My 2004 Rendezvous starts shaking at 35 mph and stop at 50 mph. If I let off the gas the shaking stops. whats wrong

How old are your tires ? have one out of round or busted cords inside , maybe a wheel weight feel off . take it to the tire shop have the balance checked !

This is common for inner axle shaft joints had a bad worn spot in them so as you accelerate these joints need to slide in & out freely there are binding.

bad inner axle joints.

First replace the catalytic converter. it is clogging up.. this may take of the #3 misfire. Most likely the #3 coil pack is bad.

start with the wheels,they need to be balanced "dynamically"after that, if it shakes, get back to us....

BAD SPARK PLUGS AND WIRES DIRTY FUEL INJECTORS AND STOPPED UP FUEL FILTER OR WEAK FUEL PUMP WILL CAUSE ENGINE TO SURGE.

If the engine is misfiring and that is the source of the shaking then the check engine light will be flashing like crazy, other wise it is not the engine causing this, I know was a Ford tech for 25 years.

bad ujoints

I have this same car with exactly the same problem. Begins shaking at 40mph and stops shaking as soon as you let off the gas, but then begins again as soon as you press on the gas and smooths out as you get over 50. And the shaking is not felt through the steering wheel. Solution: Replace the transmission mounts. There are two of them, one on each side mounted on the frame right next to the shock strut. There is also a front and rear engine mount, but I replaced the two as described and shaking is gone.

It sounds like you need a tune change at least the wires and plugs it also could be a worn or broke motor or tranny mount.