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Grant T.

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Geometry

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Question:

What's the interior angle of a regular pentagon?

Grant T.

Answer:

108 degrees. Take a point in the center of the pentagon and draw lines to the vertices. You have drawn five identical lines. You also have five identical isosceles triangles. The sum of the angles of the triangles at the center of the pentagon must equal 360 degrees, a full circle. But you have 5 angles, so 360/5= 72. Now each triangle has to equivalent angles and one 72 degree angle. If a triangle's angles add to 180, the two equivalent angles are (180-72)/2=54, but the interior angle of a pentagon is two of these angles. So take away the divide by two and get 180-(360/n), where n=5, number of side of polygon. 180-(360/5)=108

Biology

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Question:

What is the Central Dogma?

Grant T.

Answer:

The Central Dogma is foundational to biology. To summarize, it's DNA to RNA to proteins. The genetic code, DNA, is transcribed on a messenger RNA, like writing down (transcription) a recipe from the cookbook (DNA) onto a little sticky-note (mRNA) that you can carry around with you, which has instructions for just the cake (protein) you want. Then you can go to the kitchen (ribosome) and bake (translation) your cake. This is the transformation from code to functional units of protein.

Algebra

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Question:

factor x^2+x-6

Grant T.

Answer:

(x+3)(x-2) Factoring is just another way of writing the same thing: (x+3)(x-2)=x^2+x-6 The two numbers in the factors must multiply to the third term, -6. So that could be 1 and -6, -1 and 6, 2 and -3, or -2 and 3. Now look at the second term, +x. There's a hidden 1 there. So which of the four pairs of numbers add to 1? -2 and 3, so pick those numbers for your factors: (x+3)(x-2)

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