You have 3000 dollars to spend on a laptop. suppose the tax rate 6.78%. what is the maximum you can spend on a laptop if you know you will also be purchasing a 25 dollar case?

  $2784.51

Step-by-step explanation:

You require ...

  (total with tax) ≤ 3000

  (total with tax) = (total before tax) + 0.0678·(total before tax)

So,

  (total before tax) · 1.0678 ≤ 3000

  total before tax ≤ 2809.51

With ...

  total before tax = laptop cost + case cost

we have ...

  laptop cost + case cost ≤ 2809.51

  laptop cost ≤ 2809.51 - 25

  laptop cost ≤ 2784.51

The maximum you can spend on a laptop is $2784.51.

i'm sorry mate, but i am not seeing any figures. i am unable to solve this for you.

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