Find the equation of the line that is perpendicular to y = 2 3 x – 13 and passes though the point (4, –1). A) y = 2 3 x – 5 B) y = 3 2 x – 5 C) y = – 2 3 x + 5 D) y = – 3 2 x + 5

The answer to your question is the letter D.

Step-by-step explanation:

Data

Perpendicular to y = 2/3 x - 13

Point = (4, -1)

Process

1.- Determine the slope of the original line. The slope is the coefficient of the x.

        y = 2/3 x - 13

        slope = 2/3

2.- Determine the slope of the perpendicular line. The new slope is the reciprocal.

        new slope = -3/2

3.- Find the equation of the new line

         (y + 1) = -3/2(x - 4)

-Simplify

          y + 1 = -3/2x + 6

          y = -3/2x + 6 - 1

4.- Result

          y = -3/2x + 5

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180