Question

u is the midpoint of $overline{tv}$. if $tu = 9x$ and $tv = 16x + 10$, what is $tv? simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since \(U\) is the mid - point of \(\overline{TV}\), then \(TU=\frac{1}{2}TV\). Given \(TU = 9x\) and \(TV=16x + 10\), we have the equation \(9x=\frac{1}{2}(16x + 10)\).

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(9x=\frac{1}{2}(16x + 10)\) by 2 to get \(18x=16x + 10\). Then subtract \(16x\) from both sides: \(18x-16x=16x + 10-16x\), which simplifies to \(2x=10\). Divide both sides by 2: \(x = 5\).

Step3: Find the value of \(TV\)

Substitute \(x = 5\) into the expression for \(TV\). \(TV=16x+10\), so \(TV=16\times5+10=80 + 10=90\).

Answer:

90