Ichiro picks a marble from Bag 1 and then picks another marble from Bag 2. The possible results can be organized in a table. Use the drop-down menus to complete the table.

What should be done to solve the equation? x+14=21 add 14 to both sides of the equation. subtract 14 from the left side of the equation. add 14 to the left side and subtract 14 from the right side of the equation. subtract 14 from both sides of the equation.

James wants to promote his band on the internet. site a offers website hosting for $4.95 per month with a $49.95 startup fee. site b offers website hosting for $9.95 per month with no startup fee. for how many months would james need to keep the website for site a to be a better choice than site b? define a variable for the situation. write an inequality that represents the situation. solve the inequality to find out how many months he needs to keep the website for site a to be less expensive than site b. using words, describe how many months he needs to keep the website for site a to be less expensive than site b.

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .