Am i correct on the question above?

-3/2 + 1/2 sqrt(5)

Step-by-step explanation:

sqrt(2) - sqrt(10)

sqrt(2) + sqrt(10)

To clear the square root in the denominator, we multiply by the conjugate

sqrt(2) - sqrt(10).  What we do to the bottom, we do to the top

sqrt(2) - sqrt(10)        sqrt(2) - sqrt(10)

*

sqrt(2) + sqrt(10)          sqrt(2) - sqrt(10)

sqrt(2) * sqrt(2) -sqrt(2)sqrt(10) -sqrt(2) sqrt(10) +sqrt(10)sqrt(10)

sqrt(2) * sqrt(2) -sqrt(2)sqrt(10) +sqrt(2) sqrt(10) - sqrt(10)sqrt(10)

Combining like terms

sqrt(2) * sqrt(2) -2sqrt(2)sqrt(10) -sqrt(2) sqrt(10) + sqrt(10)sqrt(10)

sqrt(2) * sqrt(2)  - sqrt(10)sqrt(10)

2 - 2 sqrt(20) +10

      2-10

12 - 2 sqrt(20)

-8

sqrt(20) = sqrt(4) sqrt(5) = 2sqrt(5)

Replacing sqrt(20)

12 - 2 *2 sqrt(5)

-8

12 -4 sqrt(5)

-8

Factor out a 4

4(3 -sqrt(5))

  4 (-2)

Canceling the 4

3-sqrt(5)

-2

Breaking the fraction into 2 pieces

-3/2 + 1/2 sqrt(5)

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

answer:   c ?

step-by-step explanation: