If (P(t)=75+6t), (P(6)+P(18)) is equal to twice which (P(k))?

Correct answer: P(12)

This is a linear function, so the sum of its values at two inputs equals twice its value at the midpoint of those inputs. The midpoint of 6 and 18 is \(\frac{6+18}{2}=12\). Hence, \(P(6)+P(18)=2P(12)\). Checking directly, \(P(6)=111\) and \(P(18)=183\), so their sum is 294, while \(2P(12)=2\times147=294\). Exam tip: for a linear function, use \(P(a)+P(b)=2P\left(\frac{a+b}{2}\right)\).