Create a quadratic equation for the given problem and then solve the equation with a related function using a graphing calculator. If necessary, round your answer to the nearest hundredth.

A bird is in a tree 42 feet off the ground and drops a twig that lands on a rosebush 38 feet below. The function h(t) = −16t2 + 42, where t represents the time in seconds, h gives the height, in feet, of the twig above the ground as it falls. When will the twig land on the bush?

The twig will hit the rosebush after about
second(s).

Pete is making decorations for a dinner party. the instructions tell him to use 9 flowers for a medium-sized decoration. complete each statement to adjust the flowers for different-sized decorations based on these instructions.

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Even if a person is in very good shape, applying to be a police officer requires commitment to fitness. applicants must pass a physical fitness test. in order to prepare for the test, janet purchases an activity tracker to court her steps. her goal is to walk 10,000 steps each day. she measures heard average step length to be 30 inches. play janet runs, her average steps length increases to 36 in. how many steps would she have to take to run 1 mile 50280 round to the nearest step