Question

hakeem has 10 gallons of gas in his car at the beginning of a trip. every hour hakeem drives, he uses 3 gallons of gas. answer the questions below regarding the relationship between the gallons of gas remaining in the tank and the total hours driven.
answer attempt 1 out of 5
the independent variable x represents the
the
dependent variable is the
, because the
depends on the
.
a function relating these variables is h(x) =
.
so h(3) =
, meaning 3
.

Explanation:

Part 1: Identifying Variables

• The independent variable \( x \) represents the total hours driven (since it's the variable we can control or that changes independently).
• The dependent variable is the gallons of gas remaining (because the amount of gas left depends on how many hours Hakeem has driven).
• The reasoning is that the gallons of gas remaining depends on the total hours driven.

Part 2: Function Relationship

Step 1: Determine the initial amount and rate of change

The initial amount of gas is 10 gallons, and the rate of gas consumption is 3 gallons per hour. So, the amount of gas remaining \( H(x) \) is the initial amount minus the gas used in \( x \) hours. The gas used in \( x \) hours is \( 3x \) (since 3 gallons are used each hour).

Step 2: Formulate the function

So, the function is \( H(x) = 10 - 3x \).

Part 3: Evaluating \( H(3) \)

Step 1: Substitute \( x = 3 \) into the function

Substitute \( x = 3 \) into \( H(x) = 10 - 3x \). So, \( H(3) = 10 - 3(3) \).

Step 2: Calculate the result

First, calculate \( 3(3) = 9 \). Then, \( 10 - 9 = 1 \). This means that after 3 hours of driving, there is 1 gallon of gas remaining.

Final Answers:

• The independent variable \( x \) represents the \(\boldsymbol{\text{total hours driven}}\), the dependent variable is the \(\boldsymbol{\text{gallons of gas remaining}}\), because the \(\boldsymbol{\text{gallons of gas remaining}}\) depends on the \(\boldsymbol{\text{total hours driven}}\).
• A function relating these variables is \( H(x) = \boldsymbol{10 - 3x} \).
• So \( H(3) = \boldsymbol{1} \), meaning 3 \(\boldsymbol{\text{hours of driving}}\) results in \(\boldsymbol{1 \text{ gallon of gas remaining}}\).

Answer:

Part 1: Identifying Variables

• The independent variable \( x \) represents the total hours driven (since it's the variable we can control or that changes independently).
• The dependent variable is the gallons of gas remaining (because the amount of gas left depends on how many hours Hakeem has driven).
• The reasoning is that the gallons of gas remaining depends on the total hours driven.

Part 2: Function Relationship

Step 1: Determine the initial amount and rate of change

The initial amount of gas is 10 gallons, and the rate of gas consumption is 3 gallons per hour. So, the amount of gas remaining \( H(x) \) is the initial amount minus the gas used in \( x \) hours. The gas used in \( x \) hours is \( 3x \) (since 3 gallons are used each hour).

Step 2: Formulate the function

So, the function is \( H(x) = 10 - 3x \).

Part 3: Evaluating \( H(3) \)

Step 1: Substitute \( x = 3 \) into the function

Substitute \( x = 3 \) into \( H(x) = 10 - 3x \). So, \( H(3) = 10 - 3(3) \).

Step 2: Calculate the result

First, calculate \( 3(3) = 9 \). Then, \( 10 - 9 = 1 \). This means that after 3 hours of driving, there is 1 gallon of gas remaining.

Final Answers:

• The independent variable \( x \) represents the \(\boldsymbol{\text{total hours driven}}\), the dependent variable is the \(\boldsymbol{\text{gallons of gas remaining}}\), because the \(\boldsymbol{\text{gallons of gas remaining}}\) depends on the \(\boldsymbol{\text{total hours driven}}\).
• A function relating these variables is \( H(x) = \boldsymbol{10 - 3x} \).
• So \( H(3) = \boldsymbol{1} \), meaning 3 \(\boldsymbol{\text{hours of driving}}\) results in \(\boldsymbol{1 \text{ gallon of gas remaining}}\).