The segment joining the midpoints of sides pq and pr (the midsegment) in traingle pqr has length 8x^12x+36. if the length of qr is 4x^2+60x+120, find all possible measures of the midsegment

The possible measures of the midsegment are 32 units and 212 units.

Step-by-step explanation:

Given:

A triangle PQR with the midsegment made by sides PQ and PR has length equal to and the base length QR opposite to the midsegment is .

From midsegment theorem, we know that, the midsegment is a line parallel to the base opposite to it and half the length of the base length.

Therefore, Midsegment = Base length QR

Now, midsegment can be calculated using the values of 'x'.

First, plug in -1 for 'x'. This gives,

Now, plug in 4 for 'x'. This gives,

Therefore, the possible measures of the midsegment are 32 units and 212 units

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3