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

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 \((g \cdot h)(t)=g(t)*h(t)=(t-4)*(t-5)=t^2-9t+20\).

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

Step 6 ：Final Answer: \(\boxed{t^2-9t+20}\)