Why do we convert from a mixed number to an improper fraction by multiplying the denominator of the fraction by the whole number and then adding the numerator?

If f(x)=-x^2+6x-1 and g(x)=3x^2-4x-1,find(f+g)(x)

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling

How does reflecting or rotating a figure change the interior angles of the figure?