Mathematics
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An antibiotic kills 60% of bacteria in a sample of 100,000 each day. the equation

An antibiotic kills 60% of bacteria in a sample of 100,000 each day. the equation represents the population, p1, after d days. four days after introducing the antibiotic to the first sample, a scientist introduces the same antibiotic to a second population, p2. the number of bacteria after d days in the second population is represented by the equation . which equation is equivalent to p2?
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dbailey6190
dbailey6190
4,4(14 marks)

\triangle ABC\sim \triangle DEC\\ \\\angle B\cong \angle E\\ \\3BC=2EC

Step-by-step explanation:

Right triangle ABC is reflected over AC to form triangle AFC.

Triangle AFC dilated by a scale factor of two-thirds to form triangle DEC.

Reflection is a rigid transformation which preserves lengths and angles, then

\triangle ABC\cong \triangle AFC

Dilation is a transformation which maps the triangle into similar triangle, so

\triangle AFC \sim \triangle DEC

Thus,

\triangle ABC \sim \triangle DEC

Similar triangle have congruent corresponding angles, so

\angle B\cong \angle E

and proportional corresponding sides

\dfrac{BC}{EC}=\dfrac{AB}{DE}=\dfrac{2}{3}\Rightarrow \\ \\3BC=2EC\\ \\3AB=2DE

Thus, correct options are:

\triangle ABC\sim \triangle DEC\\ \\\angle B\cong \angle E\\ \\3BC=2EC


Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triang

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