Question
Use the image to answer the question.Given that ABCD is a rectangle with AO=4x−3 and BO=5x−10 , what is the value of x?(1 point)Responsesx=176x equals Start Fraction 17 over 6 End Fractionx=7x equals 7x=−43x equals negative Start Fraction 4 over 3 End Fractionx=−13x equals negative 13
Answers
GPT-4o mini
To find the value of \( x \) given that \( ABCD \) is a rectangle and that \( AO = 4x - 3 \) and \( BO = 5x - 10 \), we need to use the property that opposite sides of a rectangle are equal.
In a rectangle, the lengths of two adjacent sides are equal when measured from the same point (the origin \( O \) in this case). Therefore, we can set the two expressions equal to each other:
\[
4x - 3 = 5x - 10
\]
Now, let's solve for \( x \).
1. Rearranging the equation to collect all \( x \) terms on one side:
\[
4x - 5x = -10 + 3
\]
2. This simplifies to:
\[
-x = -7
\]
3. Multiplying both sides by -1:
\[
x = 7
\]
Thus, the value of \( x \) is
\[
\boxed{7}
\]
In a rectangle, the lengths of two adjacent sides are equal when measured from the same point (the origin \( O \) in this case). Therefore, we can set the two expressions equal to each other:
\[
4x - 3 = 5x - 10
\]
Now, let's solve for \( x \).
1. Rearranging the equation to collect all \( x \) terms on one side:
\[
4x - 5x = -10 + 3
\]
2. This simplifies to:
\[
-x = -7
\]
3. Multiplying both sides by -1:
\[
x = 7
\]
Thus, the value of \( x \) is
\[
\boxed{7}
\]