Answer:
Step-by-step explanation:
The Pythagorean Theorem is incredibly useful. It states that
(Refer to the image labeled diagram 1). C is the hypotenuse of the triangle, or the longest side. It is always opposite of the right angle in the triangle. a and b are the other two sides, in no specific order. I attached 2 examples.
Hope it helps <3
Answer:
It was not my intention to post that answer, as it does not solve the question, but hope it helps somehow.
Step-by-step explanation:
![$\text{b)} \frac{\sin(a)}{\sin(a)-\cos(a)} - \frac{\cos(a)}{\cos(a)-\sin(a)} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $](https://tex.z-dn.net/?f=%24%5Ctext%7Bb%29%7D%20%5Cfrac%7B%5Csin%28a%29%7D%7B%5Csin%28a%29-%5Ccos%28a%29%7D%20-%20%20%20%5Cfrac%7B%5Ccos%28a%29%7D%7B%5Ccos%28a%29-%5Csin%28a%29%7D%20%3D%20%5Cfrac%7B1%2B%5Ccot%5E2%20%28a%29%7D%7B1-%5Ccot%5E2%20%28a%29%7D%20%24)
You want to verify this identity.
![$\frac{\sin(a)(\cos(a)-\sin(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} - \frac{\cos(a)(\sin(a)-\cos(a))}{(\sin(a)-\cos(a))(\cos(a)-\sin(a))} = \frac{1+\cot^2 (a)}{1-\cot^2 (a)} $](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Csin%28a%29%28%5Ccos%28a%29-%5Csin%28a%29%29%7D%7B%28%5Csin%28a%29-%5Ccos%28a%29%29%28%5Ccos%28a%29-%5Csin%28a%29%29%7D%20-%20%20%20%5Cfrac%7B%5Ccos%28a%29%28%5Csin%28a%29-%5Ccos%28a%29%29%7D%7B%28%5Csin%28a%29-%5Ccos%28a%29%29%28%5Ccos%28a%29-%5Csin%28a%29%29%7D%20%3D%20%5Cfrac%7B1%2B%5Ccot%5E2%20%28a%29%7D%7B1-%5Ccot%5E2%20%28a%29%7D%20%24)
The common denominator is
![(\sin(a)-\cos(a))(\cos(a)-\sin(a))= \boxed{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}](https://tex.z-dn.net/?f=%28%5Csin%28a%29-%5Ccos%28a%29%29%28%5Ccos%28a%29-%5Csin%28a%29%29%3D%20%5Cboxed%7B2%5Ccos%20%28a%29%5Csin%28a%29-%5Ccos%20%5E2%28a%29-%5Csin%20%5E2%28a%29%7D)
Solving the first and second numerator:
![\sin(a)(\cos(a)-\sin(a))=\sin(a)\cos(a)-\sin^2(a)](https://tex.z-dn.net/?f=%5Csin%28a%29%28%5Ccos%28a%29-%5Csin%28a%29%29%3D%5Csin%28a%29%5Ccos%28a%29-%5Csin%5E2%28a%29)
![\cos(a)(\sin(a)-\cos(a))= \cos(a)\sin(a)-\cos^2(a)](https://tex.z-dn.net/?f=%5Ccos%28a%29%28%5Csin%28a%29-%5Ccos%28a%29%29%3D%20%5Ccos%28a%29%5Csin%28a%29-%5Ccos%5E2%28a%29)
Now we have
![$\frac{ \sin(a)\cos(a)-\sin^2(a) -(\cos(a)\sin(a)-\cos^2(a))}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$](https://tex.z-dn.net/?f=%24%5Cfrac%7B%20%5Csin%28a%29%5Ccos%28a%29-%5Csin%5E2%28a%29%20-%28%5Ccos%28a%29%5Csin%28a%29-%5Ccos%5E2%28a%29%29%7D%7B2%5Ccos%20%28a%29%5Csin%28a%29-%5Ccos%20%5E2%28a%29-%5Csin%20%5E2%28a%29%7D%24)
![$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}$](https://tex.z-dn.net/?f=%24%5Cfrac%7B%20-%5Csin%5E2%28a%29%20%2B%5Ccos%5E2%28a%29%7D%7B2%5Ccos%20%28a%29%5Csin%28a%29-%5Ccos%20%5E2%28a%29-%5Csin%20%5E2%28a%29%7D%24)
Once
![-\sin^2(a) +\cos^2(a) = \cos(2a)](https://tex.z-dn.net/?f=-%5Csin%5E2%28a%29%20%2B%5Ccos%5E2%28a%29%20%3D%20%5Ccos%282a%29)
![2\cos (a)\sin(a) = \sin(2a)](https://tex.z-dn.net/?f=2%5Ccos%20%28a%29%5Csin%28a%29%20%3D%20%5Csin%282a%29)
Also, consider the identity:
![\boxed{\sin^2(a)+\cos^2(a)=1}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Csin%5E2%28a%29%2B%5Ccos%5E2%28a%29%3D1%7D)
![$\frac{ -\sin^2(a) +\cos^2(a)}{2\cos (a)\sin(a)-\cos ^2(a)-\sin ^2(a)}=\boxed{\frac{ \cos(2a)}{\sin(2a)-1}}$](https://tex.z-dn.net/?f=%24%5Cfrac%7B%20-%5Csin%5E2%28a%29%20%2B%5Ccos%5E2%28a%29%7D%7B2%5Ccos%20%28a%29%5Csin%28a%29-%5Ccos%20%5E2%28a%29-%5Csin%20%5E2%28a%29%7D%3D%5Cboxed%7B%5Cfrac%7B%20%5Ccos%282a%29%7D%7B%5Csin%282a%29-1%7D%7D%24)
That last claim is true.
<span>When rounding to the nearest ten, look at the number in the ones place. If the number is below five then the number in the tens column would stay the same, so your answer would be 360. If the number in the ones column is five or above the number in the tens column would round up, so the answer would be 370.
When rounding to the nearest hundred, look at the number in the tens place. If the number is below five then the number in the hundreds place would stay the same, so your answer would be 300. If the number in the tens place is five or more then you would round up, so the answer would be 400.</span>
we have given y interms of x.
we have given that add 2 to x.
which means ![y=x+2](https://tex.z-dn.net/?f=%20y%3Dx%2B2%20)
so we have
.
so when x
.
.
.
Answer:
20 square units
Step-by-step explanation:
Point D should be D(4, -1) if a rectangle is to be formed. A picture is attached to this answer.
The rectangle's dimensions are 4 by 5, so it's area is 4 x 5 = 20 square units. The picture is small enough that you could even just count squares inside the rectangle!