To solve this problem you must apply the proccedure shown below:
1. First, you must understand the information given in the exercise. You have that: nine less than two-thirds a number is greater than twenty-five.
2. Let's call
to the number mentioned above. You have that "nine less than two-thirds a number" means a substraction and " is greater than twenty-five" can be expressed with the symbol >.
Therefore, you have that the answer is:
![9-2/3(x)>25](https://tex.z-dn.net/?f=%209-2%2F3%28x%29%3E25%20)
- AC is congruent to itself
- AC bisects angle BAD, so that angles BAC and DAC are congruent
- Both angles B and D are right angles, so they are congruent
This means triangles BAC and DAC are a pair of angle-angle-side triangles, so they are congruent to one another. Corresponding parts of congruent triangles are congruent, so the line segments BC and DC are congruent and have the same length.
Then
![8n+2=2n+20\implies6n=18\implies n=3](https://tex.z-dn.net/?f=8n%2B2%3D2n%2B20%5Cimplies6n%3D18%5Cimplies%20n%3D3)
Answer:
![P(t) = 100e^{0.0251t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7B0.0251t%7D)
The doubling time is of 27.65 minutes.
Step-by-step explanation:
Exponential equation of growth:
The exponential equation for population growth is given by:
![P(t) = P(0)e^{kt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20P%280%29e%5E%7Bkt%7D)
In which P(0) is the initial value and k is the growth rate.
A freshly inoculated bacterial culture of Streptococcus contains 100 cells.
This means that
. So
![P(t) = 100e^{kt}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7Bkt%7D)
When the culture is checked 60 minutes later, it is determined that there are 450 cells present.
This means that
, and we use this to find k. So
![450 = 100e^{60k}](https://tex.z-dn.net/?f=450%20%3D%20100e%5E%7B60k%7D)
![e^{60k} = 4.5](https://tex.z-dn.net/?f=e%5E%7B60k%7D%20%3D%204.5)
![\ln{e^{60k}} = \ln{4.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B60k%7D%7D%20%3D%20%5Cln%7B4.5%7D)
![60k = \ln{4.5}](https://tex.z-dn.net/?f=60k%20%3D%20%5Cln%7B4.5%7D)
![k = \frac{\ln{4.5}}{60}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B%5Cln%7B4.5%7D%7D%7B60%7D)
![k = 0.0251](https://tex.z-dn.net/?f=k%20%3D%200.0251)
So
![P(t) = 100e^{0.0251t}](https://tex.z-dn.net/?f=P%28t%29%20%3D%20100e%5E%7B0.0251t%7D)
Doubling time:
This is t for which P(t) = 2P(0) = 200. So
![200 = 100e^{0.0251t}](https://tex.z-dn.net/?f=200%20%3D%20100e%5E%7B0.0251t%7D)
![e^{0.0251t} = 2](https://tex.z-dn.net/?f=e%5E%7B0.0251t%7D%20%3D%202)
![\ln{e^{0.0251t}} = \ln{2}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B0.0251t%7D%7D%20%3D%20%5Cln%7B2%7D)
![0.0251t = \ln{2}](https://tex.z-dn.net/?f=0.0251t%20%3D%20%5Cln%7B2%7D)
![t = \frac{\ln{2}}{0.0251}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Cln%7B2%7D%7D%7B0.0251%7D)
![t = 27.65](https://tex.z-dn.net/?f=t%20%3D%2027.65)
The doubling time is of 27.65 minutes.
Pythagorean theorem: a² + b² = c²
to find out if these numbers make a triangle, you must put them into the pythagorean theorem
7² + 8² = 15²
49 + 64 =/= 225
so no, these numbers do not make a triangle. hope this helped! ♥