Answer:
12 1/2 dollars
Step-by-step explanation:
add 10 9/10 and 6 3/5
you have least common multiple of the demoninators which is 10
so 6 3/5 is equal to 6 6/10
the you can add which gets you 16 15/10
simplified is 17 5/10 then you can change it to 17 1/2
then you subtract that from 30
30-17 1/2 = 12 1/2 dollars
Answer:it is 18*20 effective every year
Step-by-step explanation:
67° all three angles should equal 180°
28 divided by 4 = 6. Mark saw 6 birds!
Answer:
The solution is ![x =0.](https://tex.z-dn.net/?f=x%20%3D0.)
Step-by-step explanation:
The equation
![\bold{(1).}\: sin(\dfrac{3\pi }{2} +x)+sin(\dfrac{3\pi }{2} +x) =-2](https://tex.z-dn.net/?f=%5Cbold%7B%281%29.%7D%5C%3A%20sin%28%5Cdfrac%7B3%5Cpi%20%7D%7B2%7D%20%2Bx%29%2Bsin%28%5Cdfrac%7B3%5Cpi%20%7D%7B2%7D%20%2Bx%29%20%3D-2)
can be rewritten as
![2* sin(\dfrac{3\pi }{2} +2) =-2](https://tex.z-dn.net/?f=2%2A%20sin%28%5Cdfrac%7B3%5Cpi%20%7D%7B2%7D%20%2B2%29%20%3D-2)
and can be further simplified to
.
Now, taking the inverse sine of both sides we get:
![sin^{-1}(sin(\dfrac{3\pi }{2} +x) =sin^{-1}(-1)](https://tex.z-dn.net/?f=sin%5E%7B-1%7D%28sin%28%5Cdfrac%7B3%5Cpi%20%7D%7B2%7D%20%2Bx%29%20%3Dsin%5E%7B-1%7D%28-1%29)
![\bold{(2).}\: \dfrac{3\pi }{2} +2 =sin^{-1}(-1)](https://tex.z-dn.net/?f=%5Cbold%7B%282%29.%7D%5C%3A%20%20%5Cdfrac%7B3%5Cpi%20%7D%7B2%7D%20%2B2%20%3Dsin%5E%7B-1%7D%28-1%29)
The value of the right side on the interval
is
,
which makes the equation (2)
![\dfrac{3\pi }{2}+x =\dfrac{3\pi}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B3%5Cpi%20%7D%7B2%7D%2Bx%20%20%3D%5Cdfrac%7B3%5Cpi%7D%7B2%7D)
solving for
gives
![\boxed{x = 0}](https://tex.z-dn.net/?f=%5Cboxed%7Bx%20%3D%200%7D)
which is our solution.