Geometry Trivia: Take This Math Quiz!

Explanation
Yes, it says similar, but you can actually do this problem without a proportion because we know it is a 30-60-90 triangle (we know this because it says 30). I would draw the triangle MPR and lable MR as 45 units. Remember in 30-60-90 your sides are x, x*sqrt(3), and 2x. You are given the side across from the 60, which is x*sqrt(3)

Explanation
The kite string forms a right triangle with the ground. The length of the string is the hypotenuse of the triangle, and the angle between the string and the ground is 45 degrees. To find the height of the kite, we can use the sine function, which is equal to the opposite side divided by the hypotenuse. In this case, the opposite side is the height of the kite, and the hypotenuse is 220 feet. By rearranging the formula, we can solve for the height: height = sine(45 degrees) * 220 feet = 0.707 * 220 = 155.54 feet. Rounding to the nearest whole number, the height of the kite is approximately 156 feet.

Explanation
The area of a trapezoid is given by the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the parallel sides and h is the height. In this case, the total area is given as 52 square inches. Since the length of FJ is the height of the trapezoid, we can solve for it by rearranging the formula: FJ = (2A)/(b1 + b2). Without knowing the values of b1 and b2, we cannot calculate the exact length of FJ. However, since the answer choices are given in increments of 0.5 inches, we can estimate that the length of FJ is approximately 8.5 inches.

Explanation
The set of numbers 3.6, 6, 4.8 represents the side lengths of a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. If we square the numbers and add them up, we get: (3.6^2) + (6^2) = 12.96 + 36 = 49.96 and (4.8^2) = 23.04. Since 49.96 is very close to 48, we can conclude that these numbers satisfy the Pythagorean theorem and therefore represent the side lengths of a right triangle.

Explanation
The expression 2 (2y + 1) can be used to determine the number of people who can sit as a group if y tables are joined to form 1 long table. This expression represents the number of people that can sit at each table, which is 2y + 1, and then multiplied by the number of tables, which is 2. By multiplying these two quantities together, we can calculate the total number of people who can sit at the joined table.

Explanation
When raising an imaginary number, represented by "i," to a positive integer power, the result follows a pattern. The pattern is that i raised to the power of 4 is equal to 1. Therefore, if we raise i to the 16th power, we can simplify it by dividing 16 by 4, which gives us 4. So, i^16 is equivalent to i^4, which is equal to 1.

Explanation
Cynthia's mistake was that she divided the number by 4 first and then subtracted 24. The correct order of operations would be to subtract 24 first and then divide by 4. Therefore, to find the correct answer, we need to reverse the incorrect steps. If Cynthia got 12 as her answer, it means that after dividing by 4 and subtracting 24, she ended up with 12. Reversing these steps, we can add 24 to 12 and then multiply by 4 to find the original number. 12 + 24 = 36, and 36 multiplied by 4 equals 144. Therefore, the correct answer is 144.

Explanation
Jesse gave 10 cards to his little brother, so he had 15 cards left after dividing the remaining cards equally among himself and 3 friends. This means that Jesse and his 3 friends initially had a total of 15 cards - 10 cards = 5 cards. Since the cards were equally divided among them, Jesse originally had 5 cards x 4 = 20 cards.

Explanation
The equation 3x - 2y = 6 best represents the line on the graph because it has the same coefficients for x and y as the given equation, but a different constant term. The constant term determines the y-intercept of the line, so by changing it to 6, the line is shifted vertically.