D), if you see the last choice you add the 2 and the 0.05 together and you would get 2.05, on the side it says 36, this is porbably just the distributive property
The most appropriate choice for polynomial will be given by
1) Zeroes of P(x) = 2,
, ![\frac{2 - \sqrt{2}i}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%20-%20%5Csqrt%7B2%7Di%7D%7B3%7D)
where ![i = \sqrt{-1}](https://tex.z-dn.net/?f=i%20%3D%20%5Csqrt%7B-1%7D)
2) Zeroes of P(x) = 3, 2i, -2i
3) Roots are 2i, -2i, ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
4) Roots are 0, 1,
, ![2 - \sqrt{5}](https://tex.z-dn.net/?f=2%20-%20%5Csqrt%7B5%7D)
What is a polynomial?
An algebraic expression of the form
is called a polynomial of degree n.
![1) P(x ) = 3x^3 -10x^2 + 10x -4\\P(2) = 3(2)^3 - 10(2)^2 +10(2) - 4\\](https://tex.z-dn.net/?f=1%29%20P%28x%20%29%20%3D%203x%5E3%20-10x%5E2%20%2B%2010x%20-4%5C%5CP%282%29%20%3D%203%282%29%5E3%20-%2010%282%29%5E2%20%2B10%282%29%20-%204%5C%5C)
![= 24 -40 + 20 -16\\= 0](https://tex.z-dn.net/?f=%3D%2024%20-40%20%2B%2020%20-16%5C%5C%3D%200)
(x - 2) is a factor of P(x)
![P(x) = 3x^2(x - 2) -4x(x - 2) +2(x-2)\\](https://tex.z-dn.net/?f=P%28x%29%20%3D%203x%5E2%28x%20-%202%29%20-4x%28x%20-%202%29%20%2B2%28x-2%29%5C%5C)
= ![(x - 2)(3x^2 - 4x + 2)](https://tex.z-dn.net/?f=%28x%20-%202%29%283x%5E2%20-%204x%20%2B%202%29)
![=(x-2)(x -a)(x - b)](https://tex.z-dn.net/?f=%3D%28x-2%29%28x%20-a%29%28x%20-%20b%29)
where,
![a = \frac{-(-4)+\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\a =\frac{ 4 + \sqrt{-8}}{6}\\a = \frac{4 + 2\sqrt{2} i}{6}\\a = \frac{2(2 + \sqrt{2}i)}{6}\\a = \frac{2 + \sqrt{2}i}{3}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B-%28-4%29%2B%5Csqrt%7B%28-4%29%5E2%20-%204%5Ctimes%203%5Ctimes%202%7D%7D%7B2%5Ctimes%203%7D%5C%5Ca%20%3D%5Cfrac%7B%204%20%2B%20%5Csqrt%7B-8%7D%7D%7B6%7D%5C%5Ca%20%3D%20%5Cfrac%7B4%20%2B%202%5Csqrt%7B2%7D%20i%7D%7B6%7D%5C%5Ca%20%3D%20%5Cfrac%7B2%282%20%2B%20%5Csqrt%7B2%7Di%29%7D%7B6%7D%5C%5Ca%20%3D%20%5Cfrac%7B2%20%2B%20%5Csqrt%7B2%7Di%7D%7B3%7D)
![b = \frac{-(-4)-\sqrt{(-4)^2 - 4\times 3\times 2}}{2\times 3}\\b =\frac{ 4 -\sqrt{-8}}{6}\\b = \frac{4 - 2\sqrt{2} i}{6}\\b = \frac{2(2 - \sqrt{2}i)}{6}\\b = \frac{2 - \sqrt{2}i}{3}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B-%28-4%29-%5Csqrt%7B%28-4%29%5E2%20-%204%5Ctimes%203%5Ctimes%202%7D%7D%7B2%5Ctimes%203%7D%5C%5Cb%20%3D%5Cfrac%7B%204%20-%5Csqrt%7B-8%7D%7D%7B6%7D%5C%5Cb%20%3D%20%5Cfrac%7B4%20-%202%5Csqrt%7B2%7D%20i%7D%7B6%7D%5C%5Cb%20%3D%20%5Cfrac%7B2%282%20-%20%5Csqrt%7B2%7Di%29%7D%7B6%7D%5C%5Cb%20%3D%20%5Cfrac%7B2%20-%20%5Csqrt%7B2%7Di%7D%7B3%7D)
Zeroes of P(x) = 2,
, ![\frac{2 - \sqrt{2}i}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%20-%20%5Csqrt%7B2%7Di%7D%7B3%7D)
where ![i = \sqrt{-1}](https://tex.z-dn.net/?f=i%20%3D%20%5Csqrt%7B-1%7D)
![2) P(x) = x^3 - 3x^2+4x-12\\P(3) = (3)^3 - 3(3)^2 +4(3) -12\\ P(3) = 0](https://tex.z-dn.net/?f=2%29%20P%28x%29%20%3D%20x%5E3%20-%203x%5E2%2B4x-12%5C%5CP%283%29%20%3D%20%283%29%5E3%20-%203%283%29%5E2%20%2B4%283%29%20-12%5C%5C%20%20%20%20%20P%283%29%20%3D%200)
(x - 3) is a factor of P(x)
![x^2(x - 3) + 4(x - 3)\\(x - 3)(x^2 + 4)\\(x - 3)(x -a)(x-b)\\](https://tex.z-dn.net/?f=x%5E2%28x%20-%203%29%20%2B%204%28x%20-%203%29%5C%5C%28x%20-%203%29%28x%5E2%20%2B%204%29%5C%5C%28x%20-%203%29%28x%20-a%29%28x-b%29%5C%5C)
where,
![a = \sqrt{-4}\\a = 2i](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%7B-4%7D%5C%5Ca%20%3D%202i)
![b = -\sqrt{-4}\\a = -2i](https://tex.z-dn.net/?f=b%20%3D%20-%5Csqrt%7B-4%7D%5C%5Ca%20%3D%20-2i)
Zeroes of P(x) = 3, 2i, -2i
![3) 2x^3 - 3x^2 +8x-12= 0\\](https://tex.z-dn.net/?f=3%29%202x%5E3%20-%203x%5E2%20%2B8x-12%3D%200%5C%5C)
x = 2 satisfies the equation
![2x^2(x -\frac{3}{2}) + 8(x-\frac{3}{2})=0\\(2x^2+8)(x - \frac{3}{2}) = 0\\](https://tex.z-dn.net/?f=2x%5E2%28x%20-%5Cfrac%7B3%7D%7B2%7D%29%20%2B%208%28x-%5Cfrac%7B3%7D%7B2%7D%29%3D0%5C%5C%282x%5E2%2B8%29%28x%20-%20%5Cfrac%7B3%7D%7B2%7D%29%20%3D%200%5C%5C)
or ![x - \frac{3}{2} = 0](https://tex.z-dn.net/?f=x%20-%20%5Cfrac%7B3%7D%7B2%7D%20%3D%200)
or ![x = \frac{3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3%7D%7B2%7D)
or ![x = \frac{3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3%7D%7B2%7D)
or ![x = \frac{3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3%7D%7B2%7D)
or
or ![x = \frac{3}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B3%7D%7B2%7D)
Roots are 2i, -2i, ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
4)
![x^4 - 5x^3 +3x^2 +x = 0\\x(x^3 -5x^2 + 3x +1) = 0\\](https://tex.z-dn.net/?f=x%5E4%20-%205x%5E3%20%20%2B3x%5E2%20%2Bx%20%3D%200%5C%5Cx%28x%5E3%20-5x%5E2%20%2B%203x%20%2B1%29%20%3D%200%5C%5C)
or ![x^3 -5x^2+3x +1 = 0](https://tex.z-dn.net/?f=x%5E3%20-5x%5E2%2B3x%20%2B1%20%3D%200)
For ![x^3 -5x^2+3x +1 = 0](https://tex.z-dn.net/?f=x%5E3%20-5x%5E2%2B3x%20%2B1%20%3D%200)
x = 1 satisfies the equation
![x^2(x -1) -4x(x-1)-1(x-1) = 0\\(x - 1)(x^2 - 4x -1) = 0\\](https://tex.z-dn.net/?f=x%5E2%28x%20-1%29%20-4x%28x-1%29-1%28x-1%29%20%3D%200%5C%5C%28x%20-%201%29%28x%5E2%20-%204x%20-1%29%20%3D%200%5C%5C)
or ![x^2 - 4x -1 = 0](https://tex.z-dn.net/?f=x%5E2%20-%204x%20-1%20%3D%200)
Roots are x = 1 or x = a or x = b
where,
![a = \frac{-(-4) + \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\a = \frac{4+\sqrt{20}}{2}\\a = \frac{4 + 2\sqrt{5}}{2}\\a = \frac{2(2 + \sqrt{5})}{2}\\a = 2 + \sqrt{5}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B-%28-4%29%20%2B%20%5Csqrt%7B%28-4%29%5E2%20-%204%5Ctimes%201%20%5Ctimes%28-1%29%7D%7D%7B2%5Ctimes%201%7D%5C%5Ca%20%3D%20%5Cfrac%7B4%2B%5Csqrt%7B20%7D%7D%7B2%7D%5C%5Ca%20%3D%20%5Cfrac%7B4%20%2B%202%5Csqrt%7B5%7D%7D%7B2%7D%5C%5Ca%20%3D%20%5Cfrac%7B2%282%20%2B%20%5Csqrt%7B5%7D%29%7D%7B2%7D%5C%5Ca%20%3D%202%20%2B%20%5Csqrt%7B5%7D)
![b = \frac{-(-4) - \sqrt{(-4)^2 - 4\times 1 \times(-1)}}{2\times 1}\\b = \frac{4-\sqrt{20}}{2}\\b = \frac{4 - 2\sqrt{5}}{2}\\b = \frac{2(2 - \sqrt{5})}{2}\\b = 2 - \sqrt{5}](https://tex.z-dn.net/?f=b%20%3D%20%5Cfrac%7B-%28-4%29%20-%20%5Csqrt%7B%28-4%29%5E2%20-%204%5Ctimes%201%20%5Ctimes%28-1%29%7D%7D%7B2%5Ctimes%201%7D%5C%5Cb%20%3D%20%5Cfrac%7B4-%5Csqrt%7B20%7D%7D%7B2%7D%5C%5Cb%20%3D%20%5Cfrac%7B4%20-%202%5Csqrt%7B5%7D%7D%7B2%7D%5C%5Cb%20%3D%20%5Cfrac%7B2%282%20-%20%5Csqrt%7B5%7D%29%7D%7B2%7D%5C%5Cb%20%3D%202%20-%20%5Csqrt%7B5%7D)
Roots are 0, 1,
, ![2 - \sqrt{5}](https://tex.z-dn.net/?f=2%20-%20%5Csqrt%7B5%7D)
To learn more about polynomial, refer to the link-
brainly.com/question/2833285
#SPJ13
Answer:
Angle C=72º
Step-by-step explanation:
If two angles are congruent they are equals then angle A is 54º and angle B is 54º and the sum of the internal angles of a triangle is 180º then.
C=180º-54º-54º=72º
To know the value of on AC and BC we have to know the value of the other side AB, to find the values of the sides we can use the law of sines;
![\dfrac{AB}{sin(72)}=\dfrac{BC}{sin(54)}=\dfrac{AC}{sin(54)}](https://tex.z-dn.net/?f=%5Cdfrac%7BAB%7D%7Bsin%2872%29%7D%3D%5Cdfrac%7BBC%7D%7Bsin%2854%29%7D%3D%5Cdfrac%7BAC%7D%7Bsin%2854%29%7D)
Answer:
Step-by-step explanation:
let Garrett orders x stickersfrom each company.
then
30+0.80x=14+1.20x