Which of the statements using operations on rational or irrational numbers always results in a rational number?

a) irrarional + irrational
b) irrational ÷ irrational
c) rational + irrational
d) rational ÷ rational

Hm a irrational number is a number like this:

So adding a rational number, like 2, it would be irrational still:

That being said, answer C is wrong

Now, what is 2/2? Or 4/1? Whole numbers are one of the 3 types of rational numbers.

Thus the answer appears to be D

Now lets use the process of elimination to double check the

The wording of your question is what will help us out here:

Which of the statements using operations on rational or irrational numbers always results in a rational number?

Because of that, any of the choices that involve a irrational number can result with another irrational number like so:

And there you go, the only answer that hasn't been proven wrong is answer D.

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If the graph is this one:http://assets.openstudy.com/updates/attachments/556b7614e4b0ae03fc84336f-haileyjcaroen-1433105982090...
Then the correct features that are present in this polar graph are Symetry about the polar axis= 0 and Symetry about the pole (0,0), so B and C. Hope this helps.