In the diagram below of triangle MNPMNP, QQ is a midpoint of \overline{MN} MN
and RR is a midpoint of \overline{NP}
NP
. If QR=11-xQR=11−x, and MP=57-7xMP=57−7x, what is the measure of MPMP?

Given that MNP is a triangle. Q is the midpoint of MN and R is the midpoint of NP.

The length of QR is 4x -11 and the length of MP is 9x - 29.

We need to determine the measure of MP.

Value of x:

The value of x can be determined using the triangle midsegment theore

Applying the theorem, we have;

Substituting the lengths, we get;

Subtracting both sides by 8x, we have;

Adding both sides of the equation by 29, we get;Thus, the value of x is 7.

Measure of MP:

The measure of MP can be determined by substituting x = 7 in the length of MP.

Thus, we have;

Thus, the measure of MP is 34.

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following