Find an equation of the slant asymptote. do not sketch the curve. y = 5x4 + x2 + x x3 − x2 + 5

Consider the triangle. which shows the order of the angles from smallest to largest? angle a, angle b, angle c angle b, angle a, angle c angle b, angle c, angle a angle c, angle a, angle b

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?

The image of abc is a'b'c. what transformations would result in this image? abc is reflected over the line x = 1, then is rotated -90° around the origin. abc is reflected over the line y = x - 1, then t: (x, y) → (x - 1, y - 1). abc is rotated 90° around the origin, then is reflected over the y-axis. abc is rotated -90° around the origin, then is reflected over the line y = -1.