Question

1. determine the length of $overline{uv}$. assume that the figure is not drawn to scale.

Explanation:

Step1: Set up an equation based on segment - addition

Since $ST + TU+UV = SV$, we have $13 + 6+(2x - 18)=4x - 29$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $13 + 6-18+2x=1 + 2x$. So the equation becomes $1 + 2x=4x - 29$.

Step3: Solve for x

Subtract $2x$ from both sides: $1=4x - 2x-29$, which simplifies to $1 = 2x-29$. Then add 29 to both sides: $1 + 29=2x$, so $30 = 2x$. Divide both sides by 2, we get $x = 15$.

Step4: Find the length of $UV$

Substitute $x = 15$ into the expression for $UV$. $UV=2x - 18$. So $UV=2\times15 - 18=30 - 18 = 12$.

Answer:

12