Help please! The points (0,-14), (1,-3), (2,0), (3,5) are on a parabola. Write the function to represent this parabola.

y= -4x^2 + 15x - 14

Step-by-step explanation:

A parabola is always in the form y = ax^2 + bx + c.

Substitute each point to produce different equations:

-14 = 0a + 0b + c = c

so c = -14

-3 = a1^2 + b1 + c = a + b - 14

so a + b = 11

0 = a2^2 + b2 + c = 4a + 2b -14 = 0

so 4a + 2b = 14

if we double a + b = 11 we get 2a + 2b = 22

Subtract this from 4a + 2b = 14 and we get 2a = -8 so a= -4 and b = 11 - a = 15

We don't need to use the (3,5) points as we have all the information we need.

y= -4x^2 + 15x - 14

Step-by-step explanation:

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)

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.