Answer:
(x - 1) (x + 1) (x - 4) (x + 4)
Step-by-step explanation:
actor the following:
x^4 - 17 x^2 + 16
x^4 - 17 x^2 + 16 = (x^2)^2 - 17 x^2 + 16:
(x^2)^2 - 17 x^2 + 16
The factors of 16 that sum to -17 are -1 and -16. So, (x^2)^2 - 17 x^2 + 16 = (x^2 - 1) (x^2 - 16):
(x^2 - 1) (x^2 - 16)
x^2 - 16 = x^2 - 4^2:
(x^2 - 1) (x^2 - 4^2)
Factor the difference of two squares. x^2 - 4^2 = (x - 4) (x + 4):
(x - 4) (x + 4) (x^2 - 1)
x^2 - 1 = x^2 - 1^2:
(x^2 - 1^2) (x - 4) (x + 4)
Factor the difference of two squares. x^2 - 1^2 = (x - 1) (x + 1):
Answer: (x - 1) (x + 1) (x - 4) (x + 4)
so hmmm let's get the area of the whole hexagon, and then get the area of the circle inside it, then <u>subtract the area of the circle from that of the hexagon's</u>, what's leftover is what we didn't subtract, namely the shaded part.
![\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cot\stackrel{\stackrel{degrees}{\downarrow }}{\left( \frac{180}{n} \right)}~ \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\[-0.5em] \hrulefill\\ n=\stackrel{hexagon}{6}\\ s=\frac{9}{2} \end{cases}\implies A=\cfrac{1}{4}(6)\left( \cfrac{9}{2} \right)^2 \cot\left( \cfrac{180}{6} \right)](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20regular%20polygon%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7B1%7D%7B4%7Dns%5E2%5Ccot%5Cstackrel%7B%5Cstackrel%7Bdegrees%7D%7B%5Cdownarrow%20%7D%7D%7B%5Cleft%28%20%5Cfrac%7B180%7D%7Bn%7D%20%5Cright%29%7D~%20%5Cbegin%7Bcases%7D%20n%3D%5Ctextit%7Bnumber%20of%20sides%7D%5C%5C%20s%3D%5Ctextit%7Blength%20of%20a%20side%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20n%3D%5Cstackrel%7Bhexagon%7D%7B6%7D%5C%5C%20s%3D%5Cfrac%7B9%7D%7B2%7D%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B1%7D%7B4%7D%286%29%5Cleft%28%20%5Ccfrac%7B9%7D%7B2%7D%20%5Cright%29%5E2%20%5Ccot%5Cleft%28%20%5Ccfrac%7B180%7D%7B6%7D%20%5Cright%29)
![A=\cfrac{1}{4}(6)\cfrac{9^2}{2^2} \cot(30^o)\implies A=\cfrac{243}{8}\cot(30^o)\implies A=\cfrac{243\sqrt{3}}{8} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{4}{5} \end{cases}\implies A=\pi \left( \cfrac{4}{5} \right)^2\implies A=\cfrac{16\pi }{25} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=A%3D%5Ccfrac%7B1%7D%7B4%7D%286%29%5Ccfrac%7B9%5E2%7D%7B2%5E2%7D%20%5Ccot%2830%5Eo%29%5Cimplies%20A%3D%5Ccfrac%7B243%7D%7B8%7D%5Ccot%2830%5Eo%29%5Cimplies%20A%3D%5Ccfrac%7B243%5Csqrt%7B3%7D%7D%7B8%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ctextit%7Barea%20of%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D%5Cfrac%7B4%7D%7B5%7D%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%20%5Cleft%28%20%5Ccfrac%7B4%7D%7B5%7D%20%5Cright%29%5E2%5Cimplies%20A%3D%5Ccfrac%7B16%5Cpi%20%7D%7B25%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
<u><em>Answer:</em></u>
<u><em>16</em></u>
<u><em>Step-by-step explanation:</em></u>
<u><em>10 divided by 5 equals 2 (10/5=2)</em></u>
<u><em>2 times 8 equals 16 (2 x 8 = 16)</em></u>
<u><em></em></u>
Answer:
They sold 67.50 in total
Step-by-step explanation:
If each of them sold 15 boxes for 2.25 then both of them got 33.75 each then you add it and that gives you 67.50
First case:
average of test score =70
number of students =p
total score of 'p' students = ( average of test score)*( number of students)
total score of 'p' students =70p
Second case:
average of test score =92
number of students =n
total score of 'n' students = ( average of test score)*( number of students)
total score of 'n' students =92n
total number of students = p+n
total average score =86
so, total score =86(p+n)
total score = total score of 'p' students +total score of 'n' students
now, we can simplify it
now, we can find p/n
................Answer
