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Home » Just Dance 2014: The Ultimate Dance Challenge You Need to Try Tonight! - Carbonext

Just Dance 2014: The Ultimate Dance Challenge You Need to Try Tonight! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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The graph of \( y = a \cdot 2^x \) passes through the points $ (0, 3)...
At \( x = 0 \): \( y = a \cdot 2^0 = a = 3 \).
Check with \( x = 2 \): \( y = 3 \cdot 2^2 = 12 \), which matches.
So \( a = 3 \).
What is the remainder when \( x^4 - 3x^2 + 2x + 5 \) is divided by \(...
Use Remainder Theorem: evaluate at \( x = 1 \).
\( 1^4 - 3(1)^2 + 2(1) + 5 = 1 - 3 + 2 + 5 = 5 \).
\( x^2 + (x+1)^2 = 145 \) → \( x^2 + x^2 + 2x + 1 = 145 \) → \( 2x^2 +...
Divide by 2: \( x^2 + x - 72 = 0 \) → \( (x + 9)(x - 8) = 0 \).
So \( x = 8 \), larger integer is 9.

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Solution: To find the average efficiency, we sum the three expressions...
\text{Average} = \frac{(5y + 1) + (2y + 7) + (3y + 4)}{3}
= \frac{5y + 2y + 3y + 1 + 7 + 4
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