Help plz, BIG POINTS, also plz show me the steps as best as possible

The correct answer is option 3.

Step-by-step explanation:

Given : ΔPQR, QM is altitude of the triangle

PM  = 8

MR = 18

To find = QM

Solution :

PR = 8 + 18  = 26

Let, PQ = x  , QR = y, QM = z

Applying Pythagoras Theorem in ΔPQR

..[1]

Applying Pythagoras Theorem in ΔPQM

..[2]

Applying Pythagoras Theorem in ΔQMR

..[3]

Putting values of and from [2] and [3 in [1].

z = ±12

z = 12 = QM ( ignoring negative value)

The length of QM is 12.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

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

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

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

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq