Factor the algebraic expression below in terms of a single trigonometric function cos x - sin 2x - 1

Jackie purchased 3 bottles of water and 2 cups of coffee for a family for $7.35. brian bought 4 bottles of water and 1 cup of coffee for his family for $7.15. how much does each bottle of water cost? how much does each cup of coffee cost? i need this done

Evaluate the discriminant of each equation. tell how many solutions each equation has and whether the solutions are real or imaginary. x^2 - 4x - 5 = 0

How many solutions does the nonlinear system of equations graphed below have? a. one b. zero c. four d. two