1.
In the figure shown below, triangle MPQ is similar to triangle PQR, MR = 45 units and RQ = 15 units. What is the length of segment PR?
Correct Answer
B. 15*squareroot(3) units
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)
2.
A kite string is 220 feet long from the kite to the ground. The string makes a 45^{o} angle with the ground. About how high off the ground is the kite?
Correct Answer
C. 156 feet
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.
3.
The total area of trapezoid FGHJ is 52 square inches. What is the approximate length of FJ?
Correct Answer
B. 8.5 in.
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.
4.
Which of the following sets of numbers represents the side lengths in units of a right triangle?
Correct Answer
B. 3.6, 6, 4.8
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.
5.
For a sports banquet Coach, Mackey must use the rectangular tables in the school cafeteria. The diagram below shows the seating arrangements that Coach Mackey can use at 1 and 2 tables. Which expression 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?
Correct Answer
D. 2 (2y + 1)
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.
6.
A pattern exists as a result of raising I, an imaginary number, to n, an integer greater than or equal to 1. Based on the table, which of the following best represents I raised to the 16th power?
Correct Answer
D. 1
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.
7.
On a certain math problem, Cynthia mistakenly divided a number by 4 then subtracted 24 and got 12 for her answer. After reading the problem again, she realized that they should have subtracted 24 before dividing by 4. What was the correct answer?
Correct Answer
C. 30
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.
8.
Jesse had a collection of baseball cards. He gave 10 cards to his little brother and equally divided the remaining cards among himself and 3 friends. He then had 15 cards. How many baseball cards did Jesse originally have in his collection?
Correct Answer
C. 70
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.
9.
Which equation best represents the line on the graph?
Correct Answer
C. 3x - 2y = 6
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.