Gonzalez manufacturing borrowed $33000. part of the money was borrowed at 8%, part at 10%, and part at 12%. the total amount borrowed at 8% and 10% was twice the amount borrowed at 12%. find the amount borrowed at each rate if the annual interest was $3360.

Answer

given,

borrowed money = $33000

Part of the money was borrowed at 8% be x, part at 10% be  y, and  part at 12% be ($33000-x-y)

x + y = 2 ($33000-x-y)

3 x + 3 y = $ 66000

x + y = $ 22000(1)

third part =$33000-($22000)

                = $ 11000

now annual interest is

0.08 x + 0.1 y +  0.12 × 11000 = $ 3360

0.08 x + 0.1 y = 2040(2)

0.1 x + 0.1 y = 2200(3)

solving equation (3) and (2)

x = $ 8000

y = $ 14000

3 rd number = $ 11000

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c