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

Answer 1

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

\[ \boxed{7} \]