Tutor profile: Dustin H.

A right triangle is given where the legs (sides a & b) are values of a = 5 and b = 2. Find the hypotenuse of the triangle c.

The Pythagorean theorem is used to find the 3rd side of a right triangle which is a^2 + b^2 = c^2. a = 5 and b = 2 so it would become 5^2 + 2^2 = c^2 which simplifying the exponents would become 25 + 4 = c^2 which combining like terms would become 29 = c^2. To find c, you must take the square root of both sides in order to get rid of the exponent 2 on the c. The answer in radical form would be the square root of 29. The answer in decimal form would be 5.39 rounded to the nearest hundredth.

Find the slope of the line that passes through the points (2, 3) and (-1, 5).

The slope formula is used when given two coordinates which is in the fraction y-y over x-x. So, on top of the fraction is the difference in the y's which would be 3 - 5 which is -2. The bottom of the fraction is the difference in the x's which would be 2 - -1 which is 3. Therefore, the slope (in a fraction) is -2/3. Remember if you begin with the first y coordinate on top, you must begin with the first x coordinate on bottom.

Sally went to the movie theater and bought 2 tubs of popcorn and 4 drinks and spent $11.00. Robert also went to the movie theater and bought 3 tubs of popcorn and 5 drinks and spent $15.00. Create a systems of equations to represent Sally and Robert's purchases and solve the system to tell how much a tub of popcorn costs and how much does a drink costs?

This is a systems of equations problem. We will assign the variable "x" for popcorn and the variable "y" for drinks. The system will be set up as follows: 2x + 4y = 11 3x + 5y = 15 The elimination method would be the best way to solve this system. If I want to eliminate the x's, I would multiply the top equation by -3 and the bottom equation by 2 in order to create "opposites" for my x's and therefore eliminate them when combining like terms vertically. The result would be that x = 2.5 and y = 1.5 so a tub of popcorn would be $2.50 and a drink would be $1.50.