# Tutor profile: Rachel L.

## Questions

### Subject: Writing

When writing an analytical paper, what is the most important part?

The most important part of an analytical paper is the thesis. The thesis is the glue that holds the entire paper together. It sets the stage for the paper's ultimate conclusion to be drawn and ensures that the writer stays on track and does not stray from the main point.

### Subject: Pre-Algebra

Simplify the following expression: 3(2+4)-3x5+7-2x5

3(2+4)-3x5+7-2x5 To simplify this expression you must follow the order of operations. Recall the acronym PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. 3(6)-3x5+7-2x5 So first we simplify inside the parentheses (2+4)=6. 3(6)-15+7-10 Then we do the multiplications: 3(6)=18, -3x5=-15, -2x5=-10. 18-15+7-10 Now we add and subtract as we move from left to right for the remaining simplifications. 3+7-10 10-10 =0 Thus we conclude that the original expression is equivalent to zero.

### Subject: Algebra

Find the roots of the following parabolic equation: 2x^2+11x+12=0

2x^2+11x+12=0 2x^2+3x+8x+12=0 Separate the middle term (11x) into two terms whose sum is 11x. (2x^2+3x)+(8x+12)=0 x(2x+3)+4(2x+3)=0 Group the first term (2x^2) with either middle term (3x or 8x) and the last term (12) with the remaining middle term (3x or 8x) so that the groupings will allow a greatest common factor to be factored out of each. (x+4)(2x+3)=0 Now factor out the common factor from each group, that is the quantity (2x+3). This leaves the following two factors: (x+4) and (2x+3). x+4=0 2x+3=0 Now apply the Zero Product Property to set each factor equal to zero to find the values of the roots. x=-4 and x=-3/2 By solving for x you find that the roots are -4 and -3/2.

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