The answer is A.
Angles 1 and 2 are congruent, therefore angle 2 = 122.
The sum of all three angles in a single triangle would be 180.
180 - 122 = 58
Therefore, each of the other angles have to be LESS than 58.
Answer:
THE ANSWER SHOULD BE B
HAVE A GOOD DAY
Step-by-step explanation:
D because you know it can’t be a or b and the bigger number goes first
Answer:
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
Step-by-step explanation:
Given
![Rooms = 240](https://tex.z-dn.net/?f=Rooms%20%3D%20240)
![Price= \$40](https://tex.z-dn.net/?f=Price%3D%20%5C%2440)
![Increment = \$2](https://tex.z-dn.net/?f=Increment%20%3D%20%5C%242)
First, we calculate the revenue.
![Revenue (r) = Price (p) * Number\ of\ Rooms(n)](https://tex.z-dn.net/?f=Revenue%20%28r%29%20%3D%20Price%20%28p%29%20%2A%20Number%5C%20of%5C%20Rooms%28n%29)
![r = p*n](https://tex.z-dn.net/?f=r%20%3D%20p%2An)
Let x be the change in rate.
i.e.
For every 2x increment in price (p) i.e. p + 2x
There will be 4 fewer rooms (n) i.e. n - 4x
So, the revenue is updated as:
![r = (p + 2x) * (n - 4x)](https://tex.z-dn.net/?f=r%20%3D%20%28p%20%2B%202x%29%20%2A%20%28n%20-%204x%29)
![Price = 40](https://tex.z-dn.net/?f=Price%20%3D%2040)
So:
![r = (40 + 2x) * (n - 4x)](https://tex.z-dn.net/?f=r%20%3D%20%2840%20%2B%202x%29%20%2A%20%28n%20-%204x%29)
![Rooms = 240](https://tex.z-dn.net/?f=Rooms%20%3D%20240)
So:
![r = (40 + 2x) * (240 - 4x)](https://tex.z-dn.net/?f=r%20%3D%20%2840%20%2B%202x%29%20%2A%20%28240%20-%204x%29)
Expand
![r = 40 * 240 - 40 * 4x + 2x * 240 - 2x*4x](https://tex.z-dn.net/?f=r%20%3D%2040%20%2A%20240%20-%2040%20%2A%204x%20%2B%202x%20%2A%20240%20-%202x%2A4x)
![r = 9600 - 160x + 480x - 8x^2](https://tex.z-dn.net/?f=r%20%3D%209600%20-%20160x%20%2B%20480x%20-%208x%5E2)
Reorder
![r = -8x^2 - 160x + 480x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20-%20160x%20%2B%20480x%20%2B%209600)
![r = -8x^2 +320x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20%2B320x%20%2B%209600)
The maximum of a function is calculated as:
![Max = -\frac{b}{2a}](https://tex.z-dn.net/?f=Max%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
In: ![r = -8x^2 +320x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20%2B320x%20%2B%209600)
![c = 9600](https://tex.z-dn.net/?f=c%20%3D%209600)
So:
![Max = -\frac{b}{2a}](https://tex.z-dn.net/?f=Max%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
![Max = -\frac{320}{-8}](https://tex.z-dn.net/?f=Max%20%3D%20-%5Cfrac%7B320%7D%7B-8%7D)
![Max = \frac{320}{8}](https://tex.z-dn.net/?f=Max%20%3D%20%5Cfrac%7B320%7D%7B8%7D)
![Max = 40](https://tex.z-dn.net/?f=Max%20%3D%2040)
To get the maximum revenue;
Substitute 40 for x in ![r = -8x^2 +320x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20%2B320x%20%2B%209600)
![r = -8(40)^2 + 320 * 40 + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8%2840%29%5E2%20%2B%20320%20%2A%2040%20%2B%209600)
![r = 9600](https://tex.z-dn.net/?f=r%20%3D%209600)
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600