In parallelogram ABCD  BC is parallel to AD;  BC = 3x -1, CD = 2x +1 and   AD = 4(x – 2). Find x.

2x + 5y + 5z = 0, - x - y = 0 and 2x + 4y + 3z = 0 are the three straight lines. These lines intersect each other at (1.7, -1.6). The inverse of a straight line is also a straight line. Find out the inverse straight line of these lines (Show all the steps).

A farmer finds there is linear relationship between the numbers of bean stalks , n, she plants and the yield , y, each plant produces 30 oz of beans .When she plants 34 stalks , each plants produces 28 oz of beans. Find a linear relationship in the form y=mn b that gives the yield when n stalks are planted.

A child is walking to school in winter. The sidewalk is S = 300 feet long and then turns at a right angle and goes anotherl = 40 feet before reaching the door of the school. The child, however, cuts through the snow x feet before the corner, and travels through the snow on BC. If the speed of the child through the snow is of the speed of the child on the sidewalk, then where should the child leave the sidewalk in order to get to school most quickly?