# Tutor profile: Jake R.

## Questions

### Subject: Pre-Calculus

Evaluate the limit of 3x/(x^2) as x goes to infinity.

This expression could be factored into x/x * 3/x. x/x could be simplified to 1, which goes away and leaves the expression at 3/x. Because there is just a constant in the numerator and there is a variable x in the denominator, the denominator will keep getting larger as x goes towards infinity. Whenever the denominor gets larger and larger but the numerator stays the same, the limit of that expression will go to 0.

### Subject: Statistics

Mr. Jackson is missing 1 test score out of the 5 from his class. The test scores he has are 82, 85, 90, and 98 percent. He remembers that the mean score in his class was a 91 percent. What is score of the missing test?

Knowing that the mean score can be found by adding together all the test scores and then dividing by the number of test scores, you can set up one equation. In this equation, let m = the missing score. You will divide all the test scores by the number of tests, which here will be 5. The quotient of this should equal the mean of 91. The equation would read as such: (82 + 85 + 90 + 98 + X)/5 = 91 After working out the algebra, you get that X = 100. So this missing test score was a 100 percent.

### Subject: Algebra

Simplify the following expression by combining like terms: 2x + 4x^2 - 6x^2 - 9 + 1 - 3x - x

I like to first start by identifying which terms in the expression are considered "like terms". "Like terms" means that the terms variables AND their exponents are the same. In this expression, we can see that there will eventually be only 3 terms in the simplified expression because there are 3 types of terms: the x^2 terms, the x terms, and the constants (with no variable). Next, before moving any terms around. I like to make all the subtracted terms into the addition of their negative. So the above expression would turn into this: 2x + 4x^2 + -6x^2 + -9 + 1 + -3x + -x Then I like to group the terms together by just moving them around. I would rewrite this expressions as (4x^2 + -6x^2) + (2x + -3x + -x) + (-9 + 1) Finally, we can simplify within the parentheses by doing addition, leaving us with an expression with only 3 terms that looks like this: (-2x^2) + (-2x) + (-8) OR -2x^2 - 2x - 8

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