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Let $C(x)$ be the cost to produce $x$ batches of widgets, and let $R(x)$ be the revenue in thousands of dollars. Complete parts (a) through (d) below.
\[
R(x)=-x^{2}+10 x \cdot C(x)=x+8
\]
(a) Graph both functions:

Identify the vertex of $R(x)$
The vertex of $R(x)$ is at $(5.25)$
(Type an ordered pair Simplify your ansiver)
Identify the $y$-intercept of $C(x)$
The $y$-intercept of $C(x)$ is at $y=\square$
(Simplify your answer.)

Step 1 ：Let $C(x)$ be the cost to produce $x$ batches of widgets, and let $R(x)$ be the revenue in thousands of dollars. The functions are given by $R(x)=-x^{2}+10 x$ and $C(x)=x+8$.

Step 2 ：First, we identify the vertex of $R(x)$. The vertex of $R(x)$ is at $(5,25)$.

Step 3 ：Next, we identify the $y$-intercept of $C(x)$. The $y$-intercept of a function is the point where the graph of the function intersects the y-axis. This occurs when $x = 0$. So, to find the $y$-intercept of $C(x)$, we need to evaluate $C(0)$.

Step 4 ：Substitute $x = 0$ into the function $C(x)$, we get $C(0) = 0 + 8 = 8$.

Step 5 ：Final Answer: The y-intercept of $C(x)$ is at $y=\boxed{8}$.