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question:Simplify the expression: 2x + 3x^2 + 1 - (6 - 2x - 3x^2).
answer:First, distribute the negative sign inside the parentheses: 2x + 3x^2 + 1 - 6 + 2x + 3x^2. Next, combine like terms: 2x + 2x + 3x^2 + 3x^2 + 1 - 6. This simplifies to 4x + 6x^2 - 5. So the final simplified expression is boxed{6x^2 + 4x - 5}.The answer is: 6x^2+4x-5
question:Adam has an orchard. Every day for x days he picks 4 apples from his orchard. After a month, Adam has collected all the remaining apples, which were 230. Adam has collected 350 apples in total from his orchard. 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 number of days Adam picked apples from his orchard. Let's break down the information given: Number of apples picked per day: 4 Total number of remaining apples after a month: 230 Total number of apples collected from the orchard: 350 We can set up the equation as follows: Number of apples picked per day * Number of days + Total number of remaining apples = Total number of apples collected 4x + 230 = 350 Let's simplify and solve for x: 4x = 350 - 230 4x = 120 To isolate x, we divide both sides of the equation by 4: x = 120 / 4 x = 30 The value of x is 30. 30 The answer is: 30
question:Solve for y: 3y+7y = 282-8(y-3).
answer:Simplifying both sides of the equation, we have 10y = 282-8y+24. Combining like terms, we get 18y = 306. Dividing both sides by 18, we find y = boxed{17}. The answer is: 17
question:f Arthur treated himself to dinner at a nice restaurant to celebrate his recent promotion and ordered an 8 appetizer, a 20 ribeye steak (with a voucher for half off), two glasses of red wine for 3 each, and a slice of caramel cheesecake for 6, and he tipped the waitress 20% of what the full cost of his meal would have been without the discount, what is the total amount, including the tip, that Arthur spent on dinner?
answer:The full cost of Arthur's meal without the discount would be 8 + 20 + (3 x 2) + 6 = 40. The discount on the ribeye steak is 50% off, so the discounted price is 20 / 2 = 10. The total cost of Arthur's meal, including the discount, is 8 + 10 + (3 x 2) + 6 = 30. Arthur wants to tip the waitress 20% of what the full cost of his meal would have been without the discount, so his tip would be 20% of 40, which is (40 x 20%) = 8. The total amount, including the tip, that Arthur spent on dinner is 30 + 8 = 38. 38 The answer is: 38