# Tutor profile: Van M.

## Questions

### Subject: Geometry

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

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

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

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

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

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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