Which statement describes the rate of change of the following function? f(x) = -5x - 7

A.
The function has a varying rate of change when x < 7.
B.
The function has a varying rate of change when x < 5.
C.
The function has a constant rate of change, decreasing for all x at a rate of 7.
D.
The function has a constant rate of change, decreasing for all x at a rate of 5.

Given:

The function is

To find:

The rate of change of the given function.

Solution:

We have,

       ...(i)

It is a linear function because the degree or power of x in this function is 1.

Slope of a linear function is always constant.

The slope intercept form of a linear function is

     ...(ii)

where, m is slope and b is y-intercept.

On comparing (i) and (ii), we get

It means, the function has a constant rate of change, decreasing for all x at a rate of 5.

Therefore, the correct option is D.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47