Question

the function \\(g(x) = 32 - 0.08x\\) models the gallons of gasoline remaining in a trucks fuel tank after driving \\(x\\) miles. after how many miles will the truck run out of fuel?

32
256
80
400

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Linear Models",
"Linear Functions"
],
"new_concepts": [],
"current_concepts": [
"Linear Models",
"Linear Functions",
"Function Evaluation"
]
}
</pre_analysis>

<reasoning>

Set the fuel function to zero

\[
g(x) = 0
\]

Substitute the function expression

\[
32 - 0.08x = 0
\]

Solve for x

\[

$$\begin{aligned} 0.08x &= 32 \\ x &= \frac{32}{0.08} \\ x &= 400 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 32</mcq-option>
<mcq-option>(B) 256</mcq-option>
<mcq-option>(C) 80</mcq-option>
<mcq-correct>(D) 400</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Models"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Linear Models",
"Linear Functions"
],
"new_concepts": [],
"current_concepts": [
"Linear Models",
"Linear Functions",
"Function Evaluation"
]
}
</pre_analysis>

<reasoning>

Set the fuel function to zero

\[
g(x) = 0
\]

Substitute the function expression

\[
32 - 0.08x = 0
\]

Solve for x

\[

$$\begin{aligned} 0.08x &= 32 \\ x &= \frac{32}{0.08} \\ x &= 400 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 32</mcq-option>
<mcq-option>(B) 256</mcq-option>
<mcq-option>(C) 80</mcq-option>
<mcq-correct>(D) 400</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Linear Models"
]
}
</post_analysis>