 18 } { 11 }$
C) $\frac { 18 } { 11 }$
D) $\frac { 6 } { 11 }$

Question 12

$$\frac { 1 } { 3 } ( 9 x - 15 ) = \frac { 1 } { 2 } ( 10 x - 6 )$$

A) $- 1$
B) $- 15$
C) 1
D) $\frac { 1 } { 15 }$

Question 13

$$\frac { r + 6 } { 5 } = \frac { r + 8 } { 7 }$$

A) 2
B) $- 1$
C) $- 2$
D) 1

Question 14

$$( y - 7 ) - ( y + 2 ) = 4 y$$

A) $= \frac { 1 } { 2 }$
B) $- \frac { 9 } { 7 }$
$C ) = \frac { 9 } { 4 }$
D) $- \frac { 9 } { 5 }$

Question 15

$$- 3 x + 4 ( - 2 x - 7 ) = - 31 - 8 x$$

A) $- 1$
B) $\frac { 59 } { 19 }$
C) 1
D) $\frac { 59 } { 3 }$

Question 16

$$6 ( 3 x - 1 ) = 24$$

A) 1
В) $\frac { 5 } { 3 }$
C) $\frac { 25 } { 18 }$
D) $\frac { 23 } { 18 }$

Question 17

$$\frac { 2 } { 5 } x - \frac { 1 } { 3 } x = 5$$

A) 75
B) $- 150$
C) $- 75$
D) 150

Question 18

$$24 x - 2 = 6$$

A) $- \frac { 1 } { 3 }$
B) $\frac { 7 } { 24 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 1 } { 6 }$

Question 19

$$- 4.6 = y + 8$$

A) $- 3.4$
B) $3.4$
C) $12.6$
D) $- 12.6$

Question 20

$$19 t - 47 = 7 t - 15$$

A) $- \frac { 19 } { 62 }$
B) $\frac { 8 } { 3 }$
C) $- \frac { 13 } { 22 }$
D) $- \frac { 8 } { 3 }$

Question 21

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the
question.
What is the $y$ -intercept of the graph of $y = f ( x )$ ?

A) 0
B) $- 3$
C) 3
D) $- 1$

Question 22

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. $- 4$
b. $x = 0$
B) a. $- 5$
b. $x = - 5$
C) a. 0
b. $x = - 4$
D) a. $- 4$
b. $x = - 4$

Question 23

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. $5.5$
b. $x = 5.5$
B) a. 0
b. $x = 5.5$
C) a. $5.5$
b. $x = 0$
D) a. 5
b. $x = 5$

Question 24

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the
question.
What is the $y$ -intercept of the graph of $y = f ( x )$ ?

A) 1
B) $- 3$
C) 0
D) 3

Question 25

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the
question.
What is the $x$ -intercept of the graph of $y = f ( x )$ ?

A) $- 1$
B) 0
C) 6
D) $- 2$

Question 26

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the
question.
What is the $y$ -intercept of the graph of $y = f ( x )$ ?

A) 1
B) 5
C) $- 3$
D) 0

Question 27

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. 5
b. $x = 0$
B) a. $- 5$
b. $x = - 5$
C) a. 5
b. $x = 5$
D) a. 0
b. $x = 5$

Question 28

Find the zero of f(x).
$$f ( x ) = 6 x + 12$$

A) $- 12$
B) 2
C) $- 2$
D) 12

Question 29

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. $- 5$
b. $x = 0$
B) a. 0
b. $x = - 5$
C) a. $- 6$
b. $x = - 6$
D) a. $- 5$
b. $x = - 5$

Question 30

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$$- 5 x + 9 = - 1 + 8 x$$

A) $x = 0.375$
B) $x = 1.3$
C) $x = 0.769$
D) $x = - 1.3$

Question 31

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. 0
b. $x = 4$
B) a. 4
b. $x = 0$
C) a. 5
b. $x = 5$
D) a. 4
b. $x = 4$

Question 32

Find the zero of f(x).
$$f ( x ) = \frac { 1 } { 6 } x$$

A) 6
B) does not exist
C) 0
D) $- 6$

Question 33

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. 0
b. $x = 2.5$
B) a. $2.5$
b. $x = 0$
C) a. $- 2.5$
b. $x = - 2.5$
D) a. $2.5$
b. $x = 2.5$

Question 34

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. 15
b. $x = 15$
B) a. 15
b. $x = 0$
C) a. 0
b. $x = 15$
D) a. 15
b. $x = - 15$

Question 35

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. $- 2$
b. $x = - 2$
B) a. 0
b. $x = - 2$
C) a. $- 2$
b. $x = 0$
D) a. $- 1$
b. $x = - 1$

Question 36

Find the zero of f(x).
$$f ( x ) = 9 x$$

A) 0
B) does not exist
C) 9
D) $- 9$

Question 37

Find the zero of f(x).
$$f ( x ) = \frac { 1 } { 5 } x + \frac { 1 } { 10 }$$

A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$
C) $- \frac { 1 } { 10 }$
D) $\frac { 1 } { 10 }$

Question 38

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. 0
b. $x = 12$
B) a. 12
b. $x = 0$
C) a. 12
b. $x = 12$
D) a. 0
b. $x = 0$

Question 39

You are given a table showing input and output values for a given function $y _ { 1 } = f ( x )$ x). Use the table to answer the
question.
\[\begin{array}{l}
\text { What is the } y \text {-intercept of the graph of } y = f ( x ) \text { ? }\\

A) 10
B) 0
C) 7
D) 1

Question 40

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ .

A) a. $- 6.5$
b. $x = 0$
B) a. 0
b. $x = - 6.5$
C) a. $- 6.5$
b. $x = - 6.5$
D) a. $6.5$
b. $x = 6.5$

Question 41

Solve the formula for the specified variable.
$- 6 \mathrm { k } + \mathrm { ar } = \mathrm { r } - 9 \mathrm { y }$ for $\mathrm { r }$

A) $r = \frac { a - 1 } { 6 k - 9 y }$ or $r = \frac { 1 - a } { - 6 k + 9 y }$
B) $r = \frac { - 6 k + a } { 1 - 9 y }$ or $r = \frac { 6 k - a } { 9 y - 1 }$
C) $r = \frac { 6 k - 9 y } { a - 1 }$ or $r = \frac { - 6 k + 9 y } { 1 - a }$
D) $r = \frac { - 6 k + 9 y } { a - 1 }$ or $r = \frac { 6 k - 9 y } { 1 - a }$

Question 42

Solve the equation for y.
$$x - 5 y = 4$$

A) $y = 5 x - 4$
B) $y = \frac { 1 } { 5 } x - 4$
C) $y = \frac { 1 } { 5 } x - \frac { 4 } { 5 }$
D) $y = x - \frac { 4 } { 5 }$

Question 43

Solve the formula for the specified variable.
$\mathrm { P } = \mathrm { a } + \mathrm { b } + \mathrm { c }$ for $a$

A) $a = P - b - c$
B) $a = b + c - P$
C) $a = b + P - c$
D) $a = P + b + c$

Question 44

Solve the equation for y.
$3 x - 10 y = - 6$

A) $y = \frac { 10 } { 3 } x - 2$
B) $y = 3 x + 11$
C) $y = - \frac { 3 } { 10 } x + \frac { 3 } { 5 }$
D) $y = \frac { 3 } { 10 } x + \frac { 3 } { 5 }$

Question 45

Solve the formula for the specified variable.
$\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for $\mathrm { b }$

A) $b = \frac { A } { 2 h }$
B) $b = \frac { \mathrm { Ah } } { 2 }$
$C ) b = \frac { 2 A } { h }$
D) $b = \frac { h } { 2 A }$

Question 46

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$- 4 x + 4 - 7 ( x + 1 ) = 3 x - 2$

A) $x = - 0.25$
B) $x = - 0.643$
C) $x = - 0.071$
D) $x = - 2.25$

Question 47

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$$8 x + 4 ( 1 + x ) = 3 ( x - 6 ) + 10 x$$

A) $x = 7$
B) $x = - 22$
C) $x = - 7$
D) $x = 22$

Question 48

Solve the formula for the specified variable.
$$\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \text { for } \mathrm { C }$$

A) $C = \frac { 5 } { F - 32 }$
B) $C = \frac { F - 32 } { 9 }$
C) $C = \frac { 9 } { 5 } ( F - 32 )$
D) $\mathrm { C } = \frac { 5 } { 9 } ( \mathrm {~F} - 32 )$

Question 49

Solve the formula for the specified variable.
$a + b = s + r$ for $r$

A) $r = a + b - s$
B) $r = s ( a + b )$
C) $r = \frac { a } { s } + b$
D) $r = \frac { a + b } { s }$

Question 50

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$$\frac { x - 8 } { 4 } + \frac { x + 5 } { 5 } = x + 7$$

A) $x = - 7.273$
B) $x = - 10.909$
C) $x = - 14.545$
D) $\mathrm { x } = - 18.182$

Question 51

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$$( 8 x - 3 ) + 5 = 9 ( x - 3 )$$

A) $x = - 29$
B) $x = - 19$
C) $x = - 5$
D) $x = 29$

Question 52

Solve the formula for the specified variable.
$V = \frac { 1 } { 3 } B h$ for $h$

A) $h = \frac { V } { 3 B }$
B) $h = \frac { B } { 3 V }$
$\mathrm { C } h = \frac { 3 \mathrm {~B} } { \mathrm {~V} }$
D) $h = \frac { 3 V } { B }$

Question 53

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$$\frac { x + 6 } { 5 } - 7 = \frac { x + 8 } { 7 } - 7$$

A) $x = 2$
B) $x = - 2$
C) $x = - 1$
D) $x = 1$

Question 54

Solve the formula for the specified variable.
$\mathrm { S } = 2 \pi \mathrm { rh } + 2 \pi \mathrm { r } ^ { 2 }$ for $h$

A) $h = S - r$
B) $h = \frac { S } { 2 \pi r } - 1$
C) $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$
D) $h = 2 \pi ( S - r )$

Question 55

Solve the formula for the specified variable.
$\mathrm { A } = \frac { 1 } { 2 } \mathrm {~h} \left( \mathrm {~b} _ { 1 } + \mathrm { b } _ { 2 } \right)$ for $\mathrm { b } _ { 1 }$

A) $b _ { 1 } = \frac { h b _ { 2 } - 2 A } { h }$
B) $b _ { 1 } = \frac { 2 \mathrm { Ab } _ { 2 } - \mathrm { h } } { \mathrm { h } }$
C) $b _ { 1 } = \frac { A - h b _ { 2 } } { 2 h }$
D) $b _ { 1 } = \frac { 2 A - h b _ { 2 } } { h }$

Question 56

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate.
$$\frac { x + 8 } { 5 } = \frac { 13 } { 10 } - \frac { x - 3 } { 4 }$$

A) $x = 10.5$
B) $x = 26$
C) $x = 0$
D) $x = 1$

Question 57

Solve the formula for the specified variable.
$\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$ for $\mathrm { r }$

A) $r = \frac { A } { n }$
B) $r = \frac { P n } { A - P }$
C) $r = \frac { A - P } { P n }$
D) $r = \frac { P - A } { P n }$

Question 58

Solve the equation for y.
$$6 x + 9 y = 17$$

A) $y = \frac { 2 } { 3 } x - \frac { 17 } { 9 }$
B) $y = 6 x - 17$
C) $y = - \frac { 2 } { 3 } x + \frac { 17 } { 9 }$
D) $y = \frac { 2 } { 3 } x + \frac { 17 } { 9 }$

Question 59

Solve the formula for the specified variable.
$I = \frac { n E } { n r + R }$ for $n$

A) $n = \operatorname { IR } ( \operatorname { Ir } - \mathrm { E } )$
B) $n = \frac { - R } { I r - E }$
C) $n = \frac { - I R } { I r - E }$
D) $n = \frac { I R } { I r + E }$

Question 60

Solve the equation for y.
$$6 x - 9 y = 1$$

A) $y = \frac { 3 } { 2 } x + \frac { 1 } { 6 }$
B) $y = \frac { 2 } { 3 } x - \frac { 1 } { 9 }$
C) $y = 6 x - 1$
D) $y = \frac { 2 } { 3 } x + \frac { 1 } { 9 }$

Question 61

Solve the equation for y.
Suppose the sales of a particular brand of appliance satisfy the relationship $S ( x ) = 80 x + 3600$ , where $S ( x )$ represents the number of sales in year $x$ , with $x = 0$ corresponding to 2010 . In what year would the sales be $4320 ?$

A) 2018
B) 2021
C) 2020
D) 2019

Question 62

Solve the equation for y.
The mathematical model $$C = 400 x + 60,000$$ represents the cost in dollars a company has in manufacturing x items during a month. How many items were produced if costs reached $380,000?

A) 650 items
B) 1100 items
C) 800 items
D) 379,600 items

Question 63

Solve the equation for y.
Mark has $75 to spend on salmon at $5.00 per pound and/or chicken at $3.00 per pound. If he buys s pounds of salmon and c pounds of chicken, the equation 5s $$5 s + 3 c = 75$$ must be satisfied. How much salmon did Mark buy if
He bought 5 pounds of chicken?

A) 17 lb
B) 16 lb
C) 19 lb
D) 12 lb

Question 64

Construct a scatter plot of the data in the table.

- $\begin{array}{rr|r|r|r|r|r|r|r|r|r}x & -10 & -8 & -5 & -4 & -2 & 2 & 4 & 6 & 8 & 9 \\\hline y& 1& -7 & -2 & 4 & 4 & -2 & -3 & 5 & -8 & -4\end{array}$

A)

B)

C)

D)

Question 65

Solve the equation for y.
The future value of a simple interest investment is given by $\mathrm { S } = \mathrm { P } ( 1 + \mathrm { rt } )$ , where $\mathrm { P }$ is the principal invested at a simple interest rate $\mathrm { r }$ for $\mathrm { t }$ years. What principal $\mathrm { P }$ must be invested for $t = 4$ months at the simple interest rate $r = 11 \%$ so that the future value grows to $\$ 3600$ .

A) $127.33
B) $3243.24
C) $3472.67
D) $3503.65

Question 66

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function.

A) No, data points do not lie close to a line
B) Yes, exactly linear
C) Yes, approximately linear

Question 67

Solve the equation for y.
A student earned scores of 85, 83, 90, 94, 88, and 84 on the first six tests in a biology class. What score is needed on the seventh test to produce an 86 average?

A) 79
B) 78
C) 80
D) 81

Question 68

Construct a scatter plot of the data in the table.

- $\begin{array}{r|r|r|r|r|r|r|r|r|r}\mathrm{x} & -14 & 4 & 6 & 9 & 11 & 16 & -5 & -2 & -12 \\\hline \mathrm{y} & 3 & 5 & 6 & 11 & 7 & 7 & 7 & 2 & 2\end{array}$

A)

B)

C)

D)

Question 69

Solve the equation for y.
The temperature of water in a certain lake on a day in October can be determined by using the model $y = 15.2 - 0.537 x$ where x is the number of feet down from the surface of the lake and y is the Celsius temperature of the water at that depth. Based on this model, how deep in the lake is the water 8 degrees? Round
To the nearest foot.

A) 69 ft
B) 32 ft
C) 43 ft
D) 13 ft

Question 70

Solve the equation for y.
$y - 2 x ^ { 2 } + 5 = 0$

A) $y = 2 x ^ { 2 } - 5$
B) $y = - 2 x ^ { 2 } - 5$
C) $y = - 2 x ^ { 2 } + 5$
D) $y = 2 x ^ { 2 } + 5$

Question 71

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function.

A) Yes, exactly linear
B) Yes, approximately linear
C) No, data points do not lie close to a line

Question 72

Solve the equation for y.
When going more than 38 miles per hour, the gas mileage of a certain car fits the model $$y = 43.81 - 0.395 x$$ where x is the speed of the car in miles per hour and y is the miles per gallon of gasoline. Based on this model, at what
Speed will the car average 15 miles per gallon? (Round to nearest whole number.)

A) 73 mph
B) 98 mph
C) 149 mph
D) 48 mph

Question 73

Construct a scatter plot of the data in the table.

- $\begin{array}{r|r|r|r|r|r|r}x & 20 & 23 & -18 & 3 & -23 & -10 \\\hline y & -89 & -43 & 32 & -48 & 68 & -8\end{array}$

A)

B)

C)

D)

Question 74

Construct a scatter plot of the data in the table.

- $\begin{array}{r|r|r|r|r|r|r|r|r}\mathrm{x} & 0.75 & 0.86 & 0.33 & 0.25 & -0.12 & 0.97 & 0.71 & -0.05 \\\hline \mathrm{y} & 0.57 & 0.1 & 0.72 & 0.12 & -0.91 & 0.54 & 0.1 & 0.13\end{array}$

A)

B)

C)

D)

Question 75

Solve the equation for y.
A repair company's charge for repairing a certain type of copy machine fits the model y = 47.38 + 0.617x where y is the number of dollars charged and x is the number of minutes the repair person is on the job. How many
Minutes would it take for the cost of repair to reach $120? (Round to the nearest minute.)

A) 187 min
B) 118 min
C) 271 min
D) 12 min

Question 76

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear.
$$\begin{array} { c | c c c c c } \mathrm { x } & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm { y } & 9 & 13 & 17 & 21 & 25\end{array}$$

A) nonlinear
B) exactly linear
C) approximately linear

Question 77

Solve the equation for y.
The temperature, t, in degrees Fahrenheit, of water being heated is $$65 + \frac { 1 } { 4 } m$$ where m is the number of minutes since heating began. How long will it take for the temperature of the water to reach 70 degrees Fahrenheit?

A) 17 min
B) 40 min
C) 20 min
D) 14 min

Question 78

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function.

A) Yes, exactly linear
B) Yes, approximately linear
C) No, data points do not lie close to a line

Question 79

Solve the equation for y.
An average score of 90 for 5 exams is needed for a final grade of A. John's first 4 exam grades are 79, 89, 97, and 95. Determine the grade needed on the fifth exam to get an A in the course.

A) 100
B) 85
C) 95
D) 90

Question 80

Use the data shown in the scatter plot to determine whether the data should be modeled by a linear function.

A) Yes, approximately linear
B) No, data points do not lie close to a line
C) Yes, exactly linear