1. Find all values of the variable in the interval [-2∏, 2∏] that satisfy the given equation. a. (sin θ + 1)(tan θ) = 0
b. sec θ + 2 = 0
2. Find the solutions in the interval [0, 2∏).
a. sin 2θ = cos θ
b. 3 cos² x + sin x = 3

The length of a rectangle is x times the square root of 100. the width is one-half y more than three-halves x. given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y? a) 5xy − 15x = 125 b) 5xy + 15x = 125 c) 15x2 − 5xy = 125 d) 15x2 + 5xy = 125

Becca wants to mix fruit juice and soda to make a punch. she can buy fruit juice for $3 a gallon and soda for $4 a gallon. if she wants to make 28 gallons of punch at a cost of $3.25 a gallon, how many gallons of fruit juice and how many gallons of soda should she buy?

Einstein office equipment has a rental plan for office machines. a fax machine that lists for $722.98 can be rented for 22% of the price annually. the state imposes a usage charge of 3.2%. if stephen hawking travel decides to rent the fax machine, what will its total monthly rental charge be?