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That's a really interesting question. Anyone have any ideas?

The sum of the coefficients is 1,238,370.

EXTREMELY similar :      (see if you can do this one)

https://web2.0calc.com/questions/right-triangle_17#r1

median side   of  2 6 7  is the 6 side

6 out of (2+6+7) = 6/15          6/15 * 345 = 138 yards

2432 ounces / 128 ounces / gal =   2432/128  gal = 19 gal

The yellow is 1/4 of the whole circle area

cicle area = pi r^2  

   1/4 pi 5²  mi²  =   area of yellow

This is a right triangle (check it with pythag theorem)

sin A = opp side / hypot

          = 9/11

Square base     17 x 17 mm²

plus FOUR triangles     4   * 1/2 17*20     mm²

three squares  6x 6         3*6*6     m²

PLUS  two triangles     2 * 1/2 ( 6)(4)     m²        add the reds

18 is to 12     as 12 is to a+5

18/12 = 12 / (a+5)

a+5  = 12 *  12/18 = 8

a = 3

Right triangle with equal leg lengths     leg length = 1/2 of 4.6 = 2.3

pythag theorem to find hypotenuse     =     sqrt ( 2.3²  + 2.3²) = 3.25

two legs at 3.25   long + 4.6 cm = 11.1 cm   perimeter

12 is to 20      as    x  is to  10

12/20 = x/10

x = 10 * 12/20 = ......... units

sin is negative in Q IV

sin^2 + cos^2 = 1

sin^2 = 1 - .6 ^2

sin^2 = .64                 take the negative root

sin =  - . 8

a + b = 20      or     b = 20-a

a^2   + (20-a)^2 = sum of squares in terms of 'a'

a^2      + a^2 -40a+400

2a^2 -40a+400 = sum of squares

The third equation has no y-term, so let's eliminate the y-term from the combination of the first two equations.

x + y + 3z  =  10     --->     x -2     --->     -2x - 2y - 6z  =  -20

-4x + 3y + 5z  =  7       --->                      -4x + 3y + 5z  =  7

Add down the columns:                             -6x - z  =  -13   

Since  kx + z  =  3        --->         z  =  3 - kx

Substituting these:        -6x - (2 - 3kx)  =  -15

                                    -6x - 2 + 3kx  =  -15

                                      6x - 2 - 3kx  =  15

                                          6x - 3kx  =  1

                                          3x(2 - k)  =  17

If  2 - k  =  0,  there is no value for x that will result in a product of 10,

so  k = 2  results in no possible solution.

For every other value of k, there will be a value of x that can produce a product of 10.

So the answer is k = 2.

Oh and I saw the other question that's from an AoPS class, namely Algebra A

Triangle side length rule    sum of two sides must be greater than the other side

x+3   must be graeter than 5     so x >2

x+ 5   is already greater than 3

5+3 > x     means x can be no larger than 7      so x   can be    3   4    5   6  7

7  8  9  10  11

                       12

                             13       7 possibles