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Home » Turtles in Time: Unlocking Secrets from Generations Past! - Network4

Turtles in Time: Unlocking Secrets from Generations Past! - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 If \( x \) and \( y \) are two numbers such that \( x + y = 10 \) and \( xy = 21 \), what is the value of \( x^2 + y^2 \)?

📌 We know \( x^2 + y^2 = (x+y)^2 - 2xy \).

📌 Substituting the given values, \( x^2 + y^2 = 10^2 - 2 \times 21 = 100 - 42 = 58 \).

📌 A solution contains 40% alcohol. How many liters of pure alcohol must be added to 10 liters of this solution to make a 60% alcohol solution?

📌 Initially, there are \( 0.4 \times 10 = 4 \) liters of alcohol.

📌 Let \( x \) be the liters of pure alcohol added.

📌 The new total volume is \( 10 + x \) liters, and the new alcohol content is \( 4 + x \) liters.

📌 The equation is \( \frac{4 + x}{10 + x} = 0.6 \).

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