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Home » Discover the Sharpest Adjectives Starting with H—Boost Your Vocabulary Instantly! - Groen Casting

Discover the Sharpest Adjectives Starting with H—Boost Your Vocabulary Instantly! - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question: Determine the center of the hyperbola $ 4x^2 - 9y^2 + 8x + 18y - 11 = 0 $.

📌 Solution: Group and complete the square: $ 4(x^2 + 2x) - 9(y^2 - 2y) = 11 $. Complete squares: $ 4[(x+1)^2 - 1] - 9[(y-1)^2 - 1] = 11 $. Expand: $ 4(x+1)^2 - 4 - 9(y-1)^2 + 9 = 11 \Rightarrow 4(x+1)^2 - 9(y-1)^2 = 6 $. Rewrite: $ \frac{(x+1)^2}{\frac{3}{2}} - \frac{(y-1)^2}{\frac{2}{3}} = 1 $. Center at $ (-1, 1) $. \boxed{(-1, 1)}1. **A chemistry experiment requires 50 mL of a 10% salt solution. If you only have a 20% salt solution and distilled water, how much of each should be mixed to obtain the desired concentration?

📌 To create a 10% salt solution from a 20% salt solution, you can use the formula for mixing solutions. Let \( x \) be the volume of the 20% solution, and \( 50 - x \) be the volume of water.

📌 The equation is:

📌 0.20x = 0.10 \times 50

📌 0.20x = 5 \\

📌 x = \frac{5}{0.20} = 25

📌 Therefore, you need 25 mL of the 20% solution and \( 50 - 25 = 25 \) mL of water.

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