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question:On a Cartesian coordinate plane, points (2,1) and (3, 4) are adjacent points on a square. What is the area of the square?

answer:The distance between (2,1) and (3,4) is sqrt{(3-2)^2 + (4-1)^2} = sqrt{1+9} = sqrt{10}. Since the sides of the square have equal length, the area of the square is (sqrt{10})^2 = boxed{10}. The answer is: 10

question:Carla's teacher tells her that she needs to collect 30 leaves and x bugs for a project that's due in 10 days. How many items does Carla need to collect each day if she always wants to collect the same daily amount? If we know the answer to the above question is 5, what is the value of unknown variable x?

answer:Carla needs to collect a total of 30 leaves and x bugs for the project. She has 10 days to complete the project. To find out how many items Carla needs to collect each day, we can divide the total number of items by the number of days: (30 + x) / 10. We are given that Carla needs to collect 5 items each day, so we can write: (30 + x) / 10 = 5. Multiplying both sides by 10, we get: 30 + x = 50. Subtracting 30 from both sides, we get: x = 20. The value of x is 20. 20 The answer is: 20

question:At the end of a circus act, there are 12 dogs on stage. Half of the dogs are standing on their back legs and the other half are standing on all 4 legs. How many dog paws are on the ground?

answer:If there are 12 dogs on stage and half of them are standing on their back legs, that means there are 12/2 = 6 dogs standing on their back legs. Each dog has 2 back legs, so there are 6 x 2 = 12 back legs. The other half of the dogs, which is also 6 dogs, are standing on all 4 legs. Each dog has 4 legs, so there are 6 x 4 = 24 legs. Therefore, there are a total of 12 back legs + 24 legs = 36 dog paws on the ground. 36 The answer is: 36

question:Osborn is testing a new way to get dressed in the morning on school days so he goes faster and can get up later. He tracks his time for the week and on Monday is takes him 2 minutes. On Tuesday it takes him 4 minutes. On Wednesday it takes him 3 minutes. On Thursday it takes him 4 minutes. Before Friday arrives he looks at his old way of getting dressed and sees that it was taking him x minutes on average to get dressed. He has to get dressed at a speed of 2 on Friday so his weekly average ties his old method. What is the value of unknown variable x?

answer:To solve this problem, we need to determine the value of x, which represents the average time it took Osborn to get dressed using his old method. Let's break down the information given: Time it took Osborn to get dressed on Monday: 2 minutes Time it took Osborn to get dressed on Tuesday: 4 minutes Time it took Osborn to get dressed on Wednesday: 3 minutes Time it took Osborn to get dressed on Thursday: 4 minutes Time Osborn needs to get dressed on Friday to tie his old method's average: 2 minutes We can set up the equation as follows: (2 + 4 + 3 + 4 + 2 + x) / 6 = x Let's simplify and solve for x: 15 + x = 6x To isolate x, we subtract 6x from both sides of the equation: 15 + x - 6x = 6x - 6x 15 - 5x = 0 To solve for x, we divide both sides of the equation by -5: (15 - 5x) / -5 = 0 / -5 3 - x = 0 To isolate x, we subtract 3 from both sides of the equation: 3 - x - 3 = 0 - 3 -x = -3 Finally, we multiply both sides of the equation by -1 to solve for x: x = 3 The value of x is 3. 3 The answer is: 3