why do the coordinate vectors of the abstract vectors with respect to the standard bases of their respective vector spaces correspond to the columns of the matrix mentioned in (a)matrices and (b)polynomials ?

During a bike challenge riders have to collect various colored ribbons each 1/2 mile they collect a red ribbon each eighth mile they collect a green ribbon and each quarter mile they collect a blue ribbion wich colors of ribion will be collected at the 3/4 markrer

When a rectangle is dilated, how do the perimeter and area of the rectangle change?

Construct the graph that models the given situation