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question:f a translation of the plane takes -3 + 2i to -7 - i, what is the complex number that this translation takes -4 + 5i to?
answer:A translation of the plane takes the form z mapsto z + w, where w is a complex number. We are given that -3 + 2i is mapped to -7 - i, so we have the equation -3 + 2i + w = -7 - i. Simplifying, we find w = -4 - 3i. To find the complex number that this translation takes -4 + 5i to, we simply add -4 - 3i to -4 + 5i. This gives us (-4 + 5i) + (-4 - 3i) = boxed{-8 + 2i}. The answer is: -8+2i
question:f Austin has 10 pairs of dress shoes to polish over the weekend and he has already polished 45% of the individual shoes, how many more shoes does he still need to polish?
answer:If Austin has 10 pairs of dress shoes, that means he has a total of 10 x 2 = 20 individual shoes. If he has already polished 45% of the shoes, that means he has polished 45/100 x 20 = 9 shoes. Therefore, he still needs to polish 20 - 9 = 11 shoes. 11 The answer is: 11
question:The formula for the total surface area of a cylinder is SA = 2pi r^2 + 2pi rh, where r is the radius and h is the height. A particular solid right cylinder of radius X feet has a total surface area of 12pi square feet. The height of this cylinder is 1. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the radius of the cylinder. We are given the total surface area of the cylinder, which is 12pi square feet. We can set up the equation as follows: SA = 2pi r^2 + 2pi rh 12pi = 2pi x^2 + 2pi x(1) Let's simplify and solve for x: 12pi = 2pi x^2 + 2pi x Dividing both sides of the equation by 2pi: 6 = x^2 + x Rearranging the equation: x^2 + x - 6 = 0 Now we can factor the quadratic equation: (x+3)(x-2) = 0 Setting each factor equal to zero: x+3=0 or x-2=0 Solving for x: x=-3 or x=2 Since the radius cannot be negative, the value of x is 2. The value of x is 2. The answer is: 2
question:Ed booked a hotel while he was on vacation. Staying at the hotel cost was 1.50 per hour every night and x per hour every morning. If Ed had 80 and he stayed in the hotel for 6 hours last night and 4 hours this morning, He was left with 63 money after paying for his stay at the hotel. What is the value of unknown variable x? What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the cost per hour of staying in the hotel every morning. Let's break down the information given: Cost per hour of staying in the hotel every night: 1.50 Number of hours Ed stayed at the hotel last night: 6 Number of hours Ed stayed at the hotel this morning: 4 Total amount of money Ed had: 80 Amount of money Ed had left after paying for his stay at the hotel: 63 We can set up the equation as follows: (Cost per hour of staying in the hotel every night * Number of hours Ed stayed at the hotel last night) + (Cost per hour of staying in the hotel every morning * Number of hours Ed stayed at the hotel this morning) = Total amount of money Ed had - Amount of money Ed had left after paying for his stay at the hotel (1.50 * 6) + (x * 4) = 80 - 63 Let's simplify and solve for x: 9 + 4x = 17 To isolate x, we subtract 9 from both sides of the equation: 9 + 4x - 9 = 17 - 9 4x = 8 To solve for x, we divide both sides of the equation by 4: x = 8 / 4 x = 2 The value of x is 2. 2 The answer is: 2