Answer: Hello there!
If D is the price of one drink and P the price of one bag of popcorn, we know that:
9*D + 2*P = $86.50
3*D + 9*P = $89.25
Now we can isolate one of the therms in the first equation and replace it in the second one:
Lets isolate D in the first equation
9*D + 2*P = $86.50
9*D = $86.50 - 2*P
D = ( $86.50 - 2*P)/9
now we can replace in in the second equation and obtain the value of P
3*D + 9*P = $89.25
3*( $86.50 - 2*P)/9 + 9*P = $89.25
( $86.50 - 2*P)/3 + 9*P = $89.25
$28.83 - (2/3)P + 9P = $89.25
(9 - 2/3)P = $89.25 - $28.83 = $60.42
(25/3)P = $60.42
P = $60.42*(3/25)= $7.25
So each bag of popcorn cost $7.25.
Now we can replace it in the first equation and find the price for the drinks:
9*D + 2*P = $86.50
9*D + 2*$7.25 = $86.50
9*D + $14.50 = $86.50
9*D = $86.50 - $14.50 = $72
D = $72/9 = $8
So each drink cost $8.
And now we know the price for one bag of popcorn and for one drink,
Sin = opposite/hyp
Sin A = 10/26 = 5/13
Sin b = 24/26 = 12/13
The answer is option A
Hope this helps
Answer:
See explanation
Step-by-step explanation:
Given
![-2(5x+8)=14+6x](https://tex.z-dn.net/?f=-2%285x%2B8%29%3D14%2B6x)
Required
Complete the steps
![-2(5x+8)=14+6x](https://tex.z-dn.net/?f=-2%285x%2B8%29%3D14%2B6x)
Multiply 5x and 8 by -2
![-10x - 16 = 14 + 6x](https://tex.z-dn.net/?f=-10x%20-%2016%20%3D%2014%20%2B%206x)
Subtract by 6x
![-10x - 6x- 16 = 14 + 6x - 6x](https://tex.z-dn.net/?f=-10x%20-%206x-%2016%20%3D%2014%20%2B%206x%20-%206x)
![-16x- 16 = 14](https://tex.z-dn.net/?f=-16x-%2016%20%3D%2014)
Add 16
![-16x- 16 + 16= 14 + 16](https://tex.z-dn.net/?f=-16x-%2016%20%2B%2016%3D%2014%20%2B%2016)
![-16x= 30](https://tex.z-dn.net/?f=-16x%3D%2030)
Divide by -16
![x= \frac{30}{-16}](https://tex.z-dn.net/?f=x%3D%20%5Cfrac%7B30%7D%7B-16%7D)
![x= -\frac{15}{8}](https://tex.z-dn.net/?f=x%3D%20-%5Cfrac%7B15%7D%7B8%7D)
<em>See attachment</em>
The area is 176.71cm squared. The circumference is 47.12
Answer:
X=22° ; Exterior Angle = 125°
Step-by-step explanation:
The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
(2x) + (103 - x) = (6x - 7)
103 + 7 = 6x - 2x + x
110 = 5x -->(Divided by 5)--> x=22°
6(22) - 7 = 125°