Apolynomial divided by a polynomial is a polynomial. always, sometimes, or never true?

Five more than the product of a number n and 8 is at least 100. write an inequality that can be used to find all positive values of n

Two positive integers are 3 units apart on a number line. their product is 108. which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108

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.