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=−13
x equals negative 13

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

x=7
x equals 7

x=−43

Answer 1

In a rectangle, the diagonals bisect each other. Therefore, the segments \(AO\) and \(BO\) are equal in length. We can set the two expressions for these segments equal to each other and solve for \(x\):

\[
4x - 3 = 5x - 10
\]

Now, let's solve this equation:

1. Subtract \(4x\) from both sides:
\[
-3 = x - 10
\]

2. Add \(10\) to both sides:
\[
7 = x
\]

Thus, the value of \(x\) is \(7\).

The correct response is:
x equals 7