Mike is having a birthday party. He is having 7 friends over and they will all share his birthday cake. and eat the same amount. However, 1/2 of the cake was accidentally ruined by Mike's dog. What fraction of the whole cake will each of the friends INCLUDING mike receive?

The first few steps in solving the quadratic equation 9x2 + 49x = 22 ? 5x by completing the square are shown. 9x2 + 49x = 22 ? 5x 9x2 + 54x = 22 9(x2 + 6x) = 22 which is the best step to do next to solve the equation by completing the square? 9(x2 + 6x + 3) = 25 9(x2 + 6x + 3) = 49 9(x2 + 6x + 9) = 31 9(x2 + 6x + 9) = 103

The position of a moving particle is given by the position function: f(t)=-9t-t^2-0.2t^3+0.1t^4 0 a. at what time does the particle reverse direction? b. when is the displacement positive? (round one decimal place and answer in interval notation) c. when is the displacement negative? (round one decimal place and answer in interval notation) d. when is the particle’s acceleration positive? (round one decimal place and answer in interval notation) e. when is the particle’s acceleration negative? (round one decimal place and answer in interval notation)

The map shows the location of the airport and a warehouse in a city. though not displayed on the map, there is also a factory 112 miles due north of the warehouse. a truck traveled from the warehouse to the airport and then to the factory. what is the total number of miles the truck traveled?