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27 and 200/3

Step-by-step explanation:

Let the no of orange pop cups be x,

Then,

2:3=18:x

2/3=18/x

2/3x=18

x=18/2/3

x=18×3/2

x=27

For no 2 everything is same except the rhs

2/3=x/100

2/3×100=x

200/3=x

Therefore 200/3 cups are needed to make 100 pineapple cups.

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)

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.