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Home » Mario Party 3 Secrets You Didn’t Know Will Blow Your Nintendo Game! - go-checkin.com

Mario Party 3 Secrets You Didn’t Know Will Blow Your Nintendo Game! - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Solution: Let $ u = 2x + 1 $, so $ x = \frac{u - 1}{2} $. Substitute into $ f(u) $: $ f(u) = 4\left(\frac{u - 1}{2}\right)^2 + 12\left(\frac{u - 1}{2}\right) + 9 = (u - 1)^2 + 6(u - 1) + 9 = u^2 - 2u + 1 + 6u - 6 + 9 = u^2 + 4u + 4 $. Thus, $ f(x^2 - 3) = (x^2 - 3)^2 + 4(x^2 - 3) + 4 = x^4 - 6x^2 + 9 + 4x^2 - 12 + 4 = x^4 - 2x^2 + 1 $. \boxed{x^4 - 2x^2 + 1}

📌 Question: Solve the inequality $ \frac{2x - 5}{x + 3} \geq 1 $ to determine the range of temperatures where a species thrives.

📌 Solution: Subtract 1: $ \frac{2x - 5}{x + 3} - 1 \geq 0 \Rightarrow \frac{2x - 5 - (x + 3)}{x + 3} \geq 0 \Rightarrow \frac{x - 8}{x + 3} \geq 0 $. Critical points at $ x = 8 $ and $ x = -3 $. Test intervals:

📌 For $ x < -3 $, test $ x = -4 $: $ \frac{-12}{-1} = 12 > 0 $.

📌 For $ -3 < x < 8 $, test $ x = 0 $: $ \frac{-8}{3} < 0 $.

📌 For $ x > 8 $, test $ x = 9 $: $ \frac{1}{12} > 0 $.

📌 Include $ x = 8 $, exclude $ x = -3 $. Solution: $ (-\infty, -3) \cup [8, \infty) $. \boxed{(-\infty, -3) \cup [8, \infty)}Question: A cone has a radius of \(3y\) units and a height of \(4y\) units. A sphere has a radius of \(2y\) units. What is the ratio of the volume of the cone to the volume of the sphere?

📌 The volume \(V\) of a cone with radius \(r\) and height \(h\) is given by the formula:

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