CPhill

              P

        5             8

Q            M             R

             11

Law of Cosines     { cos PMQ = - cos PMR }

PQ^2 = QM^2 + PM^2 - 2(QM * PM) * (-cos PMR)

PR^2 = RM^2 + PM^2 - 2 (RM * PM) * ( cos PMR)

5^2 = 5.5^2 + PM^2 + 2(5.5 * PM)cos(PMR)

8^2 = 5.5^2 + PM^2 - 2(5,5 * PM) cos (PMR)          add these

5^2 + 8^2  = 2 * 5.5^2 + 2PM^2

89 = 60.5 + 2PM^2

28.5 / 2 = PM^2

14.25 = PM^2

sqrt (14.25)  = PM ≈  3.77

                      A

          Z                Y

B                                C

If AC =12, then AY can't also = 12

https://web2.0calc.com/questions/geometry_12483#r1

No, your answer is  correct, NTS.

It's impossible for the discriminant to be < 0

Good job!!!

(c)

This is impossible......even if we had 100% of the red potion (and  no blue), the  greatest concentration that we could achieve would be 60% !!!

Simplify as

1x^2 + 8x + 9

Discriminant

8^2 - 4 (1) (9)  =  

64 - 36 = 

28

Slope  =  [ 17 -  8 ] / [ -4 -5] =  9 / -9 = -1

Equation of line

y = -1 (x -5) + 8

y = -x + 5 + 8

x + y  = 13      divide through by 13

x / 13  +  y / 13   = 1

a = 13

https://web2.0calc.com/questions/help-geometry_38540

Triangle  ABC is similar to triangle EDC

Let CD  = x  

Let BC  = 24 - x

And we have that

DC / BC =  AC / EC

You should be able to solve it now

             A    E

B                 D                  C  15

      10                  10   

EC / sin 90 = DC / sin75

EC = 10/sin75  

BD = DC

ED = ED

So....by LL,  right triangle BED  congruent to right triangle CED

So BE  = 10/sin75 ≈ 10.35