Let d be a region bounded by a simple closed path c in the xy-plane. use green's theorem to prove that the coordinates of the centroid (x, y) of d are: x = (1/2a)∫cx²dy y = (-1/2a)∫cy²dx, where a = area of d use the formulas to find the centroid of the triangle with vertices (0, 0), (a, 0), and (a, b), where a > 0 and b > 0. {x, y) = )

Linet passes through (4.5) and is perpendicular to the line shown on the condirate grid. what is the equation of line t in standard form?

Acollection of coins has value of 64 cents. there are two more nickels than dimes and three times as many pennies as dimes in this collection. how many of each kind of coin are in the collection?

(05.03 mc) part a: explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x−2 intersect are the solutions of the equation 4x = 2x−2. (4 points) part b: make tables to find the solution to 4x = 2x−2. take the integer values of x between −3 and 3. (4 points) part c: how can you solve the equation 4x = 2x−2 graphically? (2 points)