g(f(-2)) = g(27) = 2(27) - 5 = 54 - 5 = 49
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- Thus, the number of ways is $\boxed{3845}$.Question: If $ f(x) = 3x^2 - 4x + 7 $ and $ g(x) = 2x - 5 $, what is the value of $ g(f(-2)) $?
- First, evaluate $ f(-2) $:
- f(-2) = 3(-2)^2 - 4(-2) + 7 = 3(4) + 8 + 7 = 12 + 8 + 7 = 27
- Thus, the final answer is $ \boxed{49} $.
- Question: A seismologist models the time between two seismic events as a function $ T(x) = x^2 - 6x + 13 $, where $ x $ is the number of days since monitoring began. What is the minimum time between events predicted by this model?
- The function $ T(x) = x^2 - 6x + 13 $ is a quadratic. The minimum value of a quadratic $ ax^2 + bx + c $ occurs at $ x = -\frac{b}{2a} $.
