AnswersMathematics IIIMathematical Modeling: Part One

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A cell phone carrier offers two plans for text messaging. Plan cap A costs 20 dollars per month plus 0 point 0 5 dollars per text. Plan cap b costs 10 dollars per month plus 0 point 1 0 dollars per text. For how many text messages per month are the plans the same cost?

A
30
B
300
C
200
D
20
2
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If the function f of x is equal to m x plus b has an inverse function, which statement must be true?

A
m is equal to 0
B
m is not equal to 0
C
b is equal to 0
D
b is not equal to 0
3

What is the point of intersection when the system of equations is graphed on the coordinate plane? negative x plus y is equal to 4 6 x plus y is equal to negative 3

A
open paren 1 comma 3 close paren
B
open paren 1 comma negative 3 close paren
C
open paren negative 1 comma 3 close paren
D
open paren negative 1 comma negative 3 close paren
4

The cost of producing x soccer balls in thousands of dollars is represented by h of x is equal to 5 x plus 6 The revenue is represented by k times x is equal to 9 x minus 2 Which expression represents the profit, open paren k minus h close paren times x , of producing soccer balls?

A
4 x plus 4
B
4 x minus 8
C
14 x plus 4
D
14 x minus 8
5

If f of x is equal to x squared minus 25 and g of x is equal to x minus 5 , what is the domain of open paren f over g close paren of x ?

A
all real values of x except x is equal to 5 and x is equal to negative 5
B
all real values of x except x is equal to 5
C
all real values of x except x is equal to negative 5
D
all real values of x
6

The equations negative A minus 7 b is equal to 14 and negative 4 A minus 14 b is equal to 28 represent a system of linear equations. Which statement correctly explains how to eliminate the variable b when solving the system of equations?

A
Multiply the first equation by 2 and add it to the second equation. Then solve the resulting equation, negative 2 A is equal to 0 .
B
Multiply the first equation by negative 2 and add it to the second equation. Then solve the resulting equation, negative 2 A is equal to 0 .
C
Divide the second equation by 4 and add it to the first equation.
D
Divide the second equation by negative 4 and add it to the first equation.
7

Which graph shows all the values that satisfy 2 ninths x plus 3 is greater than 4 and 5 ninths ?

A
Image with description A number line lists negative 10 to 10 by 5. An open circle is on 7. An arrow goes to the left of 7.
B
Image with description A number line lists negative 10 to 10 by 5. An open circle is on negative 7. An arrow goes to the right of negative 7.
C
Image with description A number line shows integers from negative 10 to 10. An open circle is at negative 7, with a thick line extending from it to the left, ending in an arrow.
D
Image with description A number line lists negative 10 to 10 by 5. An open circle is on 7. An arrow goes to the right of 7.
8

Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?

A
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
B
The pool must have been deeper at the end of the interval than it was at the start of the interval.
C
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
D
The pool must have been empty for the entire interval.
9

The constraints of a problem are listed. What are the vertices of the feasible region? 4 x plus 3 y is less than or equal to 12 2 x plus 6 y is less than or equal to 15 x is greater than or equal to 0 y is greater than or equal to 0

A
open paren 0 comma 2 point 5 close paren , open paren 1 point 5 comma 2 close paren , open paren 4 comma 3 close paren
B
open paren 0 comma 0 close paren , open paren 0 comma 4 close paren , open paren 1 point 5 comma 2 close paren , open paren 7 point 5 comma 0 close paren
C
open paren 0 comma 0 close paren , open paren 0 comma 2 point 5 close paren , open paren 1 point 5 comma 2 close paren , open paren 3 comma 0 close paren
D
open paren 0 comma 4 close paren , open paren 1 point 5 comma 2 close paren , open paren 7 point 5 comma 0 close paren
10

Which graph shows the solution set of the compound inequality 1 point 5 x minus 1 is greater than 6 point 5 or 7 x plus 3 is less than negative 25 ?

A
Image with description A number line labeled from negative 10 to 10 in increments of 5 with tick marks every 1 unit. The graph consists of a horizontal line segment extending from an open circle at negative 4 to an open circle at 5.
B
Image with description A number line labeled from negative 10 to 10 in increments of 5 with tick marks every 1 unit. The graph consists of an open circle at 5 with a line extending to the right ending with an arrow pointing right.
C
Image with description A number line labeled from negative 10 to 10 in increments of 5 with tick marks every 1 unit. The graph consists of an open circle at negative 4 with a line extending to the left ending with an arrow pointing left.
D
Image with description A number line lists negative 10 to 10 by 5. An open circle on negative 4 and another one on 5, and the arrows go in opposite directions.
11

Celo used the simple interest formula cap A is equal to cap p times open paren 1 plus r t close paren to calculate the interest he earned on his savings last month. Which equation is equivalent to the simple interest formula?

A
cap p is equal to cap A minus open paren 1 plus r t close paren
B
cap p is equal to the fraction with numerator cap A and denominator 1 plus r t
C
cap p is equal to cap A plus open paren 1 plus r t close paren
D
cap p is equal to the fraction with numerator 1 plus r t and denominator cap A
12

The formula to determine energy is cap e is equal to 1 half m v squared What is the formula solved for v ?

A
v is equal to plus or minus square root of m over 2 cap e end root
B
v is equal to 2 cap e minus m
C
v is equal to plus or minus square root of 2 cap e over m end root
D
v is equal to plus or minus square root of 2 cap e minus m end root
13

The height in feet, h , of a model rocket t seconds after launch is given by the equation h of t is equal to 3 plus 70 t minus 16 t squared The average rate of change in h of t between t is equal to 1 second and t is equal to 3 second is 6 What does the average rate of change tell you about the rocket?

A
The rocket is at a greater height when t is equal to 3 than it is when t is equal to 1 .
B
The rocket is traveling at a constant rate of 6 feet per second between t is equal to 1 and t is equal to 3 .
C
The rocket is 6 feet higher above the ground when t is equal to 3 than it is when t is equal to 1 .
D
The rocket is traveling six times as fast when t is equal to 3 than it is when t is equal to 1 .
14

The constraints of a problem are listed. What are the vertices of the feasible region? x plus y is less than or equal to 5 y is less than or equal to 3 x is greater than or equal to 0 y is greater than or equal to 0

A
open paren 0 comma 3 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren
B
open paren 0 comma 0 close paren , open paren 0 comma 5 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
C
open paren 0 comma 0 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
D
open paren 0 comma 0 close paren , open paren 0 comma 3 close paren , open paren 2 comma 3 close paren , open paren 5 comma 0 close paren
15

Which system of equations can be graphed to find the solution(s) to 4 x squared is equal to x squared plus 7 ?

A
y is equal to 4 x squared y is equal to x squared plus 7
B
y is equal to 3 x squared y is equal to x squared plus 7
C
y is equal to 3 x squared plus 7 y is equal to x squared plus 7
D
y is equal to 4 x squared y is equal to 4 x squared plus 7
16

Which function is the inverse of f of x is equal to negative 5 x minus 4 ?

A
f inverse of x is equal to 4 x plus 4
B
f inverse of x is equal to negative 1 fifth x minus 4 fifths
C
f inverse of x is equal to negative 1 fifth x plus 4 fifths
D
f inverse of x is equal to negative 4 x plus 5
17

Which ordered pair open paren r comma s close paren is the solution to the given system of equations? 5 r plus 7 s is equal to 61 negative 5 r plus 7 s is equal to negative 19

A
open paren 8 comma 3 close paren
B
open paren 1 comma negative 2 close paren
C
open paren 1 comma 8 close paren
D
open paren 3 comma 8 close paren
18

Vicky is solving an equation where both sides are linear expressions. She sets each linear expression equal to y and graphs the resulting system. If the y -intercepts of the graphs are the same but the slopes are different, what is the greatest possible number of intersections for these graphs?

A
infinitely many
B
two
C
one
D
none

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