Among all rectangles that have a perimeter of 82, find the dimensions of the one whose area is largest. Write your answers as fractions reduced to lowest terms.

Data from 2005 for various age groups show that for each $100 increase in the median weekly income for whites, the median weekly income of blacks increases by $105. also, for workers of ages 25 to 54 the median weekly income for whites was $676 and for blacks was $527. (a) let w represent the median weekly income for whites and b the median weekly income for blacks, and write the equation of the line that gives b as a linear function of w. b = (b) when the median weekly income for whites is $760, what does the equation in (a) predict for the median weekly income for blacks?

Given the functions, f(x) = 2x^2 - 1 and g(x) = 5x, find f(g(x)) and g(f(

One side of a rectangle is 7 centimeters shorter than six times the other side. find the length of the longer side if we also know that the perimeter of the rectangle is 266 centimeters.