answer:Let n be the number of sides of the polygon. The number of diagonals of a polygon with n sides is given by the formula frac{n(n-3)}{2}. So, we have the equation n - frac{n(n-3)}{2} = 0. Simplifying, we get n = frac{n(n-3)}{2}. Multiplying both sides by 2, we have 2n = n(n-3). Expanding, we get 2n = n^2 - 3n. Rearranging, we have n^2 - 5n = 0. Factoring, we get n(n-5) = 0. So, either n = 0 or n - 5 = 0. Since the number of sides of a polygon cannot be 0, we have n = boxed{5}. The answer is: 5

answer:Punger purchases 60 packs of baseball cards, with each pack containing 7 cards, so he has a total of 60 x 7 = 420 cards. He wants to store these cards in special pages that can hold 10 cards each, so he needs 420 / 10 = 42 pages. Therefore, Punger needs to buy 42 pages to store all the cards. 42 The answer is: 42

answer:Phoebe eats 1 serving of peanut butter and gives her dog 1 serving, so together they need 1 + 1 = 2 servings per day. If they need 2 servings per day, then they will need 2 x 30 = 60 servings for 30 days. Since each jar contains 15 servings, Phoebe will need 60 / 15 = 4 jars of peanut butter. 4 The answer is: 4

answer:James pays the minor characters 15,000 each episode, so the total amount he pays them is 4 * 15,000 = 60,000. He pays the major characters x times as much as the minor characters, so he pays each major character 15,000 * x. There are 5 main characters, so the total amount he pays the main characters is 5 * (15,000 * x) = 75,000x. The total amount he pays per episode is the sum of the amount he pays the minor characters and the amount he pays the major characters: 60,000 + 75,000x. We are given that the total amount he pays per episode is 285,000, so we can write: 60,000 + 75,000x = 285,000. Simplifying the left side, we get: 75,000x + 60,000 = 285,000. Subtracting 60,000 from both sides, we get: 75,000x = 225,000. Dividing both sides by 75,000, we get: x = 3. The value of x is 3. 3 The answer is: 3