Answer:
10.5
Step-by-step explanation:
Answer:
the rate of change is 4/1
To find an inverse function first replace f(x) with y
f(x) = 8*sqrt(x)
y = 8*sqrt(x)
Then, simply switch the places of the x and y.
x = 8sqrt(y)
Now solve for the new y by squaring both sides (to get rid of the root)
x^2 = 64y
divide to get
y = x^2/64. This is the inverse function or option C.
The number of $0.50 increases to maximize the profit is X = 1.
First of all, we need to write the linear function which represents the price of the ticket for each increase of $0.50:
P - Price of each ticket.
x - number of increases.
We know that the current price is $5.00, so:

After that, let's build a linear function which shows the number of tickets sold <u>for each</u> price increase:
T - number of tickets.
x - number of increases.

With all this done, we can finally build the quadratic function which represents the money earned:
M - money earned

Now, to finish, we only have to <u>calculate the value of X</u>(number of increases) which can give us the maximum value of this function:
the X coordinate for the maximum value of a quadratic is expressed by:

In our equation, b = 100 and a = - 50 :

Thus, the number of increases which <u>maximizes</u> the profit is 1.
Learn more about linear and quadratic functions in: brainly.com/question/4119784
The formula for solving the area of a trapezoid is shown below:
Area = ((a+b)/2 ) * h
where "a" and "b" for the base and "h" for the height
a = 4x
b = 2x
c = (x-6)
The solution for the polynomial expression is shown below:
Area = (4x + 2x)/2 * (x-6)
Area = 6x/2 * (X-6)
Area = 3X * (X-6)
Area = 3X² - 18X
The answer is 3X² - 18X.