DEF is shown in the attachment.
Answer: x = 36.08
Step-by-step explanation: We can use <u>Law</u> <u>of</u> <u>Sines</u> to determine x, which is written as:
![\frac{x}{sin(F)}=\frac{55}{sin(90)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bsin%28F%29%7D%3D%5Cfrac%7B55%7D%7Bsin%2890%29%7D)
where
F is the angle at vertex F
The angle is calculated knowing that the sum of all internal angles of a triangle is 180°:
F + 49 + 90 = 180
F + 139 = 180
F = 180 - 139
F = 41
Then, Law of Sines will be:
![\frac{x}{sin(41)}=\frac{55}{sin(90)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7Bsin%2841%29%7D%3D%5Cfrac%7B55%7D%7Bsin%2890%29%7D)
Sin(90) = 1
sin (41) = 0.6560
Substituing and rearraging:
![x=\frac{55}{1}(0.6560)](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B55%7D%7B1%7D%280.6560%29)
x = 36.08
<u>The value of x is 36.08 units</u>
The probability of getting green is-3/12
And not getting green is -12/3
Anna had 6 cookies. She decided to give all of her cookies to her friends.
How many cookies does each friend get?
The radius of the cylinder's base is 8, so the volume of the cylinder is
![\pi8^218\approx3617.28](https://tex.z-dn.net/?f=%5Cpi8%5E218%5Capprox3617.28)
(using the approximation of
![\pi\approx3.14](https://tex.z-dn.net/?f=%5Cpi%5Capprox3.14)
).
The sphere has radius 6, so the volume of the sphere is
![\dfrac43\pi6^3\approx904.32](https://tex.z-dn.net/?f=%5Cdfrac43%5Cpi6%5E3%5Capprox904.32)
.
The volume of the shaded region is the difference between the two: 3617.28 - 904.32 = 2712.96. Rounded to the nearest integer gives an answer of 2713.
X=-7 Y=5 should be your answer