Answer:
y+1=2(x-1)
Step-by-step explanation:
use point slope form
As the number of files increases, the storage space used increases
Answer:
The inequality that you have is
. You can use mathematical induction as follows:
Step-by-step explanation:
For
we have:
![5^{5}=3125](https://tex.z-dn.net/?f=5%5E%7B5%7D%3D3125)
![2^{(2(5)+1)}+100=2148](https://tex.z-dn.net/?f=2%5E%7B%282%285%29%2B1%29%7D%2B100%3D2148)
Hence, we have that ![5^{5}>2^{(2(5)+1)}+100.](https://tex.z-dn.net/?f=5%5E%7B5%7D%3E2%5E%7B%282%285%29%2B1%29%7D%2B100.)
Now suppose that the inequality holds for
and let's proof that the same holds for
. In fact,
![5^{k+1}=5^{k}\cdot 5>(2^{2k+1}+100)\cdot 5.](https://tex.z-dn.net/?f=5%5E%7Bk%2B1%7D%3D5%5E%7Bk%7D%5Ccdot%205%3E%282%5E%7B2k%2B1%7D%2B100%29%5Ccdot%205.)
Where the last inequality holds by the induction hypothesis.Then,
![5^{k+1}>(2^{2k+1}+100)\cdot (4+1)](https://tex.z-dn.net/?f=5%5E%7Bk%2B1%7D%3E%282%5E%7B2k%2B1%7D%2B100%29%5Ccdot%20%284%2B1%29)
![5^{k+1}>2^{2k+1}\cdot 4+100\cdot 4+2^{2k+1}+100](https://tex.z-dn.net/?f=5%5E%7Bk%2B1%7D%3E2%5E%7B2k%2B1%7D%5Ccdot%204%2B100%5Ccdot%204%2B2%5E%7B2k%2B1%7D%2B100)
![5^{k+1}>2^{2k+3}+100\cdot 4](https://tex.z-dn.net/?f=5%5E%7Bk%2B1%7D%3E2%5E%7B2k%2B3%7D%2B100%5Ccdot%204)
![5^{k+1}>2^{2(k+1)+1}+100](https://tex.z-dn.net/?f=5%5E%7Bk%2B1%7D%3E2%5E%7B2%28k%2B1%29%2B1%7D%2B100)
Then, the inequality is True whenever
.
<h3>
Answer:</h3>
2x^2 -5x -2
<h3>
Step-by-step explanation:</h3>
See the attached for the polynomial long division.