Jake makes and sells pies. he sells each pie for $5.75. the materials to make each pie costs jake $4.00. the boxes jakes put the pies in cost $0.75 each. jake wants to know how many pies (p) he needs to sell to earn a profit of at least $50. which inequality should jake use?
50 ≤ 5.75p - 4.75p
b) 50 ≥ 5.75p - 4.75p
c) 50 ≤ 5.75p - 3.25p
d) p ≤ 5.75(50) - 4.75p

Marco has $38.43 dollars in his checking account. his checking account is linked to his amazon music account so he can buy music. the songs he purchases cost $1.29. part 1: write an expression to describe the amount of money in his checking account in relationship to the number of songs he purchases. part 2: describe what the variable represents in this situation.

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) = .

Amira is painting a rectangular banner 2 1/4 yards wide. the banner will have a blue background. amira has enough paint to cover 1 1/2 square yards of the wall. the school colors are blue and yellow, so amira wants to add yellow rectangles on the left and right sides of the blue rectangle. the yellow rectangles will each be 3/4 yards wide and the same height as the blue rectangle. what will be the total area of the two yellow rectangles?