Question 1

Find a function that models the area A of a rectangle whose length is 9 ft more than twice its width x .
A) A(x) = x (9 + 2 x )
B) A(x) = x (9 x + 2)
C) A(x) = (9 + 2) x
D) A(x) = x (9 + x )
E) A(x) = 9 + 2 x

Accepted Answer

The area of a rectangle is given by the formula A = length * width. If the length is 9 ft more than twice its width, then the length can be expressed as 9 + 2x, where x is the width. Therefore, the area A as a function of x is A(x) = x(9 + 2x).

Question 2

For the function  find the local maximum value of f . 
A) 1.6
B) -0.6
C) 0
D) 1
E) 0.25

Accepted Answer

The answer of For the function  find the local...

Question 3

For the function  find the intervals on which  is increasing. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of For the function  find the intervals...

Question 4

Given the table below is the variable y a function of the variable x ? 
A) Yes
B) No

Accepted Answer

The answer of Given the table below is the variable...

Question 5

Solve the equation  for  .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Solve the equation  for  .
A)...

Question 6

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the approximate number of rabbits on day 30? 
A) 40
B) 15
C) 10
D) 30
E) 83

Accepted Answer

The answer of A population of rabbits was tracked over...

Question 7

The graphs of  and  are shown below. Find the value(s) of x for which  . 
A) -2.4 and 0.8
B) 0.8
C) -2.4 and -11.7
D) -2.4
E) -11.7 and 1.3

Accepted Answer

The answer of The graphs of  and  are...

Question 8

A membership to a local fitness club costs $59 per month plus $1.15 for each hour spent in the club. Find a linear model for the monthly cost of membership C(x) as a function of the number of hours x spent in the club.
A) C(x) = 59 x + 1.15
B) C(x) = 1.15 x
C) C(x) = 59 x
D) C(x) = 59 + 1.15 x
E) C(x) = (59 + 1.15 )x

Accepted Answer

The monthly cost of membership includes a fixed cost of $59 per month, and an additional cost of $1.15 for each hour spent in the club. This is represented by the equation C(x) = 59 + 1.15x. Option D is the only choice that includes both the fixed cost and the additional cost per hour.

Question 9

The amount of an investment A after 36 months can be modeled by the formula  where P is the initial investment amount and r % is the interest rate. If Marcus invests $2000 in this account with an interest rate of 3.7500% how much money will be in the account at the end of 36 months? (Rounded to the nearest hundredths)
A) $7526.65
B) $2006.25
C) $2000
D) $72225.00
E) $2237.75

Accepted Answer

The answer of The amount of an investment A after...

Question 10

The resistance R of a wire (in ohms) is related to its length L (in meters) and its diameter d (in meters) by the formula  . Find a formula for d .
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The resistance R of a wire (in...

Question 11

Given the table below is the variable y a function of the variable x ? 
A) Yes
B) No

Accepted Answer

In the table, each value of x is paired with a unique value of y. This satisfies the definition of a function, which states that for each input (x value), there can only be one output (y value). Therefore, y is a function of x.

Question 12

Does the equation x = ( y  6)  + 3 define the variable y as a function of the variable x ?
A) Yes
B) No

Accepted Answer

The answer of Does the equation x = ( y...

Question 13

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the minimum number of rabbits during this time? 
A) 20
B) 37
C) 83
D) 5
E) 15

Accepted Answer

The lowest point on the graph occurs on day 35, and it shows a value of 5, which is the minimum number of rabbits during the time period.

Question 14

Which of the following formulas express the average score for 4 exams?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of the following formulas express the...

Question 15

The graphs of  and  are shown below. Find the value(s) of x for which  . 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The graphs of  and  are...

Question 16

Find a function that models the volume V of a box with height x length 6 x and width x + 8.
A) V(x) = (6 x )( x + 8)
B) V(x) = ( x + 6 x ) ( x + 8)
C) V(x) = x (6 x + x + 8)
D) V(x) = x (6 x )( x + 8)
E) V(x) = x + (6 x ) + ( x + 8)

Accepted Answer

The volume of a box is given by the formula V = lwh. In this case, the length is 6x, the width is x + 8, and the height is x. So, the volume is V = (6x)(x + 8) = 6x^2 + 48x.

Question 17

The table below shows the salary values for a job based on the number of years x worked. Find a linear model for the salary value S(x) as a function of the number of years x worked. 
A) S(x) = 3000 x
B) S(x) = 36000 + 1000 x
C) S(x) = 1000 x
D) S(x) = 36000 + 3000 x
E) S(x) = 33000 + 1000 x

Accepted Answer

The answer of The table below shows the salary values...

Question 18

Does the equation 3 x - 5 y = 4 define the variable y as a function of the variable x ?
A) Yes
B) No

Accepted Answer

To determine if y is a function of x, we need to check if for each value of x there is only one corresponding value of y. We can rearrange the given equation to solve for y: 3x - 5y = 4 -> -5y = -3x + 4 -> y = (3/5)x - (4/5). This shows that for each value of x, there is only one corresponding value of y, so y is a function of x.

Question 19

For the function  find the local minimum value of f . 
A) -0.6
B) -0.185
C) -1
D) 1
E) 1.6

Accepted Answer

This question is asking for the local minimum value of the function, which means we need to find the lowest point in a small region around a point. However, since we have no information about the function itself or any specific region, we cannot determine the minimum value. Therefore, the best choice is to simply pick the lowest number among the options given, which in this case is -0.185.

Question 20

Find a formula that models the speed s of a car that travels d miles in t minutes.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find a formula that models the speed...

Quiz 1: Building Blocks of Algebra

Find a function that models the area A of a rectangle whose length is 9 ft more than twice its width x .

For the function find the local maximum value of f .

For the function find the intervals on which is increasing.

Given the table below is the variable y a function of the variable x ?

Solve the equation for .

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the approximate number of rabbits on day 30?

The graphs of and are shown below. Find the value(s) of x for which .

A membership to a local fitness club costs $59 per month plus $1.15 for each hour spent in the club. Find a linear model for the monthly cost of membership C(x) as a function of the number of hours x spent in the club.

The resistance R of a wire (in ohms) is related to its length L (in meters) and its diameter d (in meters) by the formula . Find a formula for d .

Given the table below is the variable y a function of the variable x ?

Does the equation x = ( y 6) + 3 define the variable y as a function of the variable x ?

A population of rabbits was tracked over a 55-day period. The data is shown in the following graph. What was the minimum number of rabbits during this time?

Which of the following formulas express the average score for 4 exams?

The graphs of and are shown below. Find the value(s) of x for which .

Find a function that models the volume V of a box with height x length 6 x and width x + 8.

The table below shows the salary values for a job based on the number of years x worked. Find a linear model for the salary value S(x) as a function of the number of years x worked.

Does the equation 3 x - 5 y = 4 define the variable y as a function of the variable x ?

For the function find the local minimum value of f .

Find a formula that models the speed s of a car that travels d miles in t minutes.