Jean stocked her aquarium with 36 fresh-water fish, which cost $212. the male fish cost $5 each, while the female fish cost $7 each. find the number of male fish (x) and the number of female fish (y)

Let x = number of male fish

Let y = number of female fish.

We need to construct a system of equations to solve this problem.

36 = x + y

212 = 5x + 7y. Lets solve this by elimination. Multiply the first equation by -5

-180 = -5x + -5y

212 = 5x + 7y. Now we need to add the equations together.

32 = 2y. Divide each side by 2.

16 = y. Plug this number into one of our original equations.

36 = x + (16). Subtract 16 from both sides.

20 = x.

There are 20 male fish and 16 female fish.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

answer: the angel abc is 30°,and the abc is a triangle where the angel bac is 90°

so ac is the half of 24=12ft,and from the pythagorean theorem we find ba

ba=√bc^2-ac^2=√576-144=√432=12√3ft

so bac is 12+12√3=12(1+√3)ft