Appearance
question:Points P and R are located at (2, 1) and (12, 15) respectively. Point M is the midpoint of segment overline{PR}. Segment overline{PR} is reflected over the x-axis. What is the sum of the coordinates of the image of point M (the midpoint of the reflected segment)?
answer:The coordinates of point M can be found by taking the average of the x-coordinates and the average of the y-coordinates of points P and R. The x-coordinate of point M is frac{2+12}{2}=7 and the y-coordinate of point M is frac{1+15}{2}=8. When a point is reflected over the x-axis, the y-coordinate of the image is negated. So the image of point M has coordinates (7,-8). The sum of the coordinates is 7+(-8)=boxed{-1}. The answer is: -1
question:John can front squat 80% as much as he back squats. He used to back squat 200 kg but increased that by x kg. He can do a triple equal to 90% of the amount he front squats. He will move 540 weight if he does three triples. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the increase in weight for John's back squat. Let's break down the information given: Front squat weight = 80% of back squat weight Back squat weight = 200 kg + x kg Triple weight = 90% of front squat weight Total weight moved in three triples = 540 kg We can set up the equation as follows: Triple weight * 3 = Total weight moved in three triples 0.9 * (0.8 * (200 kg + x kg)) * 3 = 540 kg Let's simplify and solve for x: 0.9 * (0.8 * (200 kg + x kg)) * 3 = 540 kg 0.72 * (200 kg + x kg) * 3 = 540 kg 2.16 * (200 kg + x kg) = 540 kg Let's distribute and simplify further: 432 kg + 2.16x kg = 540 kg To isolate x, we subtract 432 kg from both sides of the equation: 432 kg - 432 kg + 2.16x kg = 540 kg - 432 kg 2.16x kg = 108 kg To solve for x, we divide both sides of the equation by 2.16: x = 108 kg / 2.16 x = 50 The value of x is 50 kg. 50 The answer is: 50
question:f Stephanie is decorating 24 cupcakes for a birthday party and wants to use 1 candle for half of the cupcakes and 2 candles for the other half, but she currently only has 30 candles, how many additional candles does she need to complete the cupcakes?
answer:Stephanie wants to use 1 candle for half of the cupcakes, so she needs 24 / 2 = 12 candles for those cupcakes. She also wants to use 2 candles for the other half of the cupcakes, so she needs 24 / 2 * 2 = 24 candles for those cupcakes. In total, she needs 12 + 24 = 36 candles for all the cupcakes. She currently has 30 candles, so she needs 36 - 30 = 6 additional candles. 6 The answer is: 6
question:Let d and e denote the solutions of 3x^2+10x-25=0. Find (d-e)^2.
answer:We can solve the quadratic equation by factoring or using the quadratic formula. Factoring, we have (3x-5)(x+5)=0, so the solutions are x=5/3 and x=-5. Therefore, d=5/3 and e=-5. We want to find (d-e)^2=(5/3-(-5))^2=(5/3+5)^2=(20/3)^2=boxed{frac{400}{9}}. The answer is: frac{400}{9}