Question

Use the image to answer the question.

A rectangle upper A upper B upper C upper D has diagonals between upper A upper C and upper B upper D. The diagonals insect at upper O, in the center. Segment upper A upper O is labeled 4 x minus 3. Segment upper B upper O is labeled 5 x minus 10.

Given that ABCD
is a rectangle with AO=4x−3
and BO=5x−10
, what is the value of x?

(1 point)
Responses

x=7
x equals 7

x=176
x equals Start Fraction 17 over 6 End Fraction

x=−43
x equals negative Start Fraction 4 over 3 End Fraction

x=−13
x equals negative 13
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Answer 1

In a rectangle the diagonals are equal and bisect each other, so AO = BO. Set 4x − 3 = 5x − 10. Solve: −3 = x − 10, so x = 7.