# Tutor profile: Dustin H.

## Questions

### Subject: Geometry

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.

### Subject: Pre-Algebra

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.

### Subject: Algebra

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.