Answer:
The solution would be (-19, 40)
Step-by-step explanation:
In order to solve this system by substitution, simply take the value of y in the first equation and use it in place of y in the second. This will allow you to solve for x.
5x + 2y = 15
5x + 2(-3x - 2) = 15
5x - 6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
Now that we have the value of x, we can find the value of y.
y = -3x - 3
y = -3(-19) - 3
y = 43 - 3
y = 40
Answer:
![f(x)=0.5x^2-4x+7.5](https://tex.z-dn.net/?f=f%28x%29%3D0.5x%5E2-4x%2B7.5)
Step-by-step explanation:
The general form of a quadratic function is:
![y=ax^2+bx+c](https://tex.z-dn.net/?f=y%3Dax%5E2%2Bbx%2Bc)
We'll find the general form of the function:
![f(x)=0.5(x-3)(x-5)](https://tex.z-dn.net/?f=f%28x%29%3D0.5%28x-3%29%28x-5%29)
Multiplying the expressions in parentheses:
![f(x)=0.5(x^2-5x-3x+15)](https://tex.z-dn.net/?f=f%28x%29%3D0.5%28x%5E2-5x-3x%2B15%29)
Simplifying:
![f(x)=0.5(x^2-8x+15)](https://tex.z-dn.net/?f=f%28x%29%3D0.5%28x%5E2-8x%2B15%29)
Operating:
![\mathbf{f(x)=0.5x^2-4x+7.5}](https://tex.z-dn.net/?f=%5Cmathbf%7Bf%28x%29%3D0.5x%5E2-4x%2B7.5%7D)
ANSWER
b.
EXPLANATION
The given polar equation is,
![r = \frac{12}{6 + 4 \cos( \theta) }](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B12%7D%7B6%20%2B%204%20%5Ccos%28%20%5Ctheta%29%20%7D%20)
Cross multiply to get,
![r(6 + 4 \cos( \theta) ) = 12](https://tex.z-dn.net/?f=r%286%20%2B%204%20%5Ccos%28%20%5Ctheta%29%20%29%20%3D%2012)
![6r + 4r\cos( \theta) ) = 12](https://tex.z-dn.net/?f=6r%20%2B%204r%5Ccos%28%20%5Ctheta%29%20%29%20%3D%2012)
Substitute,
![r\cos( \theta) = x](https://tex.z-dn.net/?f=%20r%5Ccos%28%20%5Ctheta%29%20%3D%20x)
and
![r = \sqrt{ {x}^{2} + {y}^{2} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%2B%20%7By%7D%5E%7B2%7D%20%7D%20)
![6 \sqrt{ {x}^{2} + {y}^{2} } + 4x = 12](https://tex.z-dn.net/?f=6%20%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%2B%20%7By%7D%5E%7B2%7D%20%7D%20%2B%204x%20%3D%2012)
![3\sqrt{ {x}^{2} + {y}^{2} } + 2x = 6](https://tex.z-dn.net/?f=3%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%2B%20%7By%7D%5E%7B2%7D%20%7D%20%2B%202x%20%3D%206)
![3\sqrt{ {x}^{2} + {y}^{2} } = 4 - 2x](https://tex.z-dn.net/?f=3%5Csqrt%7B%20%7Bx%7D%5E%7B2%7D%20%2B%20%7By%7D%5E%7B2%7D%20%7D%20%3D%204%20-%202x%20)
![9({x}^{2} + {y}^{2}) =( 4 - 2x ) ^{2}](https://tex.z-dn.net/?f=9%28%7Bx%7D%5E%7B2%7D%20%2B%20%7By%7D%5E%7B2%7D%29%20%3D%28%204%20-%202x%20%29%20%5E%7B2%7D%20)
![9{x}^{2} + 9 {y}^{2} =16 - 16x + 4x ^{2}](https://tex.z-dn.net/?f=9%7Bx%7D%5E%7B2%7D%20%2B%209%20%7By%7D%5E%7B2%7D%20%3D16%20-%2016x%20%2B%204x%20%5E%7B2%7D%20)
![5{x}^{2} + 9 {y}^{2} + 16x = 16](https://tex.z-dn.net/?f=5%7Bx%7D%5E%7B2%7D%20%2B%209%20%7By%7D%5E%7B2%7D%20%2B%2016x%20%3D%2016)
This is an ellipse whose center is shifted to the left with orientation on the x-axis
The correct choice is B.
Answer: inverse function
Step-by-step explanation:
Answer:
ii
Step-by-step explanation: