Answer:
3.8
Step-by-step explanation:
solution are in the pics
OMG, i had done this before in K12! Its 400
Answer:
s=33.3333
Step-by-step explanation:
200=5s -(100+2s)
200= 5s -100 -2
100= 3s
s= 33.333
Recall that
![\sin(x+y)=\sin x\cos y+\cos x\sin y](https://tex.z-dn.net/?f=%5Csin%28x%2By%29%3D%5Csin%20x%5Ccos%20y%2B%5Ccos%20x%5Csin%20y)
![\sin(x-y)=\sin x\cos y-\cos x\sin y](https://tex.z-dn.net/?f=%5Csin%28x-y%29%3D%5Csin%20x%5Ccos%20y-%5Ccos%20x%5Csin%20y)
Adding these together, you have
![\sin(x+y)+\sin(x-y)=2\sin x\cos y](https://tex.z-dn.net/?f=%5Csin%28x%2By%29%2B%5Csin%28x-y%29%3D2%5Csin%20x%5Ccos%20y)
![\dfrac12\sin(x+y)+\dfrac12\sin(x-y)=\sin x\cos y](https://tex.z-dn.net/?f=%5Cdfrac12%5Csin%28x%2By%29%2B%5Cdfrac12%5Csin%28x-y%29%3D%5Csin%20x%5Ccos%20y)
Replace
![x](https://tex.z-dn.net/?f=x)
with
![2x](https://tex.z-dn.net/?f=2x)
and
![y](https://tex.z-dn.net/?f=y)
with
![3x](https://tex.z-dn.net/?f=3x)
. You end up with
![\dfrac12\sin(2x+3x)+\dfrac12\sin(2x-3x)=\sin2x\cos3x](https://tex.z-dn.net/?f=%5Cdfrac12%5Csin%282x%2B3x%29%2B%5Cdfrac12%5Csin%282x-3x%29%3D%5Csin2x%5Ccos3x)
![\sin2x\cos3x=\dfrac12\sin5x+\dfrac12\sin(-x)=\dfrac12\sin5x-\dfrac12\sin x](https://tex.z-dn.net/?f=%5Csin2x%5Ccos3x%3D%5Cdfrac12%5Csin5x%2B%5Cdfrac12%5Csin%28-x%29%3D%5Cdfrac12%5Csin5x-%5Cdfrac12%5Csin%20x)
and so
![A=\dfrac12](https://tex.z-dn.net/?f=A%3D%5Cdfrac12)
and
![B=-\dfrac12](https://tex.z-dn.net/?f=B%3D-%5Cdfrac12)
.
25.50 = 7d + 2p
52.50 = 5d + 10p
These are the two equations we're going to use to determine the price of popcorn.
First we need to eliminate one set of variables. Let's eliminate the drinks.
127.50 = 35d + 10p
-367.50 = -35d + -70p
-240 = 0d - 60p
-240 = -60p
P = 4.00
So, popcorn is $4, right? Let's keep working on the problem so we can double check...
So, now let's add the $4 as the variable for P.
25.50 = 7d + 8
52.50 = 5d + 40
17.50 = 7d
12.5 = 5d
d = 2.5
d=2.5
This checks out! Since both equations state that drinks are 2.50, that means we have the right pricing for popcorn... $4.00
Popcorn is $4.00, drinks are $2.50
<em>Hope I could help! :) </em>