A group of chemists are conducting an experiment to produce a new liquid material. One chemical contains 15% sodium (Na) and the other chemical contains 30% sodium (Na). Once they mix the two samples the resulting chemical contains 22% sodium (Na). How many milliliters (ml) of each sample must be mixed to obtain 600 ml of the new chemical

A= 320 and B = 280

Step-by-step explanation:

Now, if we combine the two chemicals to get a new chemical, which is  22% sodium, then the total amount of combined sodium is  amount of sodium from both sources

<=> 0.15A + 0.3B =  0.22*(A+B)

<=> 0.07A - 0.08B =  0 (1)

-  But we have a second equation, because we  know that   A + B = 600 (2)  

Solve the system of two equations, (1) and (2), we have:

A= 320 and B = 280

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.

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step-by-step explanation:

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