The value of a new car depreciates a rate of 20% each. What is the multiplier when writing an exponential equation that models the value of the car?

Follow these steps using the algebra tiles to solve the equation −5x + (−2) = −2x + 4. 1. add 5 positive x-tiles to both sides and create zero pairs. 2. add 4 negative unit tiles to both sides and create zero pairs. 3. divide the unit tiles evenly among the x-tiles. x =

Asquare has a side that measures 11 units. what is the area of a circle with a circumference that equals the perimeter of the square? use 3.14 for π, and round your answer to the nearest hundredth. 1519.76 units2 379.94 units2 616.56 units2 154.14 units2

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) = .