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Home » The Ultimate Guide to the Best ‘Star Wars Shows’ You Were Meant to See! - Groen Casting

The Ultimate Guide to the Best ‘Star Wars Shows’ You Were Meant to See! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 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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3^2 - 4(y - 2)(y - 1) \geq 0
- 4(y^2 - 3y + 2) \geq 0
- 4y^2 + 12y - 8 \geq 0
-4y^2 + 12y + 1 \geq 0
Multiply through by \(-1\) (reversing the inequality):
4y^2 - 12y - 1 \leq 0
Solve the quadratic inequality using the quadratic formula:
y = \frac{-(-12) \pm \sqrt{(-12)^2 - 4 \cdot 4 \cdot (-1)}}{2 \cdot 4}...
y = \frac{12 \pm 4\sqrt{10}}{8} = \frac{3 \pm \sqrt{10}}{2}
Thus, the range of \(f(x)\) is:

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