Using the profit function, it is found that:
a) She earns $36 after 25 years.
b) The function was shifted right 4 units and up 1 units.
<h3>What is the profit function?</h3>
The profit, in x years after 2015, is given by:
![p(x) = 12\sqrt[3]{x + 2}](https://tex.z-dn.net/?f=p%28x%29%20%3D%2012%5Csqrt%5B3%5D%7Bx%20%2B%202%7D)
Item a:
She earns $36 after x years, considering x for which p(x) = 36, hence:
![36 = 12\sqrt[3]{x + 2}](https://tex.z-dn.net/?f=36%20%3D%2012%5Csqrt%5B3%5D%7Bx%20%2B%202%7D)
![\sqrt[3]{x + 2} = 3](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%20%2B%202%7D%20%3D%203)
![(\sqrt[3]{x + 2})^3 = 3^3](https://tex.z-dn.net/?f=%28%5Csqrt%5B3%5D%7Bx%20%2B%202%7D%29%5E3%20%3D%203%5E3)
She earns $36 after 25 years.
Item b:
The new function is:
![h(x) = 12\sqrt[3]{x - 2} + 1](https://tex.z-dn.net/?f=h%28x%29%20%3D%2012%5Csqrt%5B3%5D%7Bx%20-%202%7D%20%2B%201)
At the domain, we have that 
, that is, 
, hence it was shifted right 4 units.
At the range, we have that 
, hence it was shifted up 1 unit.
You can learn more about functions at brainly.com/question/24380382
Answer
5/48, 3/16, 0.5, 0.75
Step-by-step explanation:
Answer:
D. 360 in.²
Step-by-step explanation:
<em>Since all the answers are labeled as in.², we know that we have to find the area of the rectangular prism. The formula for area of a rectangular prism is: </em><em>lwh </em><em>(length x width x height).</em>
<em>l = 12</em>
<em>w = 6</em>
<em>h = 5</em>
12 x 6 x 5 = 360
Answer: Brian & Derek will earn $25 If they sell 8 and 12.
Step-by-step explanation:
1. m
2. One set of ordered pairs
3. b
To show why this is, I’m going to explain how to write the equation for a linear function with two random sets of ordered pairs - (1,0) and (5, 8).
First, find the slope. The formula for slope is m = (y2 - y1)/(x2-x1) where m is the slope and (x1, y1) and (x2, y2) are two sets of points.
This is why #1 is m. M is the letter used when finding slope.
To find m, I plug in the two sets of ordered pairs.
m = (8-0)/(5-1)
m = 8/4
m = 2
An equation for a line (linear function) is written in something called slope-intercept form. It looks like y = mx + b. m is the slope and b is the y-intercept (number y equals when x = 0). If m = 3 and b = 1, the equation would be y = 3x + 1.
Here, you have just solved for m and know it equals 2. Plug that value in for m.
y = 2x + b
To solve for b, plug one ordered pair in for x and y. I will use (1,0)
0 = 2(1) + b
0 = 2 + b
-2 = b
Now that you know b = -2, plug that in for b.
y = 2x - 2. Now you have the equation fo the line.
