How do I connect a dryer to a dryer vent?
What you've done sounds fine.

One thing to look for though is that your connections are the right direction. The female end of each tubing should be on the end closest to the dryer. This prevents lint from snagging on the sharp metal on the way through the vent system and creating a clog (a big fire hazard). With the female ends upstream, there won't be any sharp ends to catch on.