Determine the average rate of change for the following questions. Show your work.

1. It takes a rocket 30 seconds to travel 1 mile above the earth’s surface and 1 1/2 minutes to travel 6 miles. What is the rate of change per second for the entire trip?

2. What is the rate of change for the same rocket to complete its trip after the first mile?

3. Graph both answers; show the rate of change for the first mile and the rate of change after the first mile. (y = 2 1/2 units equal one mile, x = one unit equals 10 seconds)

Which graph corresponds to the function f(x) = x2 + 4x – 1?

Carmen begins her next painting on a rectangular canvas that is 82.7 cm long and has a area of 8,137.68 cm2. will the painting fit in a frame with an opening that is 82.7 cm long and 95 cm wide? explain

Someone answer this asap rn for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =