# Tutor profile: Jessie B.

## Questions

### Subject: Pre-Algebra

Solve for x: $$ \frac{x}{2}=\frac{5}{6}-\frac{x}{3} $$

First, rewrite the equation so that each fraction has a common denominator. $$ \frac{3x}{6}=\frac{5}{6}-\frac{2x}{6} $$ Next, get every term containing the variable x to one side of the equation. We can do that here by adding $$ \frac{2x}{6} $$ to both sides. $$ \frac{3x}{6}+ \frac{2x}{6}=\frac{5}{6} $$ Next, we'll add the two x terms. $$ \frac{5x}{6}=\frac{5}{6} $$ And finally, we'll multiply both sides by $$ \frac{6}{5} $$ to isolate x. $$ \frac{5x}{6}(\frac{6}{5})=\frac{5}{6}(\frac{6}{5}) $$ $$ x=\frac{5}{6}(\frac{6}{5})=1 $$

### Subject: Biology

Are viruses alive? There is not a correct 'yes or no' answer to this question. It is in fact widely debated among the scientific community. A primary reason for this is that the definition of 'life' is not concrete. Write a short paragraph sharing your opinion as to whether viruses are living or non-living. If you think they are living, explain what characteristic(s) of viruses led you to this conclusion. If you think they are non-living, explain what characteristic(s) viruses lack that you think are essential for life.

Example of a 'yes' answer: Yes, I do think that viruses are living. They contain nucleic acids (DNA or RNA) that encode protein. They can also replicate this genetic material, albeit with the help of host cells, to "reproduce." Viruses also participate in evolution, as through mutation, they can adapt to changing environments over time. Example of a 'no' answer: No, I do not think viruses qualify as living. While they can replicate their genetic material, they cannot do this independently; they require host cell machinery. They are simply DNA or RNA in a protein capsule and lack independent metabolism and replication, both key components of life. Without a host, they exist in a dormant, non-living state, and therefore cannot be classified as living.

### Subject: Algebra

Find the equation of the line that passes through the points (3, 2) and (1, -4).

The equation of a line is $$ y=mx+b $$, where m is the slope and b is the y intercept. First, we find the slope (m) of the line using the slope equation $$ m=(y2-y1)/(x2-x1) $$. So, $$ m=(-4-2)/(1-3)=(-6)/(-2)=3 $$. Now we have $$ y=3x+b $$. To find b, the y intercept, we just need to plug in the coordinates of any point on the line for x and y and then solve for b. We already have two points, given in the question, that we know the line definitely passes through: (3, 2) and (1, -4). You can pick either one, as any point on the line will give you the same value for b. If you want to double check your math, try both. (3, 2): $$ 2=3(3)+b $$. $$ 2=9+b $$. $$ b=2-9=-7 $$ (1, -4): $$ -4=3(1)+b $$. $$ -4=3+b $$. $$ b=-4-3=-7 $$ Now we have $$ m=3 $$ and $$ b=-7 $$, so the equation of the line is $$ y=3x-7 $$

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