10)
$\begin{array}{l} g (t) = t - 4 \\ h (t) = t - 5 \\ Find (g \cdot h) (t) \end{array}$

Answer

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Answer

Final Answer: $t^{2} - 9 t + 20$

Steps

Step 1 ：Find the product of the functions $h$ and $g$ at $t$ .

Step 2 ：For $g (t)$ , substitute $t$ into the function $g (t) = t - 4$ to get $g (t) = t - 4$ .

Step 3 ：For $h (t)$ , substitute $t$ into the function $h (t) = t - 5$ to get $h (t) = t - 5$ .

Step 4 ：The product of the functions $h$ and $g$ evaluated at $t$ is $(g \cdot h) (t) = g (t) * h (t) = (t - 4) * (t - 5) = t^{2} - 9 t + 20$ .

Step 5 ：So, $(g \cdot h) (t) = t^{2} - 9 t + 20$ .

Step 6 ：Final Answer: $t^{2} - 9 t + 20$