Lena does a weekly exercise program consisting of cardiovascular work and welght training. Each week, she exercises for at least 10 hours. She spends at most 12 hours on weight training. She spends at most 4 hours doing cardiovascular work. Let x denote the time in hours) that Lena spends doing cardiovascular
work. Let y denote the time (in hours) that she spends on weight training. Shade the region corresponding to all values of x and y that satisfy these
requirements.

What is the solution to the equation 9^(x+1) =27

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.

Determine whether the quadrilateral below is a parallelogram. justify/explain your answer (this means back it up! give specific information that supports your decision. writing just "yes" or "no" will result in no credit.)