I think u take the two numbers and times them
![\bf \stackrel{\textit{degree of the polynomial}}{x^{\stackrel{\downarrow }{6}}-2x^4-5x^2+6}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Bdegree%20of%20the%20polynomial%7D%7D%7Bx%5E%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7B6%7D%7D-2x%5E4-5x%5E2%2B6%7D)
recall <u>the fundamental theorem of algebra</u>, as many roots as the degree of the polynomial.
The first thing we must do for this case is to find the relationship between the variables.
We have then:
![AB = DC\\4y - 2 = 2y + 6](https://tex.z-dn.net/?f=%20AB%20%3D%20DC%5C%5C4y%20-%202%20%3D%202y%20%2B%206%20%20)
From here, we clear the value of "Y":
![4y - 2y = 6 + 2\\2y = 8](https://tex.z-dn.net/?f=%204y%20-%202y%20%3D%206%20%2B%202%5C%5C2y%20%3D%208%20%20)
![y = \frac{8}{2}\\y = 4](https://tex.z-dn.net/?f=%20y%20%3D%20%5Cfrac%7B8%7D%7B2%7D%5C%5Cy%20%3D%204%20%20%20)
On the other hand we have:
![AD = BC\\3x - 1 = 2x + 2](https://tex.z-dn.net/?f=%20AD%20%3D%20BC%5C%5C3x%20-%201%20%3D%202x%20%2B%202%20%20)
From here, we clear the value of "x":
![3x - 2x = 2 + 1\\x = 3](https://tex.z-dn.net/?f=%203x%20-%202x%20%3D%202%20%2B%201%5C%5Cx%20%3D%203%20%20)
Then, replacing values we have:
![AB = DC = 4y - 2 = 4 (4) - 2 = 16 - 2 = 14\\AB = DC = 14](https://tex.z-dn.net/?f=%20AB%20%3D%20DC%20%3D%204y%20-%202%20%3D%204%20%284%29%20-%202%20%3D%2016%20-%202%20%3D%2014%5C%5CAB%20%3D%20DC%20%3D%2014%20%20)
On the other hand:
![AD = BC = 2x + 2 = 2 (3) + 2 = 6 + 2 = 8\\AD = BC = 8](https://tex.z-dn.net/?f=%20AD%20%3D%20BC%20%3D%202x%20%2B%202%20%3D%202%20%283%29%20%2B%202%20%3D%206%20%2B%202%20%3D%208%5C%5CAD%20%3D%20BC%20%3D%208%20%20)
Finally, the perimeter is given by:
![P = AB + DC + AD + BC](https://tex.z-dn.net/?f=%20P%20%3D%20AB%20%2B%20DC%20%2B%20AD%20%2B%20BC%20%20)
Substituting values we have:
![P = 14 + 14 + 8 + 8\\P = 44](https://tex.z-dn.net/?f=%20P%20%3D%2014%20%2B%2014%20%2B%208%20%2B%208%5C%5CP%20%3D%2044%20%20)
Answer:
the perimeter of ABCD is:
44 units
17. Perpendicular
18. Parallel
19. Y= -5x-3
SOH CAH TOA
AC is opposite sin(45)=11/BC
BC = 11/sin(45)
BC=11 root 2