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# Tutor profile: Van M.

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Van M.
Math Tutor, 8+ years experience. Specializing in Algebra, Geometry, Precalculus
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## Questions

### Subject:Geometry

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Question:

A right triangle has a side measuring 7in and another of side measuring 24in. What is the length of the hypotenuse of the triangle?

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Van M.

In order to solve the problem, we will need to use the Pythagorean theorem. This theorem states that for any right triangle, a² + b² = c² (where c is length of the hypotenuse and a and b of the lengths of the other two sides). So if we use this formula solve for c, we will know the length of the hypotenuse. Let's use 7 for a, and 24 for b. Substituting the values in yields the equality (7)² + (24)² = c². which simplifies to 49 + 576 = c² which simplifies to 625 = c². In order to get c, we have take the square root of both sides. The square root of 625 is 25 so c = 25. Therefore the hypotenuse of the triangle is 25 inches.

### Subject:Pre-Algebra

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Question:

Solve for "i" in the following inequality: 9x + 6x - 7i > 3(5x-7u)

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Van M.

First, combined like terms on the left side of the > symbol. (9x+6x = 15x) So our new equation so far is 15x -7i > 3(5x-7u). Then, on the right side of the > symbol, we would distribute the 3 to both terms inside the parentheses. Thus we would have 15x - 21u on the right side of the inequality. Our equation currently is 15x - 7i > 15x-21u Now we would subtract 15x from both sides of the inequality. Our new equation is -7i > -21u. We're almost there! Our last step to get "i" by itself would be to divide both sides by -7. (Don't forget to flip the inequality symbol around when dividing by a negative number) Thus, our final equation is i < 3u.

### Subject:Algebra

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Question:

Factor the following expression: (16x^4 - 81)

Inactive
Van M.

Step 1: Use the difference of squares formula: reminder: the formula is a²-b² = (a+b)(a-b) in this case, a = 4x² (because the square root of 16x^4 is 4x²) and b = 9 (because the square root of 81 is 9). Therefore we can write; (4x² - 9)(4x² + 9) Step 2: Notice that 4x²-9 is still a difference of perfect squares. Apply the difference of squares formula again for this one. This time, a = 2x and b = 3 So it factors into (2x - 3)(2x + 3) Thus, your entire factored expression is (2x² - 3)(2x² + 3)(4x² + 9)

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