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:
![\displaystyle m=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Reading a Cartesian plane
- Coordinates (x, y)
- Slope Formula:
![\displaystyle m=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Find points from graph.</em>
Point (-5, 0)
Point (-9, -8)
<u>Step 2: Find slope </u><em><u>m</u></em>
Simply plug in the 2 coordinates into the slope formula to find slope<em> m</em>
- Substitute in points [Slope Formula]:
![\displaystyle m=\frac{-8-0}{-9+5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-8-0%7D%7B-9%2B5%7D)
- [Fraction] Subtract/Add:
![\displaystyle m=\frac{-8}{-4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D%5Cfrac%7B-8%7D%7B-4%7D)
- [Fraction] Divide:
![\displaystyle m=2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20m%3D2)
Step-by-step explanation:
<h3>this is given that the figure is a hexagon</h3><h3>let give a name to the given hexagon be ABCDEF</h3>
<h3>Angle a + B + C + D = 720 ( Ls sum pro. of hexagon)</h3><h3>3x-20+3x-20+4x+4x+3x-20+3x-20 = 720</h3><h3>3x+3x+3x+3x+4x+4x-20-20-20-20 = 720 (rearranging)</h3><h3>20x - 80 = 720</h3><h3>20x = 720 + 80 </h3><h3>x=800/20</h3>
<h2>x = 40 degrees </h2>
<h3>3x-20 = 100</h3><h3>4x = 160</h3>
<h2>I HOPE THAT THIS ANSWER HELPS YOU</h2>
Answer:
The length of the rectangular field is 12 ft and the width is 5 ft.
Step-by-step explanation:
The area of a rectangle is:
![\text{Area} = \text{length}\times \text{width}](https://tex.z-dn.net/?f=%5Ctext%7BArea%7D%20%3D%20%5Ctext%7Blength%7D%5Ctimes%20%5Ctext%7Bwidth%7D)
The area of a rectangular field is, <em>A</em> = 60 ft.
The length of the field is:
l = w + 7
Compute the width of the field as follows:
![\text{Area} = \text{length}\times \text{width}](https://tex.z-dn.net/?f=%5Ctext%7BArea%7D%20%3D%20%5Ctext%7Blength%7D%5Ctimes%20%5Ctext%7Bwidth%7D)
![60=(w+7)\times w\\\\60=w^{2}+7w\\\\w^{2}+7w-60=0\\](https://tex.z-dn.net/?f=60%3D%28w%2B7%29%5Ctimes%20w%5C%5C%5C%5C60%3Dw%5E%7B2%7D%2B7w%5C%5C%5C%5Cw%5E%7B2%7D%2B7w-60%3D0%5C%5C)
Factorize the last equation by splitting the middle term as follows:
![w^{2}+7w-60=0\\w^{2}+12w-5w-60=0\\w(w+12)-5(w+12)=0\\(w-5)(w+12)=0](https://tex.z-dn.net/?f=w%5E%7B2%7D%2B7w-60%3D0%5C%5Cw%5E%7B2%7D%2B12w-5w-60%3D0%5C%5Cw%28w%2B12%29-5%28w%2B12%29%3D0%5C%5C%28w-5%29%28w%2B12%29%3D0)
Now, since the width of rectangular field cannot be negative, the width is 5 ft.
Compute the length as follows:
l = w + 7
= 5 + 7
= 12
The length of the rectangular field is 12 ft.
Answer:
The answer would be 1.33 x ![10^{4}](https://tex.z-dn.net/?f=10%5E%7B4%7D)
Step-by-step
1.28 x
= 12800
5 x
= 500
12800 + 500 = 13300
13300 = 1.33 x
in scientific notation
Hope this helps:)
Sorry, I got the wrong answer earlier but I fixed it:)