Courtney is twice as old as andre and three years older than natalie. courtney is half shari’s age. the difference between shari’s age and natalie’s age is the same as the sum of courtney’s age and adre’s age. the equation below represents the ages. 2x-(x-3)=x+x/2 in the equation, the variable x represents: • courtney’s age • andre’s age • natalie’s age • shari’s age

Aline is perpendicular to another line m2= (-1/m1), where m1 is the slope of the original line and m2 is the slope of the perpendicular line. which of the following equations represents the line that passes through the point (-2,1) and is perpendicular to the line below?

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?

Michele wanted to measure the height of her school’s flagpole. she placed a mirror on the ground 48 feet from a flagpole, then walked backwards until she was able to see the top of the pole in the mirror. her eyes were 5 feet above the ground and she was 12 feet from the mirror. using similar triangles, find the height of the flagpole to the nearest hundredth of a foot.