Find the solutions for each of the following equations. give exact answers.
a) x^2 - 5 = x
b) x^2 + x = 1
c) x^2 - 3 = 5x

(show working out)

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?

One cell phone plan charges $20 per month plus $0.15 per minute used. a second cell phone plan charges $35 per month plus $0.10 per minute used. write and solve an equation to find the number of minutes you must talk to have the same cost for both calling plans.

Find the area of the surface obtained by rotating the curve z=4e^2y from y = 0 to y =1 about the y-axis. the area is square units