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x^2 +75 =0

x^2 = -75

x= +- sqrt (-75)

x = +- i sqrt 75

x = +- i sqrt(25*5)

x = 5i sqrt 5    or  - 5i sqrt 5

It is a way to solve quadratic equations .

When you have a quadratic equation of the form    a x^2 + b x + c = 0    you can use the quadratic formula to find the solutions to the equation.

The Quadratic Formula is:

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)      Substitute for 'a' 'b' and 'c'    to find the solutions ! 

√ [ 24x ]  * √[18y] * √ [15y]  =

√ [ 4 * 6 * x ] * √ [ 9 * 2 * y]  * √ [15y]   =

2√ [6x] * 3√ [2y] * √ [15y ] =

6 * √ [ 6 * 2 * 15 * x * y^2 ] =

6 * √  [ 12 * 15 * x * y^2 ] =

6 * √ [ 4 * 3 * 5 * 3 * x * y^2  ] =

6 * √ 4 * √9 * √5 * √x * √y^2  =

6 * 2 * 3 * √ [5x ] * y  =

36y √ [5x ]

The other constraint is :

500x + 150y ≤ 5000

[ The number of television ads * their cost each   +  the number of online ads * their cost each  cannot exceed $5000 ]

thank you

OK...in scientific notation we would just have  7 * 10^1

Using Alan's inequalities....look at the graph, here : https://www.desmos.com/calculator/f0gvhes7s3

Assuming the 1/2 cups of lemonade and 1/2 lemon bars can't be possibilities...the answers that make sense lie in the feasible region of the overlap of the graphs...these are    (150, 200)  and  ( 180, 100 )

I just needed it to stay in scientific notation. I'm sorry I forgot to tell you. Anyway thank you CPhill.

Remember that  when we have 10 raised to a negative power....we can "throw" that 10 across the fraction bar and make the exponent positve....so...we can write this as

3.5 * 10^8                   3.5

_________   =           ___   *   10^(8 - 6)   =    0.7  * 10^2   =  70

5 * 10^6                       5

OK

Opening balance = 1342

Add the deposit  = 1765.88   + 1342  =  3107.88

Total of checks  =  ( 47.32 + 233.95  + 78.03 + 29.87 )  = 389.17

Subtract this from 3107.88  =  3107.88 -  389.17  = 2718.71

Subtract the amount transferred to savings  = 2718.71  - 945    = $1773.71  ⇒ "A"

I saw this answered not too long ago. Perhaps someone can find the older version?

I seem to recall that it was a long answer, maybe Heureka answered it but I am not sure.   

I didn't come up with none of the answers.. I think i did something wrong can you write it out then i'll solve it

Here are the  constraint equations we need

y ≥ 4x 

x + y ≤ 50

And we want to maximize this revenue function, R

R  = 25x  + 40y

Here is a gaph of the constraints : https://www.desmos.com/calculator/kybxhc7dvb

The  revenue is maximized at the corner point  (10, 40)

So...the max revenue  is  25(10)  + 40(40)   =  250 +  1600   =  $1850

Pease help quick!

You have the following inequalities:

\(2x+1.5y\ge500\\0.25x+0.2y\le100\\x\ge150\)

Plug in the various pairs of x and y (eg x = 160, y = 110;  x = 232.5, y = 200; ...etc.) and see which pairs satisfy these inequalities.

(Strangely, it looks as though it's possible to sell a half cup of lemonade and half a lemon bar!  Unless, of course, they are clues to impossible outcomes!)

ik a childesh one but im going as a beanie baby. I need to finish the costume then all good.

Yes that sounds good :)

Boxes 1 - 2 - 3  (vertical)     go with    2 - 1 - 6 (horizontal)

Is there a baseline chirps/minute or temperature from which he (only males chirp) increases 1 chirp/.25 degree f ?

Slope = 1 c/0.25 degree = 4

40 = 4x -160

f(x) = 4x -160   ????????????    Where x = temp   and f(x) = chirps 

Looked up Dolbear's Law:

Tf = 50 + ( n60-40)/4        n60 = chirps per minute      so 40 must be the baseline

     = 50 + n60/4 -10

    = 40 +n60/4

Tf =  n60/4 + 40            there, now I'm happy.....

3 pizzas  /  (2/8 pizza/person)=

3 x 8/2 people = 12 people