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Home » Thus, the number of valid combinations is $ \boxed126 $. - Dyverse

Thus, the number of valid combinations is $ \boxed126 $. - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Solving \( n^2 + n - 110 = 0 \) using the quadratic formula, \( n = \frac{-1 \pm \sqrt{1 + 440}}{2} = \frac{-1 \pm 21}{2} \).

📌 Positive solution: \( n = 10 \).

📌 The perimeter of a rectangle is 60 meters, and its length is 5 meters more than twice its width. What is the width?

📌 Let the width be \( w \). Then the length is \( 2w + 5 \).

📌 Perimeter = \( 2(\text{length} + \text{width}) = 60 \).

📌 \( 2((2w + 5) + w) = 60 \).

📌 Simplifying: \( 2(3w + 5) = 60 \) → \( 6w + 10 = 60 \) → \( 6w = 50 \) → \( w = \frac{50}{6} = \frac{25}{3} \).

📌 #### \(\frac{25}{3}\)

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