Answer:
x = 129
Step-by-step explanation:
x and 51 are same- side exterior angles and supplementary, thus
x = 180 - 51 = 129
Including all real and imaginary zeros and taking multiplicities into account, every equation of degree n has exactly n roots
Answer:
The equation that represents the table is:
Step-by-step explanation:
Taking two points from the table
![\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%5C%3Abetween%5C%3Atwo%5C%3Apoints%7D%3A%5Cquad%20%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(2,\:9\right),\:\left(x_2,\:y_2\right)=\left(4,\:18\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%282%2C%5C%3A9%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%284%2C%5C%3A18%5Cright%29)
![m=\frac{18-9}{4-2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B18-9%7D%7B4-2%7D)
![m=\frac{9}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B9%7D%7B2%7D)
As the slope-intercept form is
![\:y=mx+b](https://tex.z-dn.net/?f=%5C%3Ay%3Dmx%2Bb)
Plugging (2, 9) to find the y-intercept 'b'
![9=\frac{9}{2}\left(2\right)+b](https://tex.z-dn.net/?f=9%3D%5Cfrac%7B9%7D%7B2%7D%5Cleft%282%5Cright%29%2Bb)
![\mathrm{Switch\:sides}](https://tex.z-dn.net/?f=%5Cmathrm%7BSwitch%5C%3Asides%7D)
![\frac{9}{2}\left(2\right)+b=9](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B2%7D%5Cleft%282%5Cright%29%2Bb%3D9)
![\mathrm{Remove\:parentheses}:\quad \left(a\right)=a](https://tex.z-dn.net/?f=%5Cmathrm%7BRemove%5C%3Aparentheses%7D%3A%5Cquad%20%5Cleft%28a%5Cright%29%3Da)
![\frac{9}{2}\cdot \:2+b=9](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B2%7D%5Ccdot%20%5C%3A2%2Bb%3D9)
![9+b=9](https://tex.z-dn.net/?f=9%2Bb%3D9)
![b=0](https://tex.z-dn.net/?f=b%3D0)
so the equation becomes
![\:y=mx+b](https://tex.z-dn.net/?f=%5C%3Ay%3Dmx%2Bb)
![y=\frac{9}{2}\left(x\right)+0](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B2%7D%5Cleft%28x%5Cright%29%2B0)
![y=\frac{9}{2}x](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B9%7D%7B2%7Dx)
Therefore, the equation that represents the table is:
The graph of the equation is also attached below.
The discount is $ 20 for the jacket hope that helps!
Distributive property, multiply a sum by multiplying each added separately and then adding the products a(b+c)=ab+ac k(m-n)=km-kn
Term, Part of an expression that is added or subtracted. These can be a single number, variable, or numbers and variables multiplied together.
Variable, A letter or symbol that represents a value.
Constant, It’s a number kn it’s own, but it has a fixed value.
Coefficient, the number in front of a variable.
Hope this helped!!