Question

find the value of x, y, and z, in the rhombus below. answer attempt 1 out of 2 x = y = z =

Explanation:

Step1: Recall rhombus property

All sides of a rhombus are equal. So we set up equations based on side - length equalities.

Step2: Set up equation for \(x\)

Set \(-9x - 10=8\). Add 10 to both sides: \(-9x=8 + 10\), so \(-9x=18\). Divide both sides by \(-9\), we get \(x=\frac{18}{-9}=-2\).

Step3: Set up equation for \(y\)

Set \(3y + 2=8\). Subtract 2 from both sides: \(3y=8 - 2\), so \(3y=6\). Divide both sides by 3, we get \(y = 2\).

Step4: Set up equation for \(z\)

Set \(-8z + 8=8\). Subtract 8 from both sides: \(-8z=8 - 8\), so \(-8z=0\). Divide both sides by \(-8\), we get \(z = 0\).

Answer:

\(x=-2\), \(y = 2\), \(z = 0\)