Question

Use algebra to solve each problem. If a diagram is not given, you MUST sketch one.Show your calculations for each question. Place your answer in the space provided.Yis between X and Z on segment XZ. XY = x + 7, XZ - 152, and YZ - 2XY. Find x to thenearest tenth.xX

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} |XY|=x+7 \\ |XZ|=152 \\ |YZ|=2|XY|\Rightarrow|XZ|=|XY|+|YZ| \\ But\colon|YZ|=2|XY|\Rightarrow|XZ|=|XY|+2|XY|\Rightarrow|XZ|=3|XY| \\ |XZ|=3|XY| \\ But\colon|XY|=x+7,|XZ|=152 \\ 152=3(x+7)\Rightarrow152=3\cdot x+3\cdot7\Rightarrow152=3x+21 \\ 152=3x+21 \\ \text{Subtract 21 from each side, we have:} \\ 152-21=3x+21-21\Rightarrow131=3x\Rightarrow3x=131 \\ 3x=131 \\ \text{Divide each side by 3, we have:} \\ (3x)/(3)=(131)/(3)\Rightarrow x=43(2)/(3)\approx43.667\cong43.7 \\ x=43.7(ToNearestTenth) \end{gathered}`