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Home » But \( 2\sqrt30 \) is simplified. - Nelissen Grade advocaten

But \( 2\sqrt30 \) is simplified. - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: A zoologist models the number of observed behaviors per day as $ y = 2x + b $, where $ x $ is the number of hours spent in the field. If 3 hours of observation yield 11 total behaviors, find the $ y $-intercept of the line.

📌 Solution: We are given a point $ (3, 11) $ lies on the line $ y = 2x + b $. Substitute $ x = 3 $ and $ y = 11 $:

📌 = 2(3) + b

📌 The $ y $-intercept is the point $ (0, b) $, so it is $\boxed{5}$.

📌 Question: A science educator uses a function $ h(x) = x^2 - 4x + c $ to model student performance, and finds that the minimum score occurs at $ x = 2 $. What value of $ c $ ensures $ h(2) = 3 $?

📌 Solution: The vertex of a parabola $ h(x) = x^2 - 4x + c $ occurs at $ x = \frac{-(-4)}{2(1)} = 2 $, which matches the given condition. Now substitute $ x = 2 $ and set $ h(2) = 3 $:

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