Answer:
$352, you will have earned $152 in interests
Answer:
slope = 2/5
Step-by-step explanation:
The rise is 2
The run is 5
Answer:
Thus, every integer is a rational number. Clearly, 3/2,-5/3, etc. are rational numbers but they are not integers. Hence, every integer is a rational number but a rational number need not be an integer.
Step-by-step explanation:
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)
Answer:
-1/-6
Step-by-step explanation:
1/6 is equivalent to-1/-6