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Home » 7^3 = 343 \equiv 343 - 38\times9 = 343 - 342 = 1 \\ - Sterling Industries

7^3 = 343 \equiv 343 - 38\times9 = 343 - 342 = 1 \\ - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 The simplified rationalized expression is $\boxed{\frac{3x\sqrt{x} + 6x + 4\sqrt{x} + 8}{x - 4}}$.

📌 Question: A chemist observes that the reaction rate of a green catalytic process is proportional to $ x^2 + 5x + 6 $, and wants to factor this expression to analyze its behavior at different temperatures. Factor the expression completely.

📌 Solution: The expression $ x^2 + 5x + 6 $ is a quadratic trinomial. We look for two numbers that multiply to 6 and add to 5. These numbers are 2 and 3:

📌 x^2 + 5x + 6 = (x + 2)(x + 3)

📌 Thus, the completely factored form is $\boxed{(x + 2)(x + 3)}$.

📌 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

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