Except for answer 10x (1÷9), which was less than ten, every answer was more than ten.
The Exterior Angle Theorem states that the exterior angle measure of a triangle is equal to the total of the inner angles' remote measures.
Since the exterior angle in this question is ∢BCD, it is equivalent to the sum of ∢ABC and ∢BAC:
60° + α = 145° → α=85
Subtract the second equation after multiplying the first by two. With this solution, you have a simpler one-variable equation to solve. You can obtain the value of x by plugging the value of y into the other equation once you have determined its value.
Determine the likelihood that one non-yellow ball will be selected as the first step in answering this question. Next, determine the likelihood that another non-yellow ball will be selected from the remaining balls, and lastly, do the same with a third ball (keep in mind that there is no substitute; a selected ball does not return to the box and cannot be selected again).
Triangles that are similar to one another have the same shape but could differ in size.
Find Roj's age in order to begin solving this puzzle. The age difference between Roj and his father is four times larger. Consequently, divide Roj's father's age by 4 to determine his age: 48 ÷ 4 = 12. Roj is currently twelve years old, but he will turn thirteen the next year when he becomes one year older. Thus, 13 is the right response.
Sam's total pay is subject to a 15% tax (Note: 15% = 0.15). He must deduct 15 from the entire amount he is paid, which is 2000 + 0.01s, leaving him with 85% (100 - 15 = 85), or 0.85. Therefore, his monthly after-tax income is 0.85 (2000 + 0.01s).
You must translate several time units into a comparable time unit in order to compare them. Observe that the identical time measurements are included in every response option. Transform each one into a device that you feel at ease with.
Please select 2 correct answers
You must convert six hours into minutes or seconds in order for the response selections to correspond with the proper answers.
Hours are equal to 60 minutes, thus multiplying hours by 60 will get you minutes.
360 minutes = 6 hours × 60
You must multiply by 60 once more in order to convert minutes to seconds because there are also 60 seconds in a minute.
21600 seconds are equal to 360 minutes × 60.
Thus, (21,600 seconds) and (360 minutes) are the proper responses.
Recognizing that the two triangles are congruent—triangles have to have the same three sides and angles—is the first step toward answering this question.
Use AAS (angle, angle, side) to determine whether the two triangles in this question are congruent: two triangles are congruent if they have one pair of equal sides and two pairs of equal angles. Angles in a triangle add up to 180°, so if two pairs of angles are equal, the third pair must also be equal.
Divide the initial pair of integers by 14. Four times through 14, we get 63. Put these four over the number 63. To calculate the remainder, remove the four batches of 14 (4 x 14 = 56) from the 63.
4 x 14 = 56.
63 – 56 = 7.
There are seven more in that division.
Bring down the dividend's next number, nine, to begin the next division.
Divide 79 by 14 now. Five times through, 14 divides into 79, therefore 5 x 14 = 70. Put the five over the nine.
To calculate the remaining amount, deduct 70 from 79. Consequently, nine is the remainder.
Bring down the eighth, the next number in the dividend, once again. Next, split 14 by 98. 14 splits into 98 exactly seven times. Put the seven above the eight.
Since 14 is a factor of 98, there are no leftovers after the final division. Thus, 457 is the right response.
