Aserver at the luminous nose restaurant goes to this same ice-cream store but decides to get a triple-decker cone. the stacking of scoops on the cone is important: a cone with peppermint atop two scoops of squirrel tastes different than a cone with two scoops of squirrel atop a scoop of peppermint, so an order of peppermint-squirrel-squirrel is different from an order of squirrelsquirrel-peppermint. how many possible triple-decker ice-cream orders are there?

Step-by-step explanation:

Lets rename the variables as

P = peppermint

S = squirrel.

Now, let's see how many different ice cream orders can we made with this two flavours.

We got 3 scoops. So we can place on the first scoop P.

And on top, we can add P P, S S, S P , or P, S.

So the Triple Decker would be ( PPP, PSS, PSP , PPS)

So we can get 4 kind of flavours with Peppermint on the first scoop.

And if we use a scoop of Squirrel on the first level. We would also have

( SPP, SSS, SSP, SPS)

So we can order 8 different ice cream orders. This is called a variation with repetition. And the math function that represents it is:

Where 2 is different variables that we can use (Pepper or Squirrel), and 3 is the number of places where we can place the variable.(the order of the scoop)

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15