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who wrote the pledge of allegiance - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 Question:** A middle school student is exploring functions and their compositions. If \(f(x) = 3x - 2\) and \(g(x) = x^2 + 1\), what is \(g(f(4))\)?

📌 First, evaluate \(f(4)\):

📌 f(4) = 3(4) - 2 = 12 - 2 = 10.

📌 Next, substitute this result into \(g(x)\):

📌 g(f(4)) = g(10) = 10^2 + 1 = 100 + 1 = 101.

📌 Thus, the value of \(g(f(4))\) is \(\boxed{101}\).

📌 Question:** A chemical engineer is modeling biofuel yield based on reactant concentrations. If the yield \(Y\) is given by \(Y = 4x^2 - 12x + 9\), compute the minimum possible yield and the value of \(x\) at which it occurs.

📌 The expression \(Y = 4x^2 - 12x + 9\) is a quadratic in standard form. Since the coefficient of \(x^2\) is positive, the parabola opens upwards, and the minimum occurs at the vertex.

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