Suppose you add x liters of pure water to the 10 L of 25% acid solution. The new solution's volume is x + 10 L. Each L of pure water contributes no acid, while the starting solution contains 2.5 L of acid. So in the new solution, you end up with a concentration of (2.5 L)/(x + 10 L), and you want this concentration to be 10%. So we have
and so you would need to add 15 L of pure water to get the desired concentration of acid.
2(21x − 7) + 4(3x + 2) = 6(2x + 9) + 3
42x - 14 + 12x + 8= 12x + 54 + 3
54x - 6= 12x + 57
54x=12x + 63
42x=63
x= 63/42
x= 3/2
They gave you an eqution with variables and then they gave you numbers that all you have to do is put in
k(h-j)+h
5(5-4)+5
5(1)+5
5+5
10
The first one is 24 the second is 96
Now, the cosecant of θ is -6, or namely -6/1.
however, the cosecant is really the hypotenuse/opposite, but the hypotenuse is never negative, since is just a distance unit from the center of the circle, so in the fraction -6/1, the negative must be the 1, or 6/-1 then.
we know the cosine is positive, and we know the opposite side is -1, or negative, the only happens in the IV quadrant, so θ is in the IV quadrant, now
recall that
therefore, let's just plug that on the remaining ones,
now, let's rationalize the denominator on tangent and secant,
