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If \((x+y)^{2} = 31\) and \((x-y)^2 = 2,\) what is the value of \(4xy\)?

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\(2k\) is increased by \(30.\)

The result is divided by \(2.\)

\(9\) is subtracted from the result.

Alex follows the instructions above in order. If his final answer is \(12,\) what is the value of \(k?\)

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If \(f(x)=3x - 15\) and \(2f(n)= 6,\) what is the value of \(f(2n)?\)

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\[8|x+2|=40\]

The above equation has two solutions. What is the absolute value of their sum?

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If \(\frac{1}{10^{x}\cdot 10^{y}} = \frac{1}{ 1000000 },\) what is the value of \(x+y?\)

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