When using cruise control, does the car automatically apply both the accelerator and the brake or only the accelerator?

In most cars it is just the accelerator, although my F350 work truck will automatically downshift when the speed starts to build up going downhill. Toyota's hybrid system does much the same thing, increasing regeneration on downhills and using engine braking if the battery gets full.

With manual transmissions it is purely accelerator but you can downshift it to hold back.

Just the accelerator - some vehicles will downshift going downhill to help hold the speed down.

If you apply the cruise control it only keeps your car at the speed you were travelling when you pressed it,when you brake it disengages unless you own a higher end car that uses radar guided cruise control.that will slow you down speed you up according to traffic and how you set it up.

Just the accelerator. When you do downhill, the car will speed up