X intercept is when the function (y) = 0.
0 = 4 - (x+3)^2
(x+3)(x+3) = 4
x^2 + 6x + 9 = 4
x^2 + 6x + 5 = 0
To factor, we find what multiplies to 5 and adds to 6. In this case, it’s 5 and 1.
(x+5)(x+1) = 0
x values of the intercepts are -5 and -1.
The coordinates are (-5,0) and (-1,0).
Answer:
See Explanation Below
Step-by-step explanation:
Given
![(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx.cos x.](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sec%5E2x%20-%20tan%5E2x%20-%202sinx.cos%20x.)
Required
Prove
To start with; we open the bracket on the left hand side
![(sin x - cos x)^2 = (sin x - cos x)(sin x - cos x)](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20%28sin%20x%20-%20cos%20x%29%28sin%20x%20-%20cos%20x%29)
![(sin x - cos x)^2 = (sin x )(sin x - cos x)- (cos x)(sin x - cos x)](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20%28sin%20x%20%29%28sin%20x%20-%20cos%20x%29-%20%28cos%20x%29%28sin%20x%20-%20cos%20x%29)
![(sin x - cos x)^2 = sin^2 x -sinx cos x - sin xcos x + cos^2 x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20-sinx%20cos%20x%20-%20sin%20xcos%20x%20%2B%20cos%5E2%20x)
![(sin x - cos x)^2 = sin^2 x -2sinx cos x + cos^2 x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20-2sinx%20cos%20x%20%2B%20cos%5E2%20x)
Reorder
![(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20%2B%20cos%5E2%20x%20-%202sinx%20cos%20x)
From trigonometry;
![sin^2x + cos^2x = 1](https://tex.z-dn.net/?f=sin%5E2x%20%2B%20cos%5E2x%20%3D%201)
So;
![(sin x - cos x)^2 = sin^2 x + cos^2 x - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sin%5E2%20x%20%2B%20cos%5E2%20x%20-%202sinx%20cos%20x)
becomes
![(sin x - cos x)^2 = 1 - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%201%20-%202sinx%20cos%20x)
Also from trigonometry;
![sec^2x - tan^2x = 1](https://tex.z-dn.net/?f=sec%5E2x%20-%20tan%5E2x%20%3D%201)
So,
![(sin x - cos x)^2 = 1 - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%201%20-%202sinx%20cos%20x)
becomes
![(sin x - cos x)^2 = sec^2x - tan^2x - 2sinx cos x](https://tex.z-dn.net/?f=%28sin%20x%20-%20cos%20x%29%5E2%20%3D%20sec%5E2x%20-%20tan%5E2x%20%20-%202sinx%20cos%20x)
Proved
Answer:
it's 512
Step-by-step explanation:
It's the same amount each month, for a year. So:
total money ÷ times money was taken out= how much has been taken out.
$600÷12=50
Answer:
<em>40</em>
Step-by-step explanation:
Given that:
Number of options available for transmission = 2 (Standard or Automatic)
Number of options for doors = 2 (2 doors or 4 doors)
Number of exterior colors available = 10
To find:
Total number of outcomes = ?
Solution:
First of all, let us calculate the number of outcomes for the transmission mode and number of doors options.
1. Standard - 2 doors
2. Standard - 4 doors
3. Automatic - 2 doors
4. Automatic - 4 doors
Number of outcomes possible = 4 (which is equal to number of transmission mode available multiplied by number of doors options i.e. 2
)
Now, these 4 will be mapped with 10 different exterior colors.
Therefore total number of outcomes possible :
Number of transmission modes
Number of doors options
Number of exterior colors
2
2
10 = <em>40</em>