Mauro has 140 ft of rope. he will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. what will the length of the longer piece be? enter your answer in the box.

Length of the longer piece be 105 ft .

Step-by-step explanation:

As given

Mauro has 140 ft of rope.

He will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece.

Let us assume that the length of the shorter piece be x.

Length of the Longer piece = 3x

Than the equation become

3x + x = 140

4x = 140

x = 35 ft

Length of the longer piece = 3 × 35

                                             = 105 ft

Therefore the length of the longer piece be 105 ft .

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.