Answer:
![\dfrac{17}{2}\sin{\dfrac{3x}{4}}+\dfrac{17}{2}\sin{\dfrac{x}{4}}](https://tex.z-dn.net/?f=%5Cdfrac%7B17%7D%7B2%7D%5Csin%7B%5Cdfrac%7B3x%7D%7B4%7D%7D%2B%5Cdfrac%7B17%7D%7B2%7D%5Csin%7B%5Cdfrac%7Bx%7D%7B4%7D%7D)
Step-by-step explanation:
The appropriate identity is ...
![\sin{\alpha}\cos{\beta}=\dfrac{1}{2}(\sin{(\alpha+\beta)}+\sin{(\alpha-\beta)})](https://tex.z-dn.net/?f=%5Csin%7B%5Calpha%7D%5Ccos%7B%5Cbeta%7D%3D%5Cdfrac%7B1%7D%7B2%7D%28%5Csin%7B%28%5Calpha%2B%5Cbeta%29%7D%2B%5Csin%7B%28%5Calpha-%5Cbeta%29%7D%29)
Filling in α=x/2 and β=x/4, we get ...
![17\sin{(x/2)}\cos{(x/4)}=\dfrac{17}{2}(\sin{(x/2+x/4)}+\sin{(x/2-x/4)})\\\\=\dfrac{17}{2}\sin{\dfrac{3x}{4}}+\dfrac{17}{2}\sin{\dfrac{x}{4}}](https://tex.z-dn.net/?f=17%5Csin%7B%28x%2F2%29%7D%5Ccos%7B%28x%2F4%29%7D%3D%5Cdfrac%7B17%7D%7B2%7D%28%5Csin%7B%28x%2F2%2Bx%2F4%29%7D%2B%5Csin%7B%28x%2F2-x%2F4%29%7D%29%5C%5C%5C%5C%3D%5Cdfrac%7B17%7D%7B2%7D%5Csin%7B%5Cdfrac%7B3x%7D%7B4%7D%7D%2B%5Cdfrac%7B17%7D%7B2%7D%5Csin%7B%5Cdfrac%7Bx%7D%7B4%7D%7D)
Answer:
Ben had biked 8 miles
Step-by-step explanation:
You would need to take 12 and divide it by three . That would make 4. After that you would take 4 and multiply it by 2 since he rode 2/3 miles of 12. Then you would end up with 8.
Answer:
See Below
Step-by-step explanation:
angle BAK = 128
Find KAS
180 - 128 = 52
KAS = 52
find BKA and ABK
360 -128 = 232
232/2 = 116
BKA =116
ABK = 116
find AKS
180 - 116 = 64
AKS =64
Now you have KAS and AKS
add together and subtract sum from 360 to find BSK
52 + 64 = 116
360 - 116 =244
Let me know if incorrect, plz.
Hope this helps=)
Answer:
![\left( -\dfrac{4}{25}, -\dfrac{98}{25} \right)](https://tex.z-dn.net/?f=%5Cleft%28%20-%5Cdfrac%7B4%7D%7B25%7D%2C%20-%5Cdfrac%7B98%7D%7B25%7D%20%5Cright%29)
Step-by-step explanation:
![x+2y=-8 \\\\y=12x-2](https://tex.z-dn.net/?f=x%2B2y%3D-8%20%5C%5C%5C%5Cy%3D12x-2)
Substitute:
![x+2(12x-2)=-8](https://tex.z-dn.net/?f=x%2B2%2812x-2%29%3D-8)
Expand:
![x+24x-4=-8](https://tex.z-dn.net/?f=x%2B24x-4%3D-8)
Simplify:
![25x=-4](https://tex.z-dn.net/?f=25x%3D-4)
Divide both sides by 25:
![x=-\dfrac{4}{25}](https://tex.z-dn.net/?f=x%3D-%5Cdfrac%7B4%7D%7B25%7D)
Plug this back into one of the original equations to find y:
![-\dfrac{4}{25}+2y=-8 \\\\\\2y=-7 \dfrac{21}{25}=-\dfrac{196}{25} \\\\\\y=-\dfrac{98}{25}](https://tex.z-dn.net/?f=-%5Cdfrac%7B4%7D%7B25%7D%2B2y%3D-8%20%5C%5C%5C%5C%5C%5C2y%3D-7%20%5Cdfrac%7B21%7D%7B25%7D%3D-%5Cdfrac%7B196%7D%7B25%7D%20%5C%5C%5C%5C%5C%5Cy%3D-%5Cdfrac%7B98%7D%7B25%7D)
The ordered pair that represents this solution is therefore:
![\left( -\dfrac{4}{25}, -\dfrac{98}{25} \right)](https://tex.z-dn.net/?f=%5Cleft%28%20-%5Cdfrac%7B4%7D%7B25%7D%2C%20-%5Cdfrac%7B98%7D%7B25%7D%20%5Cright%29)
Hope this helps!