If (P(t)=60+5t), (P(5)+P(15)) is equal to twice which (P(k))?

Correct answer: \(P(10)\)

Here, \(P(t)=60+5t\) is a linear polynomial. The midpoint of \(5\) and \(15\) is \(10\), so for a linear function, \(P(5)+P(15)=2P(10)\). Checking directly, \(P(5)=85\) and \(P(15)=135\), giving a sum of \(220\); also, \(2P(10)=2\times110=220\). \(P(9)\) is close, but \(9\) is not the midpoint of \(5\) and \(15\). Exam tip: for a linear function, the function value at the average of two inputs equals the average of their function values.