What are the measures of Angles a, b, and c? Show your work and explain your answers. (10 points)

Mathematics

1 answer:

Rus_ich [418]3 years ago

7 0

Answer:

The measure of angle a is 35 degrees, b is 55 degrees and c is 110 degrees.

∡a has an angle of 40°. Vertical angles are always congruent.

∡b is the 3rd angle in a triangle, the other two are 40° and 90° all of the interior angles in a triangle add up to 180°.

∡c is a linear angle, linear angles always add up to 180°.

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At 1pm, the number of bacteria in the dish is 1,000,000

At 12pm, the number of bacteria in the dish is 500,000

Step-by-step explanation:

Given the information on the table

$\left|\begin{array}{c|c}$Hour&$Number of Bacteria (in millions)\\---&--------------\\12 p.m.&\\1 p.m.&\\12 p.m.&\\2 p.m.&\\3 p.m.&\\4 p.m.&\\5 p.m.&32\\6 p.m.&64\end{array}\right|$

We are to follow the pattern to determine how many million bacteria were in the dish at 1 p.m. and 12 p.m.

Now:

$32=2^5\\64=2^6$

It therefore means that the bacteria population doubles every hour. Following this pattern and reducing the exponents by 1 backwards, we have:

$\left|\begin{array}{c|c}$Hour&$Number of Bacteria (in millions)\\---&--------------\\12 p.m.&2^{-1}=0.5\\1 p.m.&2^0=1\\12 p.m.&2^1=2\\2 p.m.&2^2=4\\3 p.m.&2^3=8\\4 p.m.&2^4=16\\5 p.m.&2^5=32\\6 p.m.&2^6=64\end{array}\right|$