Question

Apply the linear function f(x)=.75x+9

to the following context. A large cheese pizza costs $9, and each additional topping costs $0.75. In this function, x represents the number of toppings that you choose to put on your pizza. Determine the number of toppings you chose to put on your pizza if the total cost was $13.50.

Answer 1

Safina measured the perimeter of a shoebox to be 24 inches. Report the minimum and maximum possible perimeter based on the appropriate level of precision. Enter your responses in decimal form.(1 point)
Between a minimum of and a maximum of inches.

Answer 2

To determine the number of toppings you chose to put on your pizza, we can use the given linear function \( f(x) = 0.75x + 9 \), where \( x \) represents the number of toppings.

Given that the total cost of the pizza was $13.50, we can set up the equation:

\[
f(x) = 13.50
\]

Substituting the function into this equation:

\[
0.75x + 9 = 13.50
\]

Next, we'll solve for \( x \) by first isolating the term with \( x \):

1. Subtract 9 from both sides:

\[
0.75x = 13.50 - 9
\]

\[
0.75x = 4.50
\]

2. Now, divide both sides by 0.75:

\[
x = \frac{4.50}{0.75}
\]

\[
x = 6
\]

Thus, the number of toppings you chose to put on your pizza is **6**.

Answer 3

The perimeter of a shoebox is typically measured in whole inches. If Safina measured the perimeter to be 24 inches, we can assume that her measurement has some degree of uncertainty due to the precision of her measuring tool.

If we consider potential measuring errors, a common approach is to assume that the measurement could be off by half of the smallest unit being measured, which in this case is 1 inch. Therefore, the minimum and maximum possible perimeters based on this precision would be:

- **Minimum perimeter**: \( 24 - 0.5 = 23.5 \) inches
- **Maximum perimeter**: \( 24 + 0.5 = 24.5 \) inches

So, reporting the minimum and maximum possible perimeter in decimal form, we have:

- Between a minimum of **23.5** and a maximum of **24.5** inches.