The function c(x) = 25.50x + 50 models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house. what is the average rate of change of the function between 3 hours and 9 hours? a. $17.00 per hour b. $25.50 per hour c. $31.05 per hour d. $42.15 per hour

The average rate of change is $25.5 per hour, option B.

Step-by-step explanation:

Average Rate of Change

When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from to . It can be computed as the slope of a line .

The provided function is

We are required to compute the average rate of change between the points

Let's compute

The average rate of change is $25.5 per hour, option B.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.