Zahra has joined the Frequent Coffee Buyer program with a local cafe. The program costs $20 per month, allowing her to get a discounted coffee price of $2.5 per cup. Answer the questions below regarding the relationship between the number of cups of coffee purchased and the total monthly cost.

Question

Answer
Attempt 1 out of 2

The independent variable, x, represents the
, and the dependent variable is the
, because the
depends on the
1 total monthly cost
2 number of coffee cups purchased
A function relating these variables is A, left parenthesis, x, right parenthesis, equalsA(x)=
.
So A, left parenthesis, 7, right parenthesis, equals(7)=
, meaning 77
1 dollers will be paid for
2 cups of coffee it will cost

Answer 1

To clarify the relationship between the variables:

1. The independent variable, \( x \), represents the number of coffee cups purchased.
2. The dependent variable is the total monthly cost, because the total cost depends on the number of cups of coffee purchased.

The function relating these variables can be expressed as:

\[ A(x) = 20 + 2.5x \]

where \( 20 \) is the monthly fee for the program and \( 2.5x \) is the cost of the coffee cups purchased at a price of \( 2.5 \) per cup.

Now, calculating for \( A(7) \) (when \( x = 7 \)):

\[ A(7) = 20 + 2.5 \times 7 \] \[ A(7) = 20 + 17.5 \] \[ A(7) = 37.5 \]

So, \( A(7) = 37.5 \), meaning $37.5 will be paid for 7 cups of coffee.

Answer 2

The area of a square depends on the length of its sides. Answer the questions below regarding the relationship between the area of the square and the length of one side of the square.
Answer
Attempt 1 out of 2

The independent variable, x, represents the
, and the dependent variable is the
, because the
depends on the
.
A function relating these variables is A, left parenthesis, x, right parenthesis, equalsA(x)=
.
So A, left parenthesis, 8, right parenthesis, equalsA(8)=
, meaning if 88

Answer 3

To clarify the relationship between the variables regarding the area of a square:

1. The independent variable, \( x \), represents the length of one side of the square.
2. The dependent variable is the area of the square, because the area depends on the length of one side.

The function relating these variables is given by the formula for the area of a square:

\[ A(x) = x^2 \]

Now, calculating for \( A(8) \) (when \( x = 8 \)):

\[ A(8) = 8^2 \] \[ A(8) = 64 \]

So, \( A(8) = 64 \), meaning if the length of one side is 8 units, the area of the square is 64 square units.