If QT is the perpendicular bisector of PR, find the measure of each.

Applying the Pythagorean Theorem and the definition of perpendicular bisector, the values of x and y, as well as the measures of each segment in the image are:

Given:

PQ = 5y - 31

PT = 6x - 2y

QR = 2y + 5

PS = 4x + 4

SR = 7x - 17

Find the value of x:

PS = SR (congruent sides)

x = 7

Find the value of y:

PQ = RQ (since QT is the perpendicular bisector of PR, PT equals TR, therefore, triangles PQT and RQT are congruent).

Find the length of each side by plugging in the value of x and y:

PQ = 5y - 31 = 5(12) - 31 = 29

PT = TR = 6x - 2y = 6(7) - 2(12) = 18

QR = 2y + 5 = 2(12) + 5 = 29

PS = 4x + 4 = 4(7) + 4 = 32

SR = 7x - 17 = 7(7) - 17 = 32

Find QT using Pythagorean Theorem:

Therefore, applying the Pythagorean Theorem and the definition of perpendicular bisector, the values of x and y, as well as the measures of each segment in the image are:

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x = 7

y = 12

PQ = QR = 29

Step-by-step explanation:

In ΔPSR , PS = SR (given)

In ΔPQR , QT is perpendicular bisector of PR. So , PT = RT . As ΔPQR has a perpendicular bisector , it is an isosceles triangle.

So,

,

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

the infinity sign

step-by-step explanation: