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# Tutor profile: Andrew K.

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Andrew K.
Math and Latin Tutor for Seventeen Years
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## Questions

### Subject:Latin

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Question:

Translate the following Latin sentence into English: Fortuna animum magnum amat.

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Andrew K.

### Subject:Geometry

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Question:

You are presented with a right triangle. One of the shorter sides (the "legs") has a length of 3, The other shorter side has an unknown length. The longest side (the "hypotenuse") has a length of 5. Find the length of the unknown side.

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Andrew K.

1) We assign the variable "x" to the unknown shorter side. 2) Because this is a right triangle, we can use the formula a2 + b2 = c2 to find the unknown side length. In this formula, "a" and "b" are the shorter sides ("legs") and "c" is the longest side ("hypotenuse"). As stated before, one leg has a value of "3", the other leg is unknown and so we are assigning it a value of "x", and the hypotenuse has a value of "5". a = 3 b = x c = 5 3) We then plug the three values into the a2 + b2 = c2 equation: a2 + b2 = c2 a = 3 b = x c = 5 (3)2 + x2 = (5)2 4) Next, solve the terms without variables: (3)2 = 9 (5)2 - 25 9 + x2 = 25 5) We now just need to use basic algebra to solve for "x". We isolate "x2" by subtracting "9" from both sides of the equals sign. 9 + x2 = 25 -9 -9 x2 = 16 6) Then isolate "x" by taking the square root of the square, which cancels both. As always, you have to do the same thing to both sides of the equals sign, so you also take the square root of "16". square root of (x2) = square root of (16) x = 4 7) Since x = 4 and b = x, the "b" side of the triangle (the unknown shorter side) has a length of "4". Answer: b = 4

### Subject:Algebra

TutorMe
Question:

How does one solve for "x" in the equation "x2 - 4x = 21"?

Inactive
Andrew K.

1) You need to start by looking at the individual terms in the equation, which are the pieces of the equation that are added and subtracted. The terms in this equation are "x2", "-4x", and "21". Since one of the terms contains an "x2" and another contains an "x", you know that this is a quadratic equation. x2 - 4x = 21 2) Since this is a quadratic equation, you next need to put all terms on the left side of the equals sign. The one term on the right side of the equals sign is "21". You can move this term to the left side of the equals sign by subtracting 21 from both sides of the equation. x2 - 4x (-21) = 21 (-21) 3) On the left side of the equals sign the "-21" is just written as it is as a third term. On the right side of the equals sign, 21 - 21 = 0, and so you write "0" there. x2 - 4x - 21 = 0 4) Since you now have an x2 term, an x term, and a plain numher term on the left side of the rquals sign, you now have what is called a trinomial on that side, and you next need to factor the trinomial (which has three terms) into two binomials (which have two terms). To do this, put two sets of parentheses under the quadratic equation: x2 - 4x -21 = 0 ( ) ( ) = 0 5) You then break the first term (x2) into two x's, and place them on the left-hand sides of the two sets of parentheses: x2 - 4x -21 = 0 (x ) (x ) = 0 6) You then go to the third term (21) and break it up into all possible factors (all pairs of numbers that, when multiplied, will get 21 as an answer. 1 x 21 = 21 3 x 7 = 21 7) You next figure out which of the factor pairs create the number in the middle term (-4x) by some combination of addition or subtraction: 3 - 7 = -4 8) You then take those two numbers that added up to -4 and place them on the right-hand sides of the sets of parentheses: x2 - 4x -21 = 0 (x ) (x ) = 0 3 - 7 (x + 3) (x - 7) = 0 9) Next, take each of the binomials in the sets of parentheses, and make them equal to 0: x + 3 = 0 x - 7 = 0 10) Last, solve for "x" for each new equation. The two values for "x" are the answers. x + 3 = 0 -3 -3 x = -3 x - 7 = 0 +7 +7 x = 7 Answer: x = -3, x = 7

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