1. The side of the triangle is represented by the expression 2x + 4x - 2x, which simplifies to 4x. Since the perimeter is 10 cm, we have 3 * 4x = 10, so 12x = 10, and x = 10/12 = 5/6. Therefore, the length of each side is 4 * (5/6) = 20/6 = 10/3 cm.
2. The total number of goals scored in the first two games is 20 + 30 = 50. Let G be the number of goals scored in the third game. The average for all three games is (50 + G)/3 = 25. Solving for G: 50 + G = 75, so G = 25.
3. The area of a triangle is given by (1/2) * base * height. Here, the base is 2x - 4 and the height is 3x + 6. So the area is (1/2)(2x - 4)(3x + 6). Factoring: (1/2) * 2(x - 2) * 3(x + 2) = 3(x - 2)(x + 2) = 3(x² - 4) = 3x² - 12.
4. After 15 seconds, Andy has run 15 * 2 = 30 meters. Since he started 50 meters behind, he still has 50 - 30 = 20 meters to catch up. At a relative speed of 2 m/s, it will take him 20 / 2 = 10 more seconds. Total time from start: 15 + 10 = 25 seconds.
5. The cost of one cheap card is $2, so for 10 cards, the cost is 10 * 2 = $20. The cost of one expensive card is $3, so for 5 cards, the cost is 5 * 3 = $15. Total cost: 20 + 15 = $35.
6. The side of the square is represented by 2x + 4x - 6x, which simplifies to 0. This is impossible for a physical square, indicating an error in the problem setup or interpretation. Assuming the expression is meant to represent a non-zero length, there may be a typo. However, based on the given expression, the side length is 0, making the area 0.
7. The initial distance between them is 10 meters. They are moving toward each other at a combined speed of 5 + 5 = 10 m/s. Time to meet: 10 meters / 10 m/s = 1 second. In that time, each has traveled 5 * 1 = 5 meters. Since they started 10 meters apart and each moved 5 meters, they meet exactly halfway, 5 meters from each starting point.
Parent Tip: Review the logic above to help your child master the concept of factoring polynomials word problems worksheet.
