For which values of n will any set of 7 consecutive integers, each raised to the power of n and added together, give a total which divides by 7? (without using programming and explained very easy, enough for someone in year 7 to understand pls)

The length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

Write as a product of two polynomials. 2(3–b)+5(b–3)^2

Need to finish my juan wants to build a greenhouse in his back yard. he needs to maximize the ratio of floor area to structure volume in order to provide the most room for plants while minimizing the area to be heated. find the description of the structure that best meets juan’s criteria. a.) a hemisphere with a diameter of 12 feet b.) a cube with a side length of 12 feet c.) a cone with a diameter of 12 feet and a height of 10 feet d.) a square pyramid with a base side length of 12 feet and a height of 9 feet