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=−43
x equals negative Start Fraction 4 over 3 End Fraction
x=176
x equals Start Fraction 17 over 6 End Fraction
x=7
x equals 7
x=−13
x equals negative 13
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1 answer
In a rectangle, the diagonals bisect each other, which means that segments AO and BO are equal in length. Therefore, we can set the expressions for AO and BO equal to each other:
\[ 4x - 3 = 5x - 10 \]
To solve for \(x\), first, subtract \(4x\) from both sides:
\[ -3 = x - 10 \]
Next, add 10 to both sides:
\[ 7 = x \]
So, the value of \(x\) is \(7\).
Thus, the correct response is:
x = 7.
