ElectricPavlov

If they are perpindicular , then the slope, m of line 1   will be   - 1/m of the second line...

   re-arrange the equations into   y = mx + b form to easily see the slopes

2y + x + 3 = 0   becomes

y = - 1/2 x - 3/2      slope , m = - 1/2     does the slope of the other line = - 1/ (-1/2) = 2 ???

second line

3y + ax + 2 = 0

3y= - ax - 2

y = - a/3 x - 2/3       to be perpindicular    - a/3 must equal 2

                                        - a/3 = 2

                                            a = -6

You need the short diagonal ....perhaps that is how you found the answer

short diagonal =   sqrt (3) * side length =

                              sqrt 3  * 10        <======   this is the height of the hexagon

shaded area is then    10    x   10* sqrt 3     cm²

find 'x'  (using trig functions that you should know) =====>   the vertical dimension is 2 * x 

Start with 1 whole jar

   remove 1/2     then  1/2 is left

    removing  2/5 of the 1/2 leaves 3/5 of the 1/2

          3/5 * 1/2 = 3/10   now are left

    removing 2/3 leaves 1/3 of what is left

               1/3  * 3/10 = 3/30 of the original         and this is equal to  4           

                                                3/30 x = 4     x = 4 * 30 /3 = 40 cookies originally

1/2 - x^2 = 7/16     subtract 1/2 from both sides

- x² = -1/16

x² =1/16

x = +- 1/4

Here is my start :

find the measure of the interior angles of the hexagon :    there is     (6-2)(180) = 720 degrees in the interior angles  

                     720 /6 = 120  degrees

   the horizintal dimension of the shaded area is 10  

find 'x'  =====>   the vertical dimension is 2 x                   can you do it now?

Total ideas sent to Ned    13 x 11 = 143 ideas

Ideas about thinking were     1 - 1/4 - 1/2 = 1/4

1/4  143 = ~~ 36 ideas about thinking

( 1 3/4  +  2 1/2 ) gal   x   ( $3.58 x 2) / gal  = .................dollars

You didn't provide the table, but I expect the Unionid mussel numbers decreased as the invasive zebra mussels increased.  Zebra mussels are taking space and nutrients and algae that the Unionids need to flourish.   I think Zebra mussels even attach to unionids which kills them.

Slope of given line  is m = -2/5     perpindicular is  - 1/m = 5/2

Point slope form of the new line through -7, 2    is      y-2   = 5/2 ( x - -7)

                                                                                   y = 5/2 x + 35/2 +2

                                                                                    y = 5/2 x + 39/2

Here is a graph ( which I used as a check):

https://www.desmos.com/calculator/kvm5df9b2n