How many liters of a 40% acid solution must be added to 12 liters of a 20% solution to obtain a 25% solution

The answer is 4 liters.

Step-by-step explanation:

We want a final 25% solution, which means that the solvent should constitute 25 percent of all the liters of solution.

Let us call the litres of 40% solution, so when they are added to the 12 litres of 20% solution, the total litres of the new solution are:

of these liters, 25% must be the solvent:

Now for the 40% solution, the liters of the solvent are , and for the 20% liter solution, the liters of solve are liters. Thus the total liters of the solvent are

Therefore

me

step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.