(the second isomorphism theorem). let u and w be subspaces of a vector space v.
(a) show that the map t: w → (u+w)/u defined by
t(w) =w+u
is surjective. (you do not need to check that it is linear, though it evidently is.)
(b) by applying the first isomorphism theorem to t, conclude that
w/(un w) ≅ (u+w)/u.

Afactory adds 3 red drops and 2 blue drops of coloring to white paint to make each pint of purple paint. the factory will make 50 gallons of the purple paint.how many drops of red and blue coloring will the factory need in the 50 gallon batch of purple paint.

Jabari is power washing houses for a summer job. for every job, he charges an initial fee plus $30 for each hour of work. his total fee for a 4 -hour job, for instance, is $170 . jabari's total fee,f, for a single job is a function of the number,t, of hours it takes him to complete the job. write the function's formula.

Find the center and the radius of the circle with the equation: x^2-2x+y^2+4y+1=0?