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question:Solve for x, if 8^{4x-6}=left(frac{1}{2}right)^{x+5}.
answer:We can rewrite 8^{4x-6} as (2^3)^{4x-6}=2^{12x-18} and left(frac{1}{2}right)^{x+5} as 2^{-x-5}. So, we have 2^{12x-18}=2^{-x-5}. Since the bases are equal, we can equate the exponents, giving 12x-18=-x-5. Simplifying, we get 13x=13 and x=boxed{1}. The answer is: 1
question:Sabrina is collecting herbs to make a poultice for her grandmother. She needs twice as many basil leaves as sage leaves and 5 fewer sage leaves than verbena leaves. If she needs 12 basil leaves, how many leaves total does she need?
answer:If Sabrina needs twice as many basil leaves as sage leaves, then she needs 12/2 = 6 sage leaves. If she needs 5 fewer sage leaves than verbena leaves, then she needs 6+5 = 11 verbena leaves. Therefore, Sabrina needs a total of 12 basil leaves + 6 sage leaves + 11 verbena leaves = 29 leaves in total. 29 The answer is: 29
question:John buys 2 packs of index cards for all his students. He has 6 classes and 30 students in each class. How many packs did he buy?
answer:John has 6 classes and 30 students in each class, so he has a total of 6 * 30 = 180 students. He buys 2 packs of index cards for all his students, so he buys a total of 2 * 180 = 360 packs. Therefore, John bought 360 packs of index cards. 360 The answer is: 360
question:Gabriel is looking at her marble sets. She sees that in the first set x% of her marbles are broken. In the second set, 20% of the marbles are broken. The first set contains 50 marbles. The second set contains 60. There are 17 marbles broken in total. What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the percentage of broken marbles in the first set. Let's break down the information given: Percentage of broken marbles in the first set: x% Percentage of broken marbles in the second set: 20% Number of marbles in the first set: 50 Number of marbles in the second set: 60 Total number of broken marbles: 17 We can set up the equation as follows: (Number of marbles in the first set * Percentage of broken marbles in the first set) + (Number of marbles in the second set * Percentage of broken marbles in the second set) = Total number of broken marbles (50 * x%) + (60 * 20%) = 17 Let's simplify and solve for x: (50 * x%) + (60 * 20%) = 17 (50 * x%) + (60 * 0.20) = 17 (50 * x%) + 12 = 17 To isolate x, we subtract 12 from both sides of the equation: (50 * x%) + 12 - 12 = 17 - 12 50 * x% = 5 To solve for x, we divide both sides of the equation by 50: x% = 5 / 50 x% = 0.1 The value of x is 0.1, or 10%. 10 The answer is: 10