Question

current skill $ show w 6 x 4y + 10 y 7y - 41 find wy. figure is not drawn to scale.

Explanation:

Step1: Set up the equation for segment addition

Since \( WY = WX + XY \) and \( WY = 7y - 41 \), \( WX = 6 \), \( XY = 4y + 10 \), we have \( 6 + (4y + 10) = 7y - 41 \).

Step2: Simplify the left - hand side

Simplify \( 6+(4y + 10)\) to get \( 4y+16 \). So the equation becomes \( 4y + 16=7y - 41 \).

Step3: Solve for y

Subtract \( 4y \) from both sides: \( 16 = 3y-41 \). Then add 41 to both sides: \( 3y=16 + 41=57 \). Divide both sides by 3: \( y=\frac{57}{3}=19 \).

Step4: Find the length of WY

Substitute \( y = 19 \) into the expression for \( WY \), which is \( 7y-41 \). So \( WY=7\times19 - 41=133 - 41 = 92 \). We can also check by calculating \( WX+XY \): \( WX = 6 \), \( XY=4\times19 + 10=76 + 10 = 86 \), and \( 6 + 86=92 \).

Answer:

\( 92 \)