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Tutor profile: Jessica S.

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Jessica S.
Johns Hopkins University Undergraduate
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Questions

Subject: Pre-Algebra

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Question:

3x + 12 = 23. Solve for x.

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Jessica S.
Answer:

The key thing to keep in mind is to make sure the left hand (LH) and right hand (RH) side of the equations remain equal. When solving for a variable, you have to isolate the variable to one side of the equation. So first, subtract 12 from both sides of the equation. This will give you 3x = 23 - 12 which is equal to 3x = 11. Then, to get x by itself, divide both sides of the equation by 3. So you end up with x=11/3 as the final answer.

Subject: ACT

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Question:

The length, in inches, of a box is 2.5 inches less than twice its width, in inches. Which of the following gives the length, L inches, in terms of the width, W inches, of the box?

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Jessica S.
Answer:

This is a typical ACT question that asks you to convert a words problem into a math equation. "The length is 2.5 inches less than twice its width" is the same as "L is 2.5 inches less than 2*W". Since "less" indicates subtraction, this can then be written as "L is 2*W - 2.5". Therefore, the final answer is L = 2W - 2.5

Subject: Algebra

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Question:

Find k so that the lines with equations -4x + k*y = 10 and 4y + x = -9 are perpendicular.

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Jessica S.
Answer:

First, find the slope of the second equation listed. Subtracting x from both sides will result in: 4y = -x - 9. Then divide both sides by 4 will give you: y = (-1/4) * x - (9/4), which is in y=mx+b form. Thus, the slope is m = -1/4. Doing the same for the first equation listed will give you a slope of m = 4/k. Since the two lines must be perpendicular, the slope of the first equation must be the negative reciprocal of the other, meaning: 4/k=4. Thus, k=1.

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