1. a farmer is enclosing a rectangular area for a pigpen. he wants the length of the pen to be 15 feet longer than the width. the farmer can only afford no more than 150 feet of fencing. what is the pen's greatest possible length?

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.

The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −5 0 −1 1 3 g(x) g(x) = 2x − 7 part a: write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) part b: which function has a greater y-intercept? justify your answer. (4 points)

Which of the following multiplication expressions can be modeled by the tiles shown? check all that apply. 8(3) = 24 6(4) = 24 (3)(12) = 36 24(3) = 72 3(8) = 24 2(12) = 24