The graph below represents Function R
The equation 3x-1 represents Function S.
Which statement about Functions R and S is true?
A. The rate of change of Function R is less than the rate of change of Function S because 2/3<3.
B. The rate of change of Function R is less than the rate of change of Function S because 2<3
C. The rate of change of Function R is equal to the rate of change of Function S because both are 1
D. The rate of change of Function R is greater than the rate of change of Function S because 1>-1.

Option A: The rate of change of Function R is less than the rate of change of Function S because is true.

Explanation:

The function

The equation for function R can be determined using the slope formula,

The y-intercept is the value of y, when x = 0.

Thus, the y-intercept is .

To determine the slope, let us substitute the coordinates and .

Because, the points on the straight line have the same slope.

Thus, we have,

Thus, and

Let us substitute these values in the formula , we get,

Hence, the equation of R is

The equation of S is

Comparing the slope of these two equations, we have,

This means that the slope of R is less than the slope of S.

Hence, The rate of change of Function R is less than the rate of change of Function S because

Thus, Option A is true.

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted