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# Algebra Student Produced Response

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

$$2k$$ 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 $$k?$$

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

$8|x+2|=40$

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

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

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