Cara H.

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Geometry

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Question:

Classify triangle PQO by its sides. Then determine if the triangle is a right triangle. The points of the triangle are: P (-1, 2), Q (6,3), and O (0, 0)

Cara H.

Answer:

The first step is to use the Distance Formula to determine the side lengths. The Distance Formula is: $$ \sqrt{( x_{2} - x_{1})^2 + {(y_{2} - y_{1})^2}} $$ OP = $$ \sqrt{(-1 -0)^2 + {(2 - 0)^2}} $$ = $$ \sqrt5 $$ = approx. 2.2 OQ = $$ \sqrt{(6 - 0)^2 + {(3 - 0)^2}} $$ = $$ \sqrt45 $$ = approx. 6.7 PQ = $$ \sqrt{(6 - (-1))^2 + {(3 - 2)^2}} $$ = $$ \sqrt50 $$ = approx 7.1 Next, check for right angles. The slope of line OP is (2-0) ÷ (-1 - 0) = -2 The slope of line OQ is (3 - 0) ÷ (6 - 0) = 1/2 The product of the slopes is -2(1/2) = -1 So line OP and line OQ are perpendicular. Thus angle POQ is a right angle. Therefore, Triangle POQ is a right scalene triangle.

Pre-Algebra

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Question:

A flagpole is 40 feet tall. A rope is tied to the top of the flagpole and secured to the ground 9 feet from the base of the flagpole. What is the length of the rope to the nearest foot?

Cara H.

Answer:

To solve this problem, we must use Pythagorean Theorem which is $$a^2 + b^2 = c^2$$. In the formula, a and b represent the legs of our triangle. In this problem, a is represented by the height of the flagpole, 40; b is represented by the distance the rope is secured from the flagpole, 9. We would substitute the numbers in our formula: $$40^2 + 9^2 = c^2$$. We are now ready to solve for c. Remember to square a number, it means to multiply the number times itself. $$40^2 = 1600 $$. $$ 9^2 = 81$$. When we add the two together, our equation is now $$1681 = c^2$$. We must find the square root of 1681 in order to determine the length of the rope. If you have a calculator, you would use the square root function. C = 41. Thus your answer is the rope needs to be 41 feet long.

Algebra

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Question:

The sum of two numbers is 24. Five times the first number minus the second number is 12. What are the two numbers?

Cara H.

Answer:

When looking at a word problem, the frist step is to look for key words. In this problem, the key words are sum, is, times, and minus. Next, we need to define our variables. We are working with two numbers; so let's make the 1st number x and the 2nd number y. Now we are ready to write our first equation: x + y = 24. We know it should be an addition problem because of our key word, sum. For the second equation, we transfer the words of the second sentence into our equation. Our second equation would be 5x - y = 12. Now we are ready to solve this system of equations. I will use substitution to solve; so I must rearrange my first equation to get y by itself on one side of the equation. To do this, I will subtract x from both sides. This gives me y = 24 -x. I substitute 24-x in place of y in the second equation. My second equation would be 5x - (24-x) = 12. I must distribute the negative to 24-x. Thus the equation becomes 5x -24 + x = 12. I combine like terms next. 6x - 24 = 12. Now I must add 24 to both sides. This leaves 6x = 36. Now I divide both sides by 6 in order to isolate the x. The result is x = 6. I substitute 6 in place of x in my first equation to solve for y. 6 + y = 24. Thus y = 18. My answer would be 6, 18.

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