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Home » $ -3 \le x < \frac52 $: - High Altitude Science

$ -3 \le x < \frac52 $: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: Factor the expression $ 16x^2 - 40x + 25 $ completely.

📌 Check if the trinomial is a perfect square trinomial:

📌 16x^2 = (4x)^2, \quad 25 = (5)^2, \quad -40x = 2(4x)(-5)

📌 This confirms the expression is of the form $ a^2 - 2ab + b^2 = (a - b)^2 $:

📌 16x^2 - 40x + 25 = (4x - 5)^2

📌 Thus, the factored form is $ \boxed{(4x - 5)^2} $.

📌 Question: If $ x + \frac{1}{x} = 4 $, what is the value of $ x^2 + \frac{1}{x^2} $?

📌 We square both sides of the given equation:

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A = 78.5 + 204.1 = 282.6 \text{ cm}^2
Thus, the total surface area of the cone is:
\boxed{282.6 \text{ cm}^2}
Problem 4:
In a right triangle, the hypotenuse is 25 cm, and one leg is 7 cm. Wha...
where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs.
\(c = 25\) cm
\(a = 7\) cm
Find \(b\)
7^2 + b^2 = 25^2

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