Answer:
2/3
Step-by-step explanation:
Slope = ![\frac{y2-y1}{x2-x1}](https://tex.z-dn.net/?f=%5Cfrac%7By2-y1%7D%7Bx2-x1%7D)
(-4,2) = (x1,y1)
(-16,-6) = (x2,y2)
Slope = ![\frac{-6-2}{-16+4}](https://tex.z-dn.net/?f=%5Cfrac%7B-6-2%7D%7B-16%2B4%7D)
= ![\frac{-8}{-12}](https://tex.z-dn.net/?f=%5Cfrac%7B-8%7D%7B-12%7D)
= ![\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D)
Answer:
(-111)
Step-by-step explanation:
4 because the value of 22 has a common factor and it is balanced with the equation
Answer:
![x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-%28-2%29%20%5C%C2%B1%20%5Csqrt%7B%28-2%29%5E2%20-%204%2A1%2A-3%7D%7D%7B2%2A1%7D)
Step-by-step explanation:
Given
![0 = x^2 - 2x -3](https://tex.z-dn.net/?f=0%20%3D%20x%5E2%20-%202x%20-3)
Required
The correct quadratic formula for the above
A quadratic equation is represented as:
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
And the formula is:
![x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5C%C2%B1%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
So, we have:
![0 = x^2 - 2x -3](https://tex.z-dn.net/?f=0%20%3D%20x%5E2%20-%202x%20-3)
Rewrite as:
![x^2 - 2x - 3 = 0](https://tex.z-dn.net/?f=x%5E2%20-%202x%20-%203%20%3D%200)
By comparison:
![a= 1; b = -2; c = -3](https://tex.z-dn.net/?f=a%3D%201%3B%20b%20%3D%20-2%3B%20c%20%3D%20-3)
So, we have:
![x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%5C%C2%B1%20%5Csqrt%7Bb%5E2%20-%204ac%7D%7D%7B2a%7D)
![x = \frac{-(-2) \± \sqrt{(-2)^2 - 4*1*-3}}{2*1}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-%28-2%29%20%5C%C2%B1%20%5Csqrt%7B%28-2%29%5E2%20-%204%2A1%2A-3%7D%7D%7B2%2A1%7D)
Statement Reason
m∠EGF = 60° & m∠AGF = 90° Given
∠EGF + ∠AGF + ∠AGB = 180° Definition of supplementary angles
60° + 90° + ∠AGB = 180° Substitution
150° + ∠AGB = 180° Add the the similar values
∠AGB = 180° - 150° Subtraction property of equality
∠AGB = 30° Answer
You are free to arrange any of the reasons (and statements) as you wish.
I just want to give you the main idea.
Hope this helps.