Pam likes to practice dancing while preparing for a math tournament. She spends 80 minutes every day practicing dance and math. To help her concentrate better, she dances for 20 minutes longer than she works on math. Part A: Write a pair of linear equations to show the relationship between the number of minutes Pam practices math every day (x) and the number of minutes she dances every day (y). (5 points) Part B: How much time does Pam spend practicing math every day? Show your work. (3 points) Part C: Is it possible for Pam to have spent 60 minutes practicing dance if she practices for a total of exactly 80 minutes and dances for 20 minutes longer than she works on her math? Explain your reasoning. (2 points)

Precalculus question, image attached.

Acircus act has 3 times as many elephants as acrobats. jorge noticed that all together there were 56 legs in the circus ring. how many elephants were in the show?

The biologist has a second culture to examine. she knows that the population of the culture doubles every 15 minutes. after 1 hour and 15 minutes, her assistant found that 80,000 bacteria were present. a) what was the size of the initial population? b) predict the size of the culture at t=3 hours. what was the size of the population at 40 minutes? explain and justify your answers. c) create a graph of the population as a function of time. find an equation that can be used to predict the size of the population at any time t. d) examine the rate at which the bacteria culture is growing. how fast is the culture growing after 1 hour? after 1.5 hours? after 2 hours? use a time interval of h = 0.01 hours to estimate these rates. interpret these rates in terms of the context of the problem situation. how do these three rates compare?