Step-by-step explanation:
![\sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Csin%5E2%20%28%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20%5Calpha%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
Use the identity
![\sin^2 \theta = \dfrac{1 - \cos 2\theta}{2}](https://tex.z-dn.net/?f=%20%5Csin%5E2%20%5Ctheta%20%3D%20%5Cdfrac%7B1%20-%20%5Ccos%202%5Ctheta%7D%7B2%7D%20)
on the left side.
![\dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Ccos%20%5B2%28%5Cfrac%7B%5Cpi%7D%7B4%7D%20-%20%5Calpha%29%5D%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
![\dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Ccos%20%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%202%5Calpha%29%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
Now use the identity
![\sin \theta = \cos(\frac{\pi}{2} - \theta)](https://tex.z-dn.net/?f=%20%5Csin%20%5Ctheta%20%3D%20%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%20-%20%5Ctheta%29%20)
on the left side.
![\dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cdfrac%7B1%20-%20%5Csin%202%5Calpha%7D%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
![\frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha)](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%281%20-%20%5Csin%202%5Calpha%29%20)
You can say
x+y=5
x=5-y
You know the value of x, put it into the next equation.
3(5-y)-7y=19
15-3y-7y=19
15-19 = 10y
-4=10y
-4/10=y
-2/5=y
Put y value back into either equation to find value of x.
x+y=5
x-2/5=5
x=5+2/5
x=27/5
Therefore, x,y = (27/5, -2/5)
Hope I helped :)
They weigh about 169 pounds.
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
a
![\= HK = \= t + \= u](https://tex.z-dn.net/?f=%5C%3D%20HK%20%20%3D%20%20%5C%3D%20t%20%2B%20%5C%3D%20u)
b
![\= GL = \= s - \= t](https://tex.z-dn.net/?f=%5C%3D%20GL%20%20%3D%20%5C%3D%20s%20-%20%5C%3D%20t)
c
![\= JH = \= u + \= s](https://tex.z-dn.net/?f=%5C%3D%20%20JH%20%20%3D%20%5C%3D%20u%20%20%2B%20%5C%3D%20s)
Step-by-step explanation:
Now looking at the diagram
Following the direction of the unit vectors
![\= {HK} = \= {KI} + \= KL](https://tex.z-dn.net/?f=%5C%3D%20%7BHK%7D%20%20%3D%20%5C%3D%20%7BKI%7D%20%20%2B%20%5C%3D%20KL)
=> ![\= HK = \= t + \= u](https://tex.z-dn.net/?f=%5C%3D%20HK%20%20%3D%20%20%5C%3D%20t%20%2B%20%5C%3D%20u)
And
jjj
=> ![\= GL = \= s - \= t](https://tex.z-dn.net/?f=%5C%3D%20GL%20%20%3D%20%5C%3D%20s%20-%20%5C%3D%20t)
Also
![\= JH = \= JG + \= JI](https://tex.z-dn.net/?f=%5C%3D%20%20JH%20%20%3D%20%5C%3D%20JG%20%2B%20%5C%3D%20JI)
=> ![\= JH = \= u + \= s](https://tex.z-dn.net/?f=%5C%3D%20%20JH%20%20%3D%20%5C%3D%20u%20%20%2B%20%5C%3D%20s)
I think you do 20(20+x)=31(31+x). Basically you need to set up a proportion