A curious patterns occurs in a group of people who all shake hands with one another. It turns out that you can predict the number of handshakes that will occur if you know the number of people. If we are in a room of 5 people, we can determine the number of handshakes by this line of reasoning: The first person will shake 4 hands (she won’t shake her own). The second person will shake 3 hands (he won’t shake his own of the hand of the first person, they already shook). The third person will shake 2 hands (same reasoning). The fourth person will shake 1 hand (that of the fifth person). The fifth person will shake 0 hands. So there will be a total of 1+2+3+4=10 handshakes

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.

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Lance lived in portugal and brazil for a total of 14 months to learn portuguese. he learned an average of 130 new words per month when he lived in portugal, and an average of 150 new words per month when he lived in brazil. in total he learned 1920 new words. write a system of equations to represent the situation. use x to represent portugal, and y to represent brazil