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Home » \[ d = \frac2.500250 = 10 \] - DNSFLEX

\[ d = \frac2.500250 = 10 \] - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).

📌 #### \(x = 1.5\), \(y = 1\)

📌 If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+1)}{2}\), find \(n\) when the sum is 210.

📌 Set up the equation: \(\frac{n(n+1)}{2} = 210\).

📌 Multiply by 2: \(n(n+1) = 420\).

📌 Solve \(n^2 + n - 420 = 0\) using the quadratic formula:

📌 \(n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm 41}{2}\).

📌 The positive solution is \(n = 20\).

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