The figure below shows the first 3 steps in the construction of a Sierpinski Triangle. 1 equilateral 3 congruent 9 congruent
triangle
equilateral equilateral
triangles
triangles
Which property explains why each of the 9 small triangles in step 3 is similar to the large triangle in step 1?
A. The side-side property of congruent triangles can be used because all the sides of an equilateral triangle are similar.
B. The side-side property of similar triangles can be used because all the sides of an equilateral triangle are congruent.
C. The angle-angle property of congruent triangles can be used because all the angles of an equilateral triangle are similar.
D. The angle-angle property of similar triangles can be used because all the angles of an equilateral triangle are congruent.
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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?