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A)   'w' cannot be negative , so the largest area will occur when w = 0        526 m^2    (which is kinda comical having a w = 0 )

Are you sure you have the equation written correctly ????  Please proofread ....because none of these answers make sense!

B)    -2 (20²) + 576 = _____________   (nonsensical answer)

C)    18 144   = - 2 w² + 576       (another nonsensical answer)

z = a + bi

|(a-3) + bi| = |a + (b+1)i|

sqrt(a^2 - 6a + 9 + b^2) = sqrt(a^2 + b^2 + 2b + 1)

a^2 - 6a + 9 + b^2 = a^2 + b^2 + 2b + 1

-6a + 9 = 2b + 1

8 = 6a + 2b + 1

7 = 6a + 2b

|z + i| = |z - 1 - 2i|

|a + (b+1)i| = |(a-1) + (b-2)i|

sqrt(a^2 + b^2 + 2b + 1)  = sqrt(a^2 - 2a + 1 + b^2 - 4b + 4)

a^2 + b^2 + 2b + 1 = a^2 - 2a + 1 + b^2 - 4b + 4

2b + 1 = - 2a + 1 - 4b + 4

6b + 2a = 4

3b + a = 4

7 = 6a + 2b

3b + a = 4

a = 4 - 3b

7 = 6(4 - 3b) + 2b

7 = 24 - 18b + 2b

16b = 24 - 18b + 2b

16b = 17

b = 17/16

a = 13/16

There are probably other ones, but 13/16 + 17/16i is the one I found. 

=^._.^=

Area =  w * l

so the area is :

(𝑡^2−9 / 3𝑡−2) *   ( 15𝑡−10/ 3𝑡−9)  cm^2.           (I assumed you meant  t²   and NOT  t 2 )

(t+3)(t-3)  *    (15t-10) 

     (3t-2)(3)(t-3)                                note that the (t-3) in the numerator and denominator cancel  (t cannot = 3  or 2/3 )

(t+3)  * (15t-10)

  (3)(3t-2)

15t^2 +35t-30      = area                 when t = 1         (15 + 35-30)/(3) =   20 / 3  cm^2

   (3)(3t-2)

5    +    x / 9    = 3        subtract 5 from both sides of the equation

            x/ 9     = - 2       multiply both sides by 9

             x =  -18

Circumference of a circle (the wheel) is   

       pi * d    =   pi * (25 *2) = 50 pi   = 157 cm   = 1.57 m   = .00157 km     for ONE turn.

  b)    1 km / .00157 km/turn = 636.62 turns   

Yes, that is correct....subtract the smaller from the larger area to get the area betweem them.

4a=72 so x=18

Choose a p?  What is a p? What are you talking about? 

I suppose p stands for pick and it is the number you have chosen.

ok

The easiest way is to make q the subject of that equation. 

Then substitute in each value of p. one at a time then count how many work.  

Put the number that work over 10 and you will have your answer.

Alan, can you please explain your very first line.

That is where I got lost.         

Thanks for sharing that video, it is a really easy to understand method for solving the problem in the video. (I will try and remember it)

This problem is not the same though.  

Thank you, that would be good.  

Thank you so much for taking time out of your day it help me with this question.

I apologize for not responding to answers. I will try to be a more active member of the community.

Triangles BEP and ACE are similar.

AE / CE = EP / BE

AE = 29 1/6

Slope of  given line   =    ( -1 - -7)  / ( -5 -4)  =   6 / -9   =  - 2/3

Slope  of  perp  line  =   negative  reciprocal  =     3/2

Slope   = ( -2-6) / ( -4  - -2)  =  -8/ -2  =  4

Eq  of  line using  (-2 , 6)

y  = 4  ( x - - 2)  + 6

y  = 4 ( x + 2)  + 6

y  = 4x  + 8 + 6

y =  4x + 14

To  find  the y  int...let x  = 0

y = 4(0)  + 14

y  = 14    =  the y intercept

HOW DO I LIKE THE POST!!!! :)

Slope   =  ( 4-3)  /(7-6)  =  1/1  =   1

Equation of line  using   (6,3)

y = 1 ( x - 6)  + 3

y  = x  - 6  +  3

y  =  x - 3

For the x intercept, let  y  = 0

0  = x - 3

3  =  x   = the x intercept

A parallelogram ABCD has a perimeter equal to 124. Let E be the foot of the perpendicular from A to BC, and let F be the foot of the perpendicular from A to CD. If AE= 7 and AF=20, what is the area of the parallelogram?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

AB = x         AD = 62 - x          AE = 7          AF = 20

Triangles ABE and ADF are similar.

x / 7 = (62 - x) / 20

[ABCD] = AE * AD

OK, glad  to help.......

you're the best bro, tysm I really appreciate it haha

If  3  distinct  colors  are represented and there are only 4 balls,  then only 2 of them could be the same color....so.....the probability is   0

See the second answer here   :

https://web2.0calc.com/questions/sequence_25

See  here  : https://web2.0calc.com/questions/help-please-geometry_3

Volume  of  funnel (assuming a cone)  =    (pi/3) ( 4^2) (12)   ≈  201.06  cm^3

Each second,  the volume  of slime  in the  fummel grows  by  60 - 40  =  20 cm^3

So

201.06  / 20   ≈  10.05  sec  to  overflow