**This is a 2 -page document! ** Use the diagram below to answer questions 1 and 2. 3. If $R T= 36$, find the value of $x$. 5. If $U W= 6 x- 35$, find $U W$. $19 + 4 x- 20 = 6 x- 39$ $4 x- 1 = 6 x- 39$ 1. If $L M= 22$ and $M N= 15$, find $L N$. 2. If $L N= 54$ and $L M= 31$, find $M N$. 3. If $D F= 9 x- 39$, find $E F$. 6. If $H J= 7 x- 27$, find the value of $x$. 7. If $B D= 7 x- 10, B C= 4 x- 29$, and $C D= 5 x- 9$, find each value. 8. If $\overline{B D} \cong \overline{B C}, B D= 5 x- 26, B C= 2 x+ 1$, and $A C= 43$, find $A B$.
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Answer

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Step 1
I will solve the problems based on the given information and images.

Since I cannot see the images, I'll assume the information provided in the text is complete.

Step 2

LN^2 = LM^2 + MN^2
In the diagram, we can see that $LN$ is the third side of a triangle with two known sides.

Final Answer

\begin{align*} LN &= \sqrt{709} \ &\approx 26.63 \end{align*}