Find, if it exists, a value c in the interval [1, 4] such that the instantaneous rate of change of f(x) = 12 x at c is the same as the average rate of change of f over the interval [1, 4]. (If an answer does not exist, enter DNE.)

Rewrite the following quadratic functions in intercept or factored form. show your work. y = x^2 + 7x + 10

George is putting trim around his rectangular deck, including the gate. he will need 44 feet of trim to do the entire deck. if the deck is 13 feet long, how wide is the deck?

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?