# Tutor profile: Kelsey K.

## Questions

### Subject: Geometry

Given a right triangle with one side length being 6in and the hypotenuse of the triangle being 10in, what would be the length of the other side?

When solving to find the missing side of a right triangle we can use the Pythagorean Theorem, which states that a^2 + b^2 = c^2. This means that the one side length squared plus the other side length squared should equal the length of the hypotenuse squared. So in this case, we would plug in what we have and solve from there. We would have 6^2 + x^2 = 10^2. X in this case is standing for our missing side length. 6^2= 36 and 10^2 = 100. Therefore, we would have 36 + x^2 = 100. Then to solve for X we would subtract 36 from both sides, which would give us x ^2 = 64. The last step would be to square root both sides, which would give us x =8. We could then check our answer by plugging 8 in for x. We would get 6^2 + 8^2 = 10^2, which becomes 36 +64 =100, which becomes 100=100, which is a true statement.

### Subject: Basic Math

Which of the following is closest to 27.8 × 9.6? A. 280 B. 300 C. 2,800 D. 3,000

For this type of question, we would use logic. The first thing we can do is round 27.8 to 28. Anytime we have a number between 5-9 in the tenths place, we can round the number up, if asked or if it pertains to the question. We can also round 9.6 up to 10, following the same rule. Then knowing our times tables 28 x 10 would give us 280. Therefore, the answer would be A.

### Subject: Algebra

Solve the equation 5(- 3x - 2) - (x - 3) = -4(4x + 5) + 13

To solve this equation we want to solve for x, meaning that we want to get x by itself. The first thing we want to do is distribute where we see parentheses. For example, we would distribute the 5 to (-3x-2). When we do that we would do 5 times -3x which would give us -15x. When we distribute the 5 to the -2, we would get -10. So we would have -15x-10. We would do the same thing with distributing the negative sign to (x-3) and the -4 to (4x+5). Once we are done distributing, we would combine like terms, meaning combining just the numbers and in the other case combining all of the terms that have an x. From here we would the solve for x. When we do this, we end up getting 0=0, which means that any value of x would make this equation true.

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