Question

question: dalvin has 13 gallons of gas in his car at the beginning of a trip. every hour dalvin drives, he uses 1.25 gallons of gas. answer the questions below regarding the relationship between the gallons of gas remaining in the tank and the total hours driven. the independent variable, x, represents the < >, and the dependent variable is the < >, because the < > depends on the < >. a function relating these variables is b(x)= < >. so b(8)= < >, meaning 8 < >.

Explanation:

Step1: Identify the initial amount of gas

The initial amount of gas in the car is 13 gallons.

Step2: Determine the rate of gas - consumption

The rate of gas - consumption is 1.25 gallons per hour.

Step3: Set up the function

The function \(B(x)\) that represents the amount of gas remaining in the tank after \(x\) hours of driving is \(B(x)=13 - 1.25x\).

Step4: Evaluate \(B(8)\)

Substitute \(x = 8\) into the function \(B(x)\):
\[

$$\begin{align*} B(8)&=13-1.25\times8\\ &=13 - 10\\ &= 3 \end{align*}$$

\]

The independent variable \(x\) represents the number of hours driven. The dependent variable is the amount of gas remaining in the tank because the amount of gas remaining depends on the number of hours driven.

Answer:

The independent variable \(x\) represents the number of hours driven. The dependent variable is the amount of gas remaining in the tank. \(B(8)=3\) (meaning after 8 hours of driving, 3 gallons of gas remain in the tank)