A(0, 1), B(1, 4), C(4, 3) and D(3, 0) are the vertices of a quadrilateral ABCD. (i) Find the equations of the diagonals AC and BD. (ii) Show that the diagonals AC and BD bisect each other at right angles. (ii) Find the lengths of AC and BD.

Find the greatest common factor of the polynomial: 10x^5+15x^4-25x^3 10x^5 x^3 5x^3 5

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

What is the binomial expansion of (2x-3)^5