Answer:
The answer is A. -27
Step-by-step explanation:
-15+(-12)= -27
-3 = x^2 + 4x + 1
0 = x^2 + 4x + 1 + 3
0 = x^2 + 4x + 4
Discriminant is b^2 - 4ac.
4^2 - 4(1)(4)
16 - 4(4)
16 - 16 = 0
Discriminant Rules:
1. If b²-4ac is negative, there are no real answers.
2. If b²-4ac is zero, there is one real answer.
3. If b²-4ac is positive, there are two real answers.
Based on rule 2, the answer is ONE REAL ROOT.
For this case we have that by definition, the standard form of a linear equation is:
![ax + by = c](https://tex.z-dn.net/?f=ax%20%2B%20by%20%3D%20c)
We have the following equation of the point-slope form:
![y + 7 = - \frac {2} {5} (x-10)](https://tex.z-dn.net/?f=y%20%2B%207%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20%28x-10%29)
We manipulate the equation algebraically to convert it to the standard form:
We apply distributive property to the terms within parentheses, taking into account that:
![- * + = -\\- * - = +\\y + 7 = - \frac {2} {5} x + \frac {2} {5} (10)\\y + 7 = - \frac {2} {5} x + 4](https://tex.z-dn.net/?f=-%20%2A%20%2B%20%3D%20-%5C%5C-%20%2A%20-%20%3D%20%2B%5C%5Cy%20%2B%207%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20x%20%2B%20%5Cfrac%20%7B2%7D%20%7B5%7D%20%2810%29%5C%5Cy%20%2B%207%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7D%20x%20%2B%204)
We subtract 4 from both sides of the equation:
![y + 7-4 = -\frac {2} {5}x\\y + 3 = - \frac {2} {5}x](https://tex.z-dn.net/?f=y%20%2B%207-4%20%3D%20-%5Cfrac%20%7B2%7D%20%7B5%7Dx%5C%5Cy%20%2B%203%20%3D%20-%20%5Cfrac%20%7B2%7D%20%7B5%7Dx)
We multiply by 5 on both sides of the equation:
![5 (y + 3) = - 2x\\5y + 15 = -2x](https://tex.z-dn.net/?f=5%20%28y%20%2B%203%29%20%3D%20-%202x%5C%5C5y%20%2B%2015%20%3D%20-2x)
Adding 2x to both sides of the equation:
![2x + 5y + 15 = 0](https://tex.z-dn.net/?f=2x%20%2B%205y%20%2B%2015%20%3D%200)
Subtracting 15 from both sides of the equation:![2x + 5y = -15](https://tex.z-dn.net/?f=2x%20%2B%205y%20%3D%20-15)
Thus, the standard form of the equation is: ![2x + 5y = -15](https://tex.z-dn.net/?f=2x%20%2B%205y%20%3D%20-15)
Answer:
Option C