18. find m∠d if m∠a = 2x + 18 and m∠b = 9x – 14.

a. 73°
b. 50°
c. 130°
d. 107°

 The correct option is  (C) 130°.

Step-by-step explanation:  We are given to find the measure of ∠D from the figure, where

From the figure, we note that ABCD is a parallelogram.

So, AD is parallel to BC and AB acts as a transversal.

Then, the sum of the measures of angles A and B is equal to 180°, since they are interior angles on the same side of the transversal.

That is,

So, the measure of angle B is

We know that the measures of the opposite angles of a parallelogram is 130°, so

the measure of angle D is 130°.

Thus, m∠D = 130°.

Option (C) is CORRECT.

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)