For this case we have the following system of equations:
![y = x ^ 2 + 7x + 12\\y = 2x + 8](https://tex.z-dn.net/?f=y%20%3D%20x%20%5E%202%20%2B%207x%20%2B%2012%5C%5Cy%20%3D%202x%20%2B%208)
Equating both equations we have:
![x ^ 2 + 7x + 12 = 2x + 8\\x ^ 2 + 7x-2x + 12-8 = 0\\x ^ 2 + 5x + 4 = 0](https://tex.z-dn.net/?f=x%20%5E%202%20%2B%207x%20%2B%2012%20%3D%202x%20%2B%208%5C%5Cx%20%5E%202%20%2B%207x-2x%20%2B%2012-8%20%3D%200%5C%5Cx%20%5E%202%20%2B%205x%20%2B%204%20%3D%200)
We must find the solutions, for this we factor. We look for two numbers that, when multiplied, result in 4 and when added, result in 5. These numbers are 4 and 1:
![4 + 1 = 5\\4 * 1 = 4](https://tex.z-dn.net/?f=4%20%2B%201%20%3D%205%5C%5C4%20%2A%201%20%3D%204)
Then, the factorized equation is of the form:
![(x + 4) (x + 1) = 0](https://tex.z-dn.net/?f=%28x%20%2B%204%29%20%28x%20%2B%201%29%20%3D%200)
Thus, the solutions are:
![x_ {1} = - 4\\x_ {2} = - 1](https://tex.z-dn.net/?f=x_%20%7B1%7D%20%3D%20-%204%5C%5Cx_%20%7B2%7D%20%3D%20-%201)
We look for solutions for the variable "y":
![y_ {1} = 2 (-4) + 8 = -8 + 8 = 0\\y_ {2} = 2 (-1) + 8 = -2 + 8 = 6](https://tex.z-dn.net/?f=y_%20%7B1%7D%20%3D%202%20%28-4%29%20%2B%208%20%3D%20-8%20%2B%208%20%3D%200%5C%5Cy_%20%7B2%7D%20%3D%202%20%28-1%29%20%2B%208%20%3D%20-2%20%2B%208%20%3D%206)
Thus, the system solutions are given by:![(x_ {1}, y_ {1}): (- 4,0)\\(x_ {2}, y_ {2}): (- 1,6)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%28-%204%2C0%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%28-%201%2C6%29)
ANswer:
![(x_ {1}, y_ {1}): (- 4,0)\\(x_ {2}, y_ {2}): (- 1,6)](https://tex.z-dn.net/?f=%28x_%20%7B1%7D%2C%20y_%20%7B1%7D%29%3A%20%28-%204%2C0%29%5C%5C%28x_%20%7B2%7D%2C%20y_%20%7B2%7D%29%3A%20%28-%201%2C6%29)
Step-by-step explanation:
There are a few steps to follow when you add or subtract rational expressions with unlike denominators.
To add or subtract rational expressions with unlike denominators, first find the LCM of the denominator. The LCM of the denominators of fraction or rational expressions is also called least common denominator , or LCD.
Write each expression using the LCD. Make sure each term has the LCD as its denominator.
Add or subtract the numerators.
Simplify as needed.
The answer to this question is c=3
Answer:
Each person get = 20 cents
Step-by-step explanation:
Given - Maya and three friends have three quarters and one nickel to spend.
To find - If Maya and her friends share the money equally how much will each person get ?
Proof -
We know that
1 nickel = 5 cents
1 quarter = 25 cents
As they spent, 3 quarters and one nickel
So,
Total money spent = 3(25) + 5 = 75 + 5 = 80 cents
⇒Total money spent = 80 cents
Now,
Total people = 4 (Maya and three friends )
Now,
Given that, They share the money equally
So,
Each person get =
= 20 cents
Answer:
(x,y) --> (x, y-5)
Step-by-step explanation:
the y-intercept of f(x) = (0,2)
the y-intercept of g(x) = (0, -3)
-3 - 2 = -5