A factory employs 18 women to sew 540 dresses. The women take 6 weeks to do the job. If 12 women had been employed instead, how many weeks would it have taken them to sew the 540
dresses?

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Step-by-step explanation:

9514 1404 393

  9 weeks

Step-by-step explanation:

In problems of this nature, the usual assumption is that the time required is proportional to the work product and inversely proportional to the number of people doing the job. Here, there is no change in the amount of work, but the number of people is reduced by a factor of 12/18 = 2/3.

So, the amount of time required is expected to increase by a factor of 1/(2/3) = 3/2.

  (6 weeks)×(3/2) = 9 weeks

It would have taken 9 weeks to sew the 540 dresses.

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.