CalculatorUser

The only way to get the answer is to read the explanation ENTIRELY

List this out, trust me, it won't take long.

We see that there are 3 * 5 = 15 total possible values of x^y.

We find all the number of values that are NEGATIVE, then subtract that number from 15.

Looking at the y sets, we see that anything value of y that is -2, 0, 2, will create positive values no matter what.

So the y values can be -1 or 1.

There is only one x-value that has potential to be negative, and that is -1.

We see that -1^-1 and -1¹ both create negative values.

Since there are 2 negative values.

15 - 2 = THE ANSWER?

We check with a table

BUT WAIT! They said distinct.

So count the distinct values in the table, and you should get the answer.

Guest made a teeny tiny mistake.

The answer is actually

 \(2

EDIT: What happened to the LaTeX???????

To add on to guest's answer.

Notice the pattern

123456789101112131415161718192021222324

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24

the first digit is 1, the tenth digit is 10, the twentieth digit is 20. etc.

lel never mind the above statement my brain is wired wrong

or you can go tryhard and download Autodesk Inventor for some 3d Printing.

Find the greatest sum and the smallest sum.

smallest sum: -4 + (-3) = -7

greatest sum: 4 + 3 = 7

We can assume that \(-7\leq{x}\leq7\) would work.

BUT WAIT.

We check if the sums -6 or 6 are possible, but they aren't. We check if the sums -5 or 5 are possible, and they ARE.

We can assume that all ODD numbers between the interval \(-7\leq{x}\leq7\) work.

Now its up to you to find the answer.

EDIT: Sorry Fixed it was kind of confusing.

just curious, why did you delete all your questions and answers? i found this after checking your profile...

Notice if you isolate y in both equations, you can get four different linear inequalities that you can graph.

So isolating:

\(\frac{-3-7x}{2}\leq{y}{\leq}\frac{3-7x}{2}\)

\(-4+x\leq{y}{\leq}4+x\)

Ok now we have:

Graph:

Notice the intersection shape of the FOUR inequality inequations.

The MAXIMUM value of x + y, which is the answer you are looking for, is the vertice FARTHEST away from the origin.

There can be two vertices that fit this, but they will end up giving you the same answer.

So all you need to do is find the coordinates of where two lines intersect. (they should intersect at the said vertice)

I will leave that up to you to find this.

I agree, Wonderman, you do not have the authority to do this.

The question asker may have not recieved sufficient help.