Question

given rhombus ( klmn ) below, ( mo = 5 ). if ( ok=-4x + 9 ), solve for ( x ).

Explanation:

Step1: Use the property of rhombus diagonals

In a rhombus, the diagonals bisect each other. So \(OK = MO\).

Step2: Set up the equation

Since \(MO = 5\) and \(OK=-4x + 9\), we have the equation \(-4x+9 = 5\).

Step3: Solve the equation for \(x\)

Subtract \(9\) from both sides: \(-4x=5 - 9\), so \(-4x=-4\).
Divide both sides by \(-4\): \(x=\frac{-4}{-4}\).

Answer:

\(x = 1\)