CPhill

5x + 15  =  115    subtract 15 from both sides

5x  = 100      divide both sides by 5

x  = 20°

So.....you're correct.....!!!!

√-28  = √ [ -1 * 4 * 7 ]  =  √  i^2  * √4 * √7  =  i * 2 * √7  =  2i√7

(5 - 5i) - ( -6 - 3i) =

5 - 5i + 6 + 3i  =

11 - 2i

(- 2 - 2i ) (-4 + 6i )  =

- (2 + 2i) ( -4 + 6i)  =

- [ 2*-4 +  ( 2i * -4)  + (2 * 6i)  + (  2*6*i^2) ]

Remember, NSS...i^2  = -1

- [ -8 - 8i + 12i +  12 (-1) ]  =

- [ -8 + 4i - 12 ]  =

- [ 4i - 20 ]  =

20 - 4i

 3,052.08 = (4/3) pi (r)^3

cube root ( [  3,052.08 / pi ] * (3/4) )  = r = 9

So.....diameter = 2r  = 18 units

Yep   .....

Ratio  =

square root [ 1,808.64 / 452.16 ]  =  square root [ 4 ]  =   2

[Volume  in  ft^3] * Gallons per ft^3  = 

[11 * 10 * 7 ]  * 7.48   ≈  5760 gal

Mmmmm...on the second one....the discriminant > 0...but I don't see how that decides much of anything

I just means that we have real roots

Look at this graph :  https://www.desmos.com/calculator/iohx6ebf5u

The curve definitely exceeds 141 for a long period of time   !!!!

12x^2 - 11x  = 11

12x^2 - 11x - 11 = 0      ⇒  ax^2 + bx  + c  = 0

The discriminant is     b^2  - 4ac      

(-11) ^2  - 4(12)(-11)  =  121 + 528  >  0

So.....when the discriminant > 0....we will have two REAL solutions

-210°  = 360 - 210  =   150°

This is a 30° reference angle in the second quadrant

Tan 30°  in the second quadrant  =  y/x  = 1 / -√3

So......(x , y)  =  d. ( -√3 , 1) 

Here's one method....but....maybe not the best one....!!!

Let's find the area of a triangle with side lengrhs of AB = 9, BC =10 and CA = 11

Using Heron's Formula the semi-perimeter is  [ 30] / 2  = 15

And the area of this triangle will be

sqrt  [  15 * 6 * 5 * 4 ]  =  sqrt [ 1800]  =  30sqrt (2)

So......the height of this triangle will be

30sqrt (2)  =  10 * height / 2

30sqrt (2)  =  5 * height

height  =   [30sqrt (2)  / 5]  = 6sqrt (2) 

But....the given triangle has a scale factor of sqrt (2)  of this triangle

So....the height of ABC   drawn from A to BC  =  6 sqrt (2) * sqrt(2)  =

6 * 2  =   

12  units