what us the name of the river that begins in the appalachian mountains in the east and connects into the mississippi river?

New River or Kanawha River

Explanation:

The New River, rising on the Blue Ridge in North Carolina, runs northward and then turns westward across the Appalachian Valley and the Alleghenies (where it becomes the Kanawha River) and empties into the Mississippi River basin.

the thirteen colonies are:

connecticut, delaware, georgia, maryland, massachusetts, new jersey, new york, new hampshire, north carolina, pennsylvania, rhode island, south carolina, virginia