the diameter of one circle is represented by $12x$. the diameter of another circle is represented by $6x^2y$. what is the ratio of the radii of the two circles?

$\bigcirc 2:x^2y$
$\bigcirc 2:xy$
$\bigcirc x:2y$
$\bigcirc 2:xy$

Question

the diameter of one circle is represented by $12x$. the diameter of another circle is represented by $6x^2y$. what is the ratio of the radii of the two circles?

$\bigcirc 2:x^2y$
$\bigcirc 2:xy$
$\bigcirc x:2y$
$\bigcirc 2:xy$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Circle Ratios" ], "new_concepts": [], "current_concepts": [ "Circle Ratios", "Algebraic Simplification" ] } ## Express the radii of the two circles $$ \begin{aligned} r_1 &= \frac{12x}{2} = 6x \ r_2 &= \frac{6x^2y}{2} = 3x^2y \end{aligned} $$ ## Calculate the ratio of the radii $$ \frac{r_1}{r_2} = \frac{6x}{3x^2y} = \frac{2}{xy} $$ ## Express the ratio in colon notation $$ 2 : xy $$

(A) $2 : x^2y$

(B) $2x : y$

(C) $x : 2y$

(D) $2 : xy$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Circle Ratios" ] }

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QUESTION IMAGE

Question

Explanation:

Express the radii of the two circles

Calculate the ratio of the radii

Express the ratio in colon notation

Answer: