First find the possible dices rolls that give you 10, 11, and 12
Gives 10:
5,5
4,6
6,4
Gives 11 or 12:
5,6
6,5
6,6
The dice rolls have 6 * 6 = 36 possible combinations
The probability of getting a 10 is 3/32
The probability of getting an 11 or 12 is 3/32
multiplying those probabilities together with their reward/loss we have:
3/32 * -8 = -3/4
3/32 * 11 = 33/32
to make the game "fair" we need the probable amount of money you can win to be $0, so we can use the equation
-3/4 + 33/32 + (32/32 - 6/32)*x = 0
then you can just solve for x
A is incorrect because isosceles cannot have right angles and right triangles cannot be isosceles. A square is not a rhombus, so B is incorrect. And yes, a kite is a rhombus and a parallelogram. You didn't finish C, but right triangles cannot be isosceles, but right triangles can have two acute angles
You already have the equation! If you want it in vertex form, do this:
y = x^2 + 8x + 16 - 16 - 51, or y = x^2 + 8x + 16 -67, or
y = (x+4)^2 - 67.
The vertex is at (-4,67).
See attachment for the answer:
