Question

I am not the best at these I was hoping someone could help me.

Answer 1

`\begin{gathered} m=2 \\ YZ=25 \end{gathered}`

Step-by-step explanation:

Given that Y is between X and Z;

`XZ=XY+YZ`

Given;

`\begin{gathered} XZ=13m+6 \\ XY=9m-3 \\ YZ=6m+1 \end{gathered}`

Let us substitute the given equation into the equation above;

`\begin{gathered} XZ=XY+YZ \\ 13m+6=9m-3+6m+1 \\ 13m+6=9m+6m-3+1 \\ 13m+6=15m-2 \end{gathered}`

Let now proceed to solve the equation;

add 2 to both sides of the equation;

`\begin{gathered} 13m+6+2=15m-2+2 \\ 13m+8=15m \end{gathered}`

subtract 13m from both sides;

`\begin{gathered} 13m-13m+8=15m-13m \\ 8=2m \end{gathered}`

Then lastly divide both sides by 2;

`\begin{gathered} (8)/(2)=(2m)/(2) \\ 4=m \\ m=2 \end{gathered}`

Since we have the value of m, let now substitute into YZ to get its value;

`\begin{gathered} YZ=6m+1 \\ YZ=6(4)+1 \\ YZ=24+1 \\ YZ=25 \end{gathered}`

Therefore, the value of m and YZ is;

`\begin{gathered} m=2 \\ YZ=25 \end{gathered}`