In a cookie mix, we find spice cookies, snickerdoodle cookies, and no-bake cookies in a ratio of 3: 3: 5. if a bag of the mix contains 45 no bake cookies, how many cookies in total are there?

see the explaination

Step-by-step explanation:

let x be 3:3:5

3x:3x:5x

3x is splice cookies

3x is snickerdoodle cookies

5x is no bake cookies

where 5x is equal to 45

x is equal to 45÷5=9

so x is equal to 9

now,

3x = 3×9=27

3x = 3×9=27

5x = 45 (given)

now add all, total cookies =27+27+45

=99 cookies

so there are total 99 cookies in a cookie mix

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81