The variables are:
Matinee ticket ⇒ We can call this item as 'm'
Drink ⇒ We can call this item as 'd'
A bag of popcorn ⇒ We can call this item as 'p'
One matinee ticket costs 6.50
Two matinee ticket cost 2×6.50
Three matinee ticket cost 3×6.50
'm' matinee ticket cost m × 6.50 = 6.50m
One drink costs 5.50
Two drinks cost 2×5.50
Three drinks cost 3×5.50
'd' drinks cost d×3.50 = 3.50d
One bag of popcorn costs 6
Two bags of popcorn cost 2×6
Three bags of popcorn cost 3×6
'p' bags of popcorn cost p×6 = 6p
The expression for total cost is given by
Total = 6.50m + 3.50d + 6p
5.7 + 6.2 = 11.9 You can round it, but you don't need to. Really. Round it becomes 12. Then its more clear. But if you don't round, it is more exact.
Answer:
the simplified from each expression is divide
Answer:
Step-by-step explanation:
Formulas used:
![sin( A +B) = 2sin Acos B\\\\sin A= sin (\frac{A}{2} + \frac{A}{2}) = 2 \ sin \frac{A}{2}cos \frac{A}{2}\\\\cos(A + B) = cosA cosB - sinA sinB\\\\cos A = cos(\frac{A}{2} + \frac{A}{2}) = cos \frac{A}{2} cos \frac{A}{2} - sin \frac{A}{2} sin \frac{A}{2}](https://tex.z-dn.net/?f=sin%28%20A%20%2BB%29%20%3D%202sin%20Acos%20B%5C%5C%5C%5Csin%20A%3D%20sin%20%28%5Cfrac%7BA%7D%7B2%7D%20%2B%20%5Cfrac%7BA%7D%7B2%7D%29%20%3D%202%20%5C%20sin%20%5Cfrac%7BA%7D%7B2%7Dcos%20%5Cfrac%7BA%7D%7B2%7D%5C%5C%5C%5Ccos%28A%20%2B%20B%29%20%3D%20cosA%20cosB%20-%20sinA%20sinB%5C%5C%5C%5Ccos%20A%20%3D%20cos%28%5Cfrac%7BA%7D%7B2%7D%20%2B%20%5Cfrac%7BA%7D%7B2%7D%29%20%3D%20cos%20%5Cfrac%7BA%7D%7B2%7D%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%20-%20sin%20%5Cfrac%7BA%7D%7B2%7D%20sin%20%5Cfrac%7BA%7D%7B2%7D)
![= cos^2 \frac{A}{2} - sin^2 \frac{A}{2}](https://tex.z-dn.net/?f=%3D%20cos%5E2%20%5Cfrac%7BA%7D%7B2%7D%20-%20sin%5E2%20%5Cfrac%7BA%7D%7B2%7D)
![1 - sin^2 \frac{A}{2} = cos^2 \frac{A}{2}](https://tex.z-dn.net/?f=1%20-%20sin%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%3D%20cos%5E2%20%5Cfrac%7BA%7D%7B2%7D)
![\frac{sin\frac{A}{2}}{cos\frac{A}{2}} = tan\frac{A}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%7D%7Bcos%5Cfrac%7BA%7D%7B2%7D%7D%20%3D%20tan%5Cfrac%7BA%7D%7B2%7D)
Given :
LHS =
![\frac{sin \frac{A}{2} + sin A }{1 + cos \frac{A}{2} + cosA}\\\\=\frac{sin \frac{A}{2} + 2sin \frac{A}{2} cos \frac{A}{2} }{1 + cos \frac{A}{2} +cos ^2\frac{A}{2} -sin^2 \frac{A}{2} }\\\\= \frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + cos ^2 \frac{A}{2} + 1 - sin^2\frac{A}{2} }\\\\= \frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + cos ^2 \frac{A}{2} +cos ^2 \frac{A}{2} }\\\\](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%20%5Cfrac%7BA%7D%7B2%7D%20%2B%20sin%20A%20%7D%7B1%20%2B%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%20cosA%7D%5C%5C%5C%5C%3D%5Cfrac%7Bsin%20%5Cfrac%7BA%7D%7B2%7D%20%2B%202sin%20%5Cfrac%7BA%7D%7B2%7D%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%20%7D%7B1%20%2B%20cos%20%5Cfrac%7BA%7D%7B2%7D%20%2Bcos%20%5E2%5Cfrac%7BA%7D%7B2%7D%20-sin%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%7D%5C%5C%5C%5C%3D%20%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%20cos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%2B%201%20-%20sin%5E2%5Cfrac%7BA%7D%7B2%7D%20%7D%5C%5C%5C%5C%3D%20%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%20cos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%2Bcos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%20%20%7D%5C%5C%5C%5C)
![=\frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} + 2cos ^2 \frac{A}{2} }\\\\=\frac{sin\frac{A}{2}( 1 +2cos \frac{A}{2} ) }{cos \frac{A}{2} ( 1 + 2cos \frac{A}{2}) }\\\\=\frac{sin\frac{A}{2}}{cos\frac{A}{2}}\\\\= tan \frac{A}{2}\\\\= RHS](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%20%2B%202cos%20%5E2%20%5Cfrac%7BA%7D%7B2%7D%20%7D%5C%5C%5C%5C%3D%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%28%201%20%2B2cos%20%5Cfrac%7BA%7D%7B2%7D%20%29%20%7D%7Bcos%20%5Cfrac%7BA%7D%7B2%7D%20%28%201%20%20%2B%202cos%20%5Cfrac%7BA%7D%7B2%7D%29%20%7D%5C%5C%5C%5C%3D%5Cfrac%7Bsin%5Cfrac%7BA%7D%7B2%7D%7D%7Bcos%5Cfrac%7BA%7D%7B2%7D%7D%5C%5C%5C%5C%3D%20tan%20%5Cfrac%7BA%7D%7B2%7D%5C%5C%5C%5C%3D%20RHS)
Answer:
180 miles
Step-by-step explanation:
The are moving towards each other at 50 mph and 40 mph which is the same as 90 mph. They are moving 90 mph closer to each other every hour so in 2 hours it would be 180 miles.