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Ron P.
Mathematics teacher for six years
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Pre-Calculus
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Question:

Consider the linear equation 2x + 3y = -6. What is the slope of the line that is produced from the graph of 2x + 3y = -6?

Ron P.

There are multiple ways one could determine the slope given this equation. We are going to use the form y=mx+b for a linear equation to determine the slope, in which x is the input, y is the output, m is the slope, and b is the y-intercept. To change our equation into the form y=mx+b we follow the following steps: 2x + 3y = -6 3y = -2x-6 y = -2/3x -6 Since m represents the slope of the linear equation, -2/3 is the slope from the equation.

Geometry
TutorMe
Question:

After throwing a Frisbee over your neighbors 15 foot fence, you retrieve a ladder in order to climb over. You set the base of the ladder 12 feet away from the base of the fence and lean the ladder to the top of the fence. What is the approximate length of the ladder?

Ron P.

We know the length in feet of the fence and the length in feet of the ground from the fence to the base of the ladder. What we are assuming is that the angle formed by the fence and the ground has a measurement of 90 degrees. Since the ladder, ground, and fence create a right angle, we can use the Pythagorean Theorem to determine the length of the ladder: 15 ^2 + 12^2 = c^2 225 + 144 = c^2 369 = c^2 19.2 = c The length of the ladder is about 19.2 feet.

Algebra
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Question:

You and some friends are at a pool party celebrating your recent graduation from middle school. Unexpectedly, your friend Tommy informs you his mother cannot give you a ride home as planned, so you are stuck finding a way home. The two options you have are Uber and Lyft and you want to spend the least amount of money possible. Lyft charges a flat fee of \$10 plus \$0.45 per mile, while Uber charges \$0.25 per mile with a \$15 flat fee. a) How many miles must you travel in order for the cost of each company to be the same amount? b) Which company would be cheaper if you need to travel 20 miles? c) Which company would be cheaper if you need to travel 30 miles?

Ron P.

a) We need to first create an expression for each company. Uber charges \$0.25 per mile plus \$15 just to be picked up, so we could write .25m + 15. Lyft charges \$0.45 per mile plus a \$10 flat fee, so we could write .45m + 10. Since we are solving for the number of miles (m) and we want to know when the cost is the same (equal), we will set the expressions equal to each other and solve for m: .45m + 10 = .25m + 15 .2m = 5 m = 25 This means the cost is the same for both companies at 25 miles. b) Since the cost per mile is more expensive for Lyft, any number of miles traveled under 25 miles, Lyft would be the better deal. Therefore, Lyft would be cheaper for a ride of 20 miles. c) Since the flat fee is more expensive for Uber, any number of miles traveled over 25 miles, Uber would be the better deal. Therefore, Uber would be cheaper for a ride of 30 miles.

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