answer:To solve this problem, we need to determine the value of x, which represents the number of cakes Sunny baked initially. Let's break down the information given: Number of cakes initially baked: x Number of cakes given away: 2 Number of candles on each cake: 6 Total number of candles used: 36 We can set up the equation as follows: Number of candles on each cake * (Number of cakes initially baked - Number of cakes given away) = Total number of candles used 6 * (x - 2) = 36 Let's simplify and solve for x: 6x - 12 = 36 To isolate x, we add 12 to both sides of the equation: 6x - 12 + 12 = 36 + 12 6x = 48 To solve for x, we divide both sides of the equation by 6: x = 48 / 6 x = 8 The value of x is 8. 8 The answer is: 8

answer:We can start by factoring out 3 from 999, since the sum of the digits (9+9+9) is divisible by 3. This gives us 999 = 3 cdot 333. Next, we see that 333 is divisible by 3, again because the sum of the digits (3+3+3) is divisible by 3. So, 333 = 3 cdot 111. Finally, we see that 111 is divisible by 3 for the same reason, so 111 = 3 cdot 37. Since 37 is a prime number, it is the largest prime factor of 999. Therefore, the answer is boxed{37}.The answer is: 37

answer:To solve this problem, we need to determine the value of x, which represents the value of the expression a + 4b. We are given the equations: a + 4b = X 6a + 3b = 51 We also know that a + b = 12. We can substitute the value of a in terms of b from the second equation into the first equation: a = (51 - 3b)/6 Substituting this expression into the first equation: (51 - 3b)/6 + 4b = X Simplifying this equation: 51 - 3b + 24b = 6X 51 + 21b = 6X We also know that a + b = 12, so we can substitute the value of a from this equation into the second equation: a = 12 - b Substituting this expression into the second equation: 6(12 - b) + 3b = 51 Simplifying this equation: 72 - 6b + 3b = 51 72 - 3b = 51 3b = 21 b = 7 Substituting the value of b into the equation a + b = 12: a + 7 = 12 a = 5 Now, we can substitute the values of a and b into the equation 51 + 21b = 6X: 51 + 21(7) = 6X 51 + 147 = 6X 198 = 6X X = 33 The value of x is 33. The answer is: 33

answer:We can square the equation x + frac{1}{x} = 6 to get x^2 + 2 + frac{1}{x^2} = 36. Subtracting 2 from both sides gives x^2 + frac{1}{x^2} = boxed{34}.The answer is: 34