The first one looks like a baby mimosa (or at least a mimosa type weed - there are about 2-3 such weeds in north Georgia). One such weed is Chamberbitter.

The second picture of yours is ragweed.

Both of them should be pulled. And if you do have a 20 foot mimosa tree in your yard, you should think about getting rid of it too.

esh, I can understand that ragweed is not good to have around because of its pollen produces severe and widespread allergies. But why Mimosa? Every time when I get plants identified here, I check those plants out on the web to find more information about them. I googled mimosa, and there are nurseries even selling mimosa. Some of them are even expensive. That's funny! One thing I can tell is that mimosa seems very invasive, because they are all over in my yard. Is it the reason why I should pull it?

Yeh Mimosa is very invasive. Native to asia, and takes over lots of disturbed areas in the south. They are usually short-lived as well. Pull her out. We have so many trying to grow in our beds...such a pain!