Tutor profile: Elizabeth V.

Suppose there is a right angle triangle ABC. Angle B measures 50 degrees. The hypotenuse (BC) of the triangle measures 12cm. Use trigonometric ratios to solve for the missing side across from angle B, side AC.

First, identify which trigonometric ratio you need to use to solve for AC. In this case, the side is across from angle B. We also know the length of the hypotenuse (12cm). Thus, we can use the trigonometric ratio sine(B)=opposite/hypotenuse (remember opposite in this case is the side across from the angle. Plug in the missing variables. Sin(50)=AC/12 to isolate the variable AC, multiply both sides of the equation by 12. the equation becomes 12sin(50)=AC. The final step is to use a calculator to multiply the sine of 50 by 12. The final answer is 9.12 cms.

combine all of the like terms in this expression (2x-4y+3y) - (4x+12y-2x)

First, combine any like terms within the parenthesis. In the first set of parenthesis, -4y and 3y are like terms. When you combine them, you get -y. In the second set of parenthesis, 4x and -2x are parenthesis. When you combine them, you get 2x. The expression becomes (2x-y)-(2x+12y). Then, distribute the negative to the parenthesis. The expression becomes 2x-y-2x-12y Finally, combine any remaining like terms. The remaining like terms are 2x-2x and -y-12y 2x and -2x cancel each other out. -y-12y is -13y. -13y is the final answer.

You decide to rent a rowboat for a few hours to explore Lake Tahoe. The rental fee includes a flat rate of 12$ and then is 10$ per hour. If you spend 46$, how many hours did you rent the boat?

First, begin by writing a linear equation. Designate the variables x and y. In this case, y is the total cost, and x is the total number of hours. The equation would look like y=10x+12. Then, plug in the total cost, 42$, for y. The new equation is 42=10x+12. Finally, solve for x. First subtract 12 from both sides. This leaves you with 30 = 10x. Next, divide both sides by 10. The final answer is x=3 hours.