Where are you flying in? And where are you flying out? If it is into Cairo, then yes - Cairo, Museum, Giza Pyramids, Dashur etc - Alexandria would be easy enough in a week to 9 days, and would be reasonably relaxed.
As Michel pointed out, you could easily spend several days in each of those but if you have less time then no problem still. It gives you time to take your time and absorb where you are, and in a relaxed manner.
Attempting to combine that with Jordan is another matter though. I can only see it possible (in the time you have I mean), if perhaps you fly into Jordan from Cairo. Otherwise you'd be biting your nails the entire time, From what I've observed of the tour groups that come across from Egypt for a day to Petra, don't waste your time on those. The poor people are rushed through a small strip of the place like cattle, then bundled back onto the transport going back to Egypt. If you're desperate, I guess you could do that but it really would be an expensive fragment of Petra.