CPhill

f(x)  =x^3  - 4x^2  - 9x - 36   factors as   

x^2(x - 4) - 9(x - 4)   =

(x - 4) (x^2 - 9)  =

(x - 4) (x + 3) ( x - 3)

So only answers  2,3, and 4  are correct

f(x) = x^3 + 5x^2 +6x

A.....when x  = 2 we have  (2)^3 + 5(2)^2 + 6(2)   =  8 + 20 + 12  =  40...so....not true

B.....x^3 + 5x^2 + 6x  factors as  x  ( x + 3) ( x + 2)....so...  true

C...when x   - 2  we have  (-2)^3 + 5(-2)^2 + 6(-2)      =  -8  + 20 - 12   =  0.....so...true

D.....x - 2 is not a factor....so...f(x) divided by  x - 2  will not result in a remainder of  0 ...so....not true

√ [ 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 ]

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 )

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"

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

I think I can speak for tertre, too...we are glad to help   [ if we can  !!! ]