given the median $\overline{qr}$ and trapezoid $mnop$, what is the value of $x$?

a. 6
b. 18
c. 2
d. 5
e. 7
f. cannot be determined

Question

given the median $\overline{qr}$ and trapezoid $mnop$, what is the value of $x$?

a. 6
b. 18
c. 2
d. 5
e. 7
f. cannot be determined

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Trapezoid Midsegment Theorem" ], "new_concepts": [], "current_concepts": [ "Trapezoid Midsegment Theorem", "Trapezoid Properties" ] } ## Set up the midsegment equation $$ QR = \frac{NO + MP}{2} $$ ## Substitute the given expressions $$ 33 = \frac{(3x - 8) + (7x + 4)}{2} $$ ## Solve for x $$ \begin{aligned} 66 &= 10x - 4 \ 70 &= 10x \ x &= 7 \end{aligned} $$

A. 6

B. 18

C. 2

D. 5

E. 7

F. Cannot be determined

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Trapezoid Midsegment Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the midsegment equation

Substitute the given expressions

Solve for x

Answer: