Emmett participated in a race. during the race, he ran 5 miles north and then ran 12 miles west. what is the shortest distance that emmett must travel to return to the starting point?

I'd suggest you sketch this situation.  If you did, you'd likely see right away that the shortest distance back to the starting point would be the hypotenuse of the right triangle whose legs are of lengths 5 miles and 12 miles.

Apply the Pythagorean Theorem to solve this.

The following answers are obtained from HW, which it shows answers to.

A. The Queen can state, "All the inscriptions are false."If the Queen can state this, in which of the trunks are the treasures hidden?

False, Cannot be determined

(b) The Queen can state, "Exactly one of the inscriptions is true."If the Queen can state this, in which of the trunks are the treasures hidden?

True, Trunk 1 and 3

(c) The Queen can state, "Exactly two of the inscriptions are true."If the Queen can state this, in which of the trunks are the treasures hidden?

True, Cannot be determined

d) The Queen can state, "All the three inscriptions are true."If the Queen can state this, in which of the trunks are the treasures hidden?

False, Cannot be determined