QQuestionMathematics
QuestionMathematics
Let point $C$ be between $V$ and $W$ on $\overline{\text { FW }}$. Given that $V W= 61, V C=z+ 13$, and $C W=z+ 8$, solve for $z$.
A 18
B 19
C 20
D 21
Please select the best answer from the choices provided
A
B
C
D
12 months agoReport content
Answer
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Step 1:: Since point $C$ is between points $V$ and $W$ on $\overline{\text { FW }}$, we can write the length of segment $\overline{\text { VW }}$ as the sum of the lengths of segments $\overline{\text {VC}}$ and $\overline{\text {CW}}$.
VW = VC + CW
This gives us the equation:
Step 2:: We are given that $VW = 1$, $VC = z + 1$, and $CW = z + 1$.
61 = (z + 13) + (z + 8)
Substituting these values into the equation from Step 1, we get:
Step 3:: Simplify and solve for $z$:
61 = 2z + 21 \Rightarrow 40 = 2z \Rightarrow z = 20
Final Answer
The value of $z$ is 20, which corresponds to answer choice C.
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