If ABCD is a rhombus AD=4x+2 DC=7x-13 and BD=34 find AE (E is in the middle)

What is the equation of the line in point-slope form? y+ 4 = 1/2(x+4) y-4 = 1/2(x + 4) y-0 = 2(x - 4) y-4 = 2(8-0)

Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .

Create a graph for the demand for starfish using the following data table: quantity/price of starfish quantity (x axis) of starfish in dozens price (y axis) of starfish per dozen 0 8 2 6 3 5 5 2 7 1 9 0 is the relationship between the price of starfish and the quantity demanded inverse or direct? why? how many dozens of starfish are demanded at a price of five? calculate the slope of the line between the prices of 6 (quantity of 2) and 1 (quantity of 7) per dozen. describe the line when there is a direct relationship between price and quantity.