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Home » Since \( f(3) = g(3) \), we have: - AMAZONAWS

Since \( f(3) = g(3) \), we have: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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A company's profit is modeled by \(P(x) = -2x^2 + 40x - 150\), where x...
Vertex form: \(x = -\frac{b}{2a} = -\frac{40}{2(-2)} = 10\)
Maximum profit: \(P(10) = -2(10)^2 + 40(10) - 150\)
Calculate: \(P(10) = -200 + 400 - 150 = 50\)
If \(\log_2(x) + \log_2(x-3) = 3\), what is x?
Combine logs: \(\log_2(x(x-3)) = 3\)
Convert to exponential: \(x(x-3) = 2^3 = 8\)
Solve quadratic: \(x^2 - 3x - 8 = 0\)
Factor: \((x-4)(x+2) = 0\)
Solutions: x = 4 or x = -2 (discard negative)

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