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question:f Stu has x books and Albert has 4 times as many books as Stu, how many books do Stu and Albert have in total? If we know the answer to the above question is 45, what is the value of unknown variable x?
answer:Stu has x books. Albert has 4 times as many books as Stu, which means Albert has 4x books. The total number of books Stu and Albert have in total is the sum of the number of books Stu has and the number of books Albert has: x + 4x = 5x. We are given that the total number of books is 45, so we can write: 5x = 45. Dividing both sides by 5, we get: x = 9. The value of x is 9. 9 The answer is: 9
question:Determine the coordinates of the center of the circle described by the equation x^2 - 2x + y^2 - 4y - 28 = 0.
answer:We rewrite the equation as x^2 - 2x + y^2 - 4y = 28 and then complete the square, resulting in (x^2 - 2x + 1) + (y^2 - 4y + 4) = 33, or (x - 1)^2 + (y - 2)^2 = 33. This is the equation of a circle with center (1, 2) and radius sqrt{33}, so the coordinates of the center are boxed{(1, 2)}. The answer is: (1,2)
question:f Faith's neighborhood consists of 20 homes, and each home requires 10 solar panels, but the supplier brought 50 panels less than the required amount, how many homes in the neighborhood were able to have their solar panels installed?
answer:If each home requires 10 solar panels and there are 20 homes in the neighborhood, then the total number of solar panels required is 10 x 20 = 200. If the supplier brought 50 panels less than the required amount, then they brought 200 - 50 = 150 panels. Since each home requires 10 panels, the number of homes that were able to have their solar panels installed is 150 / 10 = 15 homes. 15 The answer is: 15
question:When simplified, what is the value of sqrt{3} times 3^{frac{1}{2}} + 12 div 3 times X - 4^{frac{3}{2}}? If we know the answer to the above question is 3, what is the value of unknown variable X?
answer:To simplify the expression, we need to follow the order of operations (PEMDAS). First, let's simplify the exponents: 3^{frac{1}{2}} can be written as sqrt{3}. 4^{frac{3}{2}} can be written as (sqrt{4})^3, which is equal to 2^3. Now, let's simplify the multiplication and division from left to right: sqrt{3} times sqrt{3} + 12 div 3 times X - 8 Simplifying further: 3 + 4X - 8 Combining like terms: 4X - 5 Given that the value of the expression is 3, we can write: 4X - 5 = 3 Adding 5 to both sides of the equation, we find: 4X = 8 Dividing both sides of the equation by 4, we get: X = 2 The value of X is 2. The answer is: 2