Got a set of True/False questions, don't know which ones I'm getting wrong though: 1. If x and y are both negative, then |x+y| = |x| + |y|(I got True for this one) 2. If |r|1, then 1/(1-|r|)

Question

Got a set of True/False questions, don't know which ones I'm getting wrong though:

1. If x and y are both negative, then |x+y| = |x| + |y|(I got True for this one)

2. If |r|>1, then 1/(1-|r|)<=1/(1-r)<=1/(1+|r|)
(I got True for this)

3.For every positive real number y, there exists a real number x such that x^2=y(True for this)

4.It is possible to have an inequality whose solution set consists of exactly one number(False for this)

5. The equation x^2+y^2+ax+by=c represents a circle for all real numbers a,b,c.

cont'd...

anonymous · Answer

6. If (a,b),(c,d) and (e,f) are on the same line, then (a-c)/(b-d) = (a-e)/(b-f) = (e-c)/(f-d)

7. For every epsilon>0, there exists a positive number x such that x<epsilon

8. If sqrt(x2-x1)^2 + (y2-y1)^2 = |x2-x1| then (x1,y1) and (x2,y2) are on the same horizontal line

anonymous · Answer

and I got plenty more of these if anyone wants to help. I feel like I'm taking shots in the dark, not gettin any feedback if these are wrong or not from my homework.

zarkon · Answer

solve $$x^2\le 0$$

anonymous · Answer

0? since that is equal.

zarkon · Answer

now look at #4

anonymous · Answer

So that would be true due to 0 then.

zarkon · Answer

yes

anonymous · Answer

Cool, thanks for that one!

anonymous · Answer

I'm getting true for #3, but I'm freaking myself out since I got T for 1-4. If y=3, then x=sqrt3, and that is a real number, so that is true, right?

anonymous · Answer

I was able to get all of these right by messing around a bit more. Answers:
1.T
2.T
3.T
4.T
5.F
6.T
7.T
8.T