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Home » Feeling Sick? These Bland Diet Foods Will Calm Your Upset Stomach FAST—No Joke! - Abbey Badges

Feeling Sick? These Bland Diet Foods Will Calm Your Upset Stomach FAST—No Joke! - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Substitute back: \(x = \frac{6}{5} + 3 = \frac{21}{5}\).

📌 #### \(x = \frac{21}{5}, y = \frac{6}{5}\)

📌 Find the derivative of \(f(x) = 4x^3 - 5x^2 + 2x - 7\).

📌 Differentiate term by term: \(f'(x) = 12x^2 - 10x + 2\).

📌 #### \(12x^2 - 10x + 2\)

📌 If the sum of the first \(n\) natural numbers is 210, find \(n\).

📌 Use the formula: \(\frac{n(n+1)}{2} = 210\).

📌 Multiply both sides by 2: \(n(n+1) = 420\).

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9x^2 - 54x - 16y^2 + 64y = 71
Complete the square for \( x \):
Factor out 9 from \( x \)-terms:
9(x^2 - 6x)
Complete the square:
x^2 - 6x = (x - 3)^2 - 9
Substitute back:
9((x - 3)^2 - 9) = 9(x - 3)^2 - 81
Complete the square for \( y \):
Factor out \(-16\) from \( y \)-terms:

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