SHOW WORK Use mathematical induction to prove the statement is true for all positive integers n or show why it is false 1^2 + 4^2 + 7^2 + ... + (3n - 2)^2 = quantity n times quantity six n squared minus three n minus one all divided by two

Adriveway is 60-feet long by 6-feet wide. the length and width of the driveway will each be increased by the same number of feet. the following expression represents the perimeter of the larger driveway: (x + 60) + (x + 6) + (x + 60) + (x + 6) which expression is equivalent to the expression for the perimeter of the larger driveway? a) 2(x + 66) b) 4x + 33 c) 4(x + 33) d) 4(x + 132)

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

Two corresponding sides of two similar triangles are 3cm and 5cm. the area of the first triangle is 12cm^2. what is the area of the second triangle?