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Home » Rearrange: \(0.2x = 10\). - Abu Waleed Tea

Rearrange: \(0.2x = 10\). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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\text{lcm}(7, 11) = 7 \cdot 11 = 77
Thus, $ n - 1 = 77k $ for some integer $ k $, and:
n = 77k + 1
We are to find the smallest such $ n > 50 $. Try $ k = 1 $:
n = 77 \cdot 1 + 1 = 78
Since $ 78 > 50 $, this is valid.
Therefore, the smallest clutch size greater than 50 that satisfies the...
\boxed{78}
Question: An ichthyologist notes that the population sizes of two fish...
We are given that $ a + b = 1000 $, and $ p \mid a $, $ p \mid b $, so...

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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:
-16(y^2 - 4y)
y^2 - 4y = (y - 2)^2 - 4
-16((y - 2)^2 - 4) = -16(y - 2)^2 + 64
Substitute and simplify:
Substitute squares back into the equation:

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