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Home » \pi (5x)^2 = 25\pi x^2. - DNSFLEX

\pi (5x)^2 = 25\pi x^2. - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Question: The functions $ f(x) = x^2 - 6x + m $ and $ g(x) = x^2 - 6x + 3m $ are evaluated at $ x = 5 $. If $ f(5) = 2g(5) $, find $ m $.

📌 Solution: Compute $ f(5) = 25 - 30 + m = -5 + m $ and $ g(5) = 25 - 30 + 3m = -5 + 3m $.

📌 Set $ f(5) = 2g(5) $:

📌 + m = 2(-5 + 3m)

📌 + m = -10 + 6m

📌 = 5m \Rightarrow m = 1

📌 The value of $ m $ is $ \boxed{1} $.**Question:** A box contains 8 red marbles, 6 blue marbles, and 4 green marbles. How many ways can 5 marbles be selected if at least one marble of each color must be included?

📌 To ensure that at least one marble of each color is selected, we must consider all valid combinations of red (R), blue (B), and green (G) marbles such that:

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