Question

s is the midpoint of (overline{rt}). if (st = x + 8) and (rt = 10x + 8), what is (st)?
simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use the mid - point property

Since \(S\) is the mid - point of \(\overline{RT}\), then \(RT = 2ST\).
Given \(ST=x + 8\) and \(RT = 10x+8\), we substitute into the equation \(RT = 2ST\). So, \(10x + 8=2(x + 8)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(10x+8 = 2x+16\).
Subtract \(2x\) from both sides: \(10x-2x + 8=2x-2x + 16\), which gives \(8x+8 = 16\).
Subtract \(8\) from both sides: \(8x+8 - 8=16 - 8\), so \(8x=8\).
Divide both sides by \(8\): \(x=\frac{8}{8}=1\).

Step3: Find the value of \(ST\)

Substitute \(x = 1\) into the formula for \(ST\). Since \(ST=x + 8\), then \(ST=1 + 8\).

Answer:

\(9\)