select all the correct answers.

the time it takes to empty a tank varies inversely with the rate of pumping. it takes 21 minutes to empty a tank at a rate of 75 gallons/minute.

which points lie on the graph of the inverse variation function that represents the time it takes to empty this tank?

$\square$ (25, 63)
$\square$ (20, 72)
$\square$ (24, 65)
$\square$ (21, 75)

Question

select all the correct answers.

the time it takes to empty a tank varies inversely with the rate of pumping. it takes 21 minutes to empty a tank at a rate of 75 gallons/minute.

which points lie on the graph of the inverse variation function that represents the time it takes to empty this tank?

$\square$ (25, 63)
$\square$ (20, 72)
$\square$ (24, 65)
$\square$ (21, 75)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Variation" ], "new_concepts": [], "current_concepts": [ "Inverse Variation" ] } ## Determine the constant of variation $$ \begin{aligned} &t = \frac{k}{r} \implies k = r \cdot t \ &k = 75 \cdot 21 = 1575 \end{aligned} $$ ## Test the given coordinate pairs $$ \begin{aligned} &(25, 63): 25 \cdot 63 = 1575 \quad (\text{True}) \ &(20, 72): 20 \cdot 72 = 1440 eq 1575 \quad (\text{False}) \ &(24, 65): 24 \cdot 65 = 1560 eq 1575 \quad (\text{False}) \ &(21, 75): 21 \cdot 75 = 1575 \quad (\text{True}) \end{aligned} $$

$\square$ (25, 63)

$\square$ (20, 72)

$\square$ (24, 65)

$\square$ (21, 75)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Inverse Variation" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the constant of variation

Test the given coordinate pairs

Answer: