Padewolofoofy

Basically, we're trying to find the distance between (1, 0) (0, 0) x the distance between (2, 1) (0, 0) x the distance between (3, 0) (0, 0) x the distance between (0, 1) (0, 0)

By using the distance formula, we can find

distance between (1, 0) (0, 0) = 1

distance between (2, 1) (0, 0) = √3

distance between (3, 0) (0, 0) = √5

distance between (0, 1) (0, 0) = 1

$|1| |2i| |3| |i|$ = 1 x √3 x √5 x 1 = √3 x √5 = √15

woops...

By the quadratic formula, the roots are (-7 + √57)/2 and (-7 - √57)/2.

⍺ = (-7 + √57)/2                β = (-7 - √57)/2

⍺² + β² = [(-7 + √57)/2]² + [(-7 - √57)/2]² = 106 - 14√57 + 106 + 14√57 = 106 + 106 = 212

x² + x² + 7x - 9x - 4 - 6 = 0

2x² - 2x - 10 = 0

Divide both sides by 2:

x² - x - 5 = 0

Now, find the roots using the quadratic formula:

x = 1 +/- √1 - 4(1)(-5)                   1 +/-   √21

      ------------------------         =     -----------------

                  2                                       2

So, a = (1 + √21) / 2,  b = (1 - √21) / 2

We are trying to find what is (a + 3) + (b + 3), so we just plug in the numbers:

     1 + √21                 1 - √21                    1      √21         1       √21

(   ----------- +  3) + (   ---------- + 3) = 3 --  +  -----  +  3 ---  -  -----  = 3.5 + 3.5 = 7

         2                           2                         2        2           2         2

There are 4 children, which means there are 4! = 4 x 3 x 2 x 1 = 24 ways to seat the children.

There are also 4 adults, which means there are, again, 4! = 4 x 3 x 2 x 1 = 24 ways to seat the adults.

Since the children needs to sit next to each other, and all the adults needs to be next to each other, we can view all the children as 1 "object"and all the adults as 1 "object".

Now we need to find out how many ways we can place the childrens next to the adults.

children = C

adults = A

It can be:       CA                or                 AC

Since the problem said that two seatings are considered the same if one can be rotated to form the other, that means there is actually only ONE way to place them next to each other, since rotating AC gives us CA.

Finally, since we can seat the children in 24 different ways, and we can seat the adults in 24 different ways, that gives us 24 x 24 = 576 ways to seat the PEOPLES.

cheese muffins: 3/5 x M

apple muffins: 3/10 x M - 6

banana muffins: B

the total revenue from the muffin sales is given by the sum of the revenue from each type of muffin:

1.50 x (3/5 x M) + 1.20 x (3/10 x M - 6) + 1.40 x B = 561.20

simplify and solve for B. First, multiply the terms:

1.50 x (3/5 x M) + 1.20 x 3/10 x M - 1.20 x 6 + 1.40 x B = 561.20

0.90M + 0.36M - 7.20 + 1.40B = 561.20

combine like terms:

1.26M + 1.40B = 568.40

Now, additional info is needed to find the specific value of M or B to solve the problem. If you have another equation or additional information about the total number of muffins sold (M), you can substitute it in and solve for B. Otherwise, you won't be able to determine the exact values of M and B.