Achemist has one solution containing 30% insecticide and another solution containing 50% insecticide how much of each solution should the chemist mix to get 200l of 42% insecticide?
show your work plz

Let's use L for the 30% insecticide and H for the 50% version.
L + H = 200 liters
0.3L + 0.5H = 0.42(L + H) = 0.42(200) = 84

We notice from the first equation that H = 200 - L (subtracting H from both sides).  So we can substitute this into the second equation to knock out one variable.

0.3L + 0.5(200 - L) = 84 liters
0.3L + 100 - 0.5L = 84 liters [distributive property]
0.3L - 0.5L + 100 = 84 liters [commutative property]
-0.2L + 100 = 84 liters
-0.2L = -16 liters [subtract 100 from each side]
L = 80 [divide both sides by -0.2]

80 + H = 200 from our first equation, so H = 120.

You should make up some of these for yourself and solve them to get the best grasp on the process and improve your understanding.

The vertex of the quadratic function is (1.5, -.75)