Answer:
![(g + f)(2) = \sqrt 3 - 3](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%282%29%20%3D%20%5Csqrt%203%20-%203)
![(\frac{f}{g})(-1) = 0](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28-1%29%20%3D%200)
![(g + f)(-1) = \sqrt{15}](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%28-1%29%20%3D%20%5Csqrt%7B15%7D)
![(g * f)(2) = -3\sqrt 3](https://tex.z-dn.net/?f=%28g%20%2A%20f%29%282%29%20%3D%20-3%5Csqrt%203)
Step-by-step explanation:
Given
![f(x) =1 - x^2](https://tex.z-dn.net/?f=f%28x%29%20%3D1%20-%20x%5E2)
![g(x) = \sqrt{11 - 4x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Csqrt%7B11%20-%204x)
See attachment
Solving (a): (g + f)(2)
This is calculated as:
![(g + f)(2) = g(2) + f(2)](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%282%29%20%3D%20g%282%29%20%2B%20f%282%29)
Calculate g(2) and f(2)
![g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}](https://tex.z-dn.net/?f=g%282%29%20%5Cto%20%5Csqrt%7B11%20-%204%20%2A%202%7D%20%3D%20%5Csqrt%7B3%7D)
![f(2) = 1 - 2^2 = -3](https://tex.z-dn.net/?f=f%282%29%20%3D%201%20-%202%5E2%20%3D%20-3)
So:
![(g + f)(2) = g(2) + f(2)](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%282%29%20%3D%20g%282%29%20%2B%20f%282%29)
![(g + f)(2) = \sqrt 3 - 3](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%282%29%20%3D%20%5Csqrt%203%20-%203)
Solving (b): ![(\frac{f}{g})(-1)](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28-1%29)
This is calculated as:
![(\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28-1%29%20%3D%20%5Cfrac%7Bf%28-1%29%7D%7Bg%28-1%29%7D)
Calculate f(-1) and g(-1)
![f(-1) = 1 - (-1)^2 = 0](https://tex.z-dn.net/?f=f%28-1%29%20%3D%201%20-%20%28-1%29%5E2%20%3D%200)
So:
![(\frac{f}{g})(-1) = \frac{f(-1)}{g(-1)}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28-1%29%20%3D%20%5Cfrac%7Bf%28-1%29%7D%7Bg%28-1%29%7D)
![(\frac{f}{g})(-1) = \frac{0}{g(-1)}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28-1%29%20%3D%20%5Cfrac%7B0%7D%7Bg%28-1%29%7D)
![(\frac{f}{g})(-1) = 0](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28-1%29%20%3D%200)
Solving (c): (g - f)(-1)
This is calculated as:
![(g + f)(-1) = g(-1) - f(-1)](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%28-1%29%20%3D%20g%28-1%29%20-%20f%28-1%29)
Calculate g(-1) and f(-1)
![g(-1) = \sqrt{11 - 4 * -1} = \sqrt{15}](https://tex.z-dn.net/?f=g%28-1%29%20%3D%20%5Csqrt%7B11%20-%204%20%2A%20-1%7D%20%3D%20%5Csqrt%7B15%7D)
![f(-1) = 1 - (-1)^2 = 0](https://tex.z-dn.net/?f=f%28-1%29%20%3D%201%20-%20%28-1%29%5E2%20%3D%200)
So:
![(g + f)(-1) = g(-1) - f(-1)](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%28-1%29%20%3D%20g%28-1%29%20-%20f%28-1%29)
![(g + f)(-1) = \sqrt{15} - 0](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%28-1%29%20%3D%20%5Csqrt%7B15%7D%20-%200)
![(g + f)(-1) = \sqrt{15}](https://tex.z-dn.net/?f=%28g%20%2B%20f%29%28-1%29%20%3D%20%5Csqrt%7B15%7D)
Solving (d): (g * f)(2)
This is calculated as:
![(g * f)(2) = g(2) * f(2)](https://tex.z-dn.net/?f=%28g%20%2A%20f%29%282%29%20%3D%20g%282%29%20%2A%20f%282%29)
Calculate g(2) and f(2)
![g(2) \to \sqrt{11 - 4 * 2} = \sqrt{3}](https://tex.z-dn.net/?f=g%282%29%20%5Cto%20%5Csqrt%7B11%20-%204%20%2A%202%7D%20%3D%20%5Csqrt%7B3%7D)
![f(2) = 1 - 2^2 = -3](https://tex.z-dn.net/?f=f%282%29%20%3D%201%20-%202%5E2%20%3D%20-3)
So:
![(g * f)(2) = g(2) * f(2)](https://tex.z-dn.net/?f=%28g%20%2A%20f%29%282%29%20%3D%20g%282%29%20%2A%20f%282%29)
![(g * f)(2) = \sqrt 3 * -3](https://tex.z-dn.net/?f=%28g%20%2A%20f%29%282%29%20%3D%20%5Csqrt%203%20%2A%20-3)
![(g * f)(2) = -3\sqrt 3](https://tex.z-dn.net/?f=%28g%20%2A%20f%29%282%29%20%3D%20-3%5Csqrt%203)
Answer:
The discriminant is 0
Step-by-step explanation:
Since the graph of the quadratic equation has only one x-intercept, we can conclude that the quadratic has only one real root.
If a quadratic equation has only one real root, then the discriminant is 0
If x = -3 is the only x-intercept of the graph of a quadratic equation then the discriminant is 0
Answer:
the answer is r= 1/2(121)
Step-by-step explanation:
the radius is half of the diameter
The room increases 0.5°F every minute
How?
in 10 minutes the room increased from 65° to 70°
that means in 5 minutes the room increased from 65° to 67.5°
that's a 2.5° increase and if you divide that by 5 your get how much it increases by 1 minute; which is 0.5°