Three distinct lines, all contained within a plane, separate that plane into distinct regions. what are all of the possible numbers of distinct regions of the plane that could be separated by any such three lines?

Renee hiked for 6 3/4 miles. after resting, renee hiked back along the same route for 5 1/4 miles. how many more miles does renee need to hike to return to the place where she started? represent your answer as a simplified mixed number, if necessary.