# Tutor profile: Karina P.

## Questions

### Subject: Pre-Calculus

What are the x intercepts for the equation: x^2 + x - 6 = 0?

Since the first x only has the SECOND power, we know our next expression is going to look something along the lines of this: (x + a) * (x +b) - only TWO x's Because (x + a) is being multiplied by (x + b), the first x is going to be multiplied by the second x AND by the b. Same goes with the a. It's going to be multiplied by the second x and the b. Think of it like this, the easiest way to multiply is to take the first value from the first set of parathesis and multiple it over to the other two values. Then we repeat with the second value from the first set of parathesis and multiple it over to the other two values. Since we know that a * b = -6. We're going to list out possible factors that make -6. The only two options are either -2 and 3 or 2 and -3 Let's pick one option and see if we can match up our original equation. Again, the easiest way to multiply is to take the first value from the first set of parathesis and multiple it over to the other two values. (x + 2) * (x - 3) x * x = x^2. x * -3 = -3x Now we're gonna do the second value. 2 * x = 2x 2 * 3 = 6 Now we add up all our answers. x^2 -3x + 2x + 6 Since -3x and 2x are the only like-terms we can add them (like terms mean you have the same number of variables being multiplied by the constant. For this example, we couldn't add the 6 to -3x because there's one x being multiplied by the 3 and no x's being multiplied to the 6). Now our answer is x^2 - x + 6 Unlike our original equation, our x is being subtracted not added. Since it's not the same as our original equation, let's try the second option, repeating the same steps. (x - 2) * (x + 3) FIRST VALUE x*x = x^2 x*3 = 3x SECOND VALUE -2 * x = -2x -2 * 3 = -6 Now add: x^2 + 3x - 2x - 6 x^2 + x - 6 Since that matches our original equation, we know that (x - 2) * (x + 3) is the right expression. Now, anything times 0 is 0. Since (x -2) is being multiplied by (x + 3), we need to find the number that makes x + 3 equal to zero. Which is -3. We also need to know what makes x - 2 equal to 0. Which is 2? So our two intercepts are 2 and -3.

### Subject: English

Correct the following sentence: To get ready for to move into my new apartment I bought a screwdriver, nails, and a hammer from the hardware store, a lamp, rug, and clock from Ikea, and flour, sugar, and honey from the grocery store.

Correct solution: To get ready to move into my new apartment, I bought a screwdriver, nails, and a hammer from the hardware store; a lamp, rug, and clock from Ikea; and flour, sugar, and honey from the grocery store. Let's move through the sentence to explain these corrections. Whenever we start a sentence with a preposition such as to, before, since, it creates a prepositional phrase. The example here is "To get ready to move into my new apartment." We must end prepositional phrases with a comma if it's at the beginning of a sentence. The cool thing about prepositional phrases is that we can "cut" and "paste" them to the end of our sentence and the sentence will still make sense. If we wanted to "cut" our phrase "to get ready to move into my new apartment" and "paste" it at the end we would simply put a comma at the end like this: I bought a screwdriver, nails, and a hammer from the hardware store; a lamp, rug, and clock from Ikea; and flour, sugar, and honey from the grocery store to get ready to move into my new apartment. The reason we're able to move prepositional phrases around is that they are "extra" info. While it may add clarifying details to the reader, the sentence can still make sense without the prepositional phrase. For example: I bought a screwdriver, nails, and a hammer from the hardware store; a lamp, rug, and clock from Ikea; and flour, sugar, and honey from the grocery store. Let's move on to our next issue. When there's a list inside of a list, we must use semicolons. Normal lists we always put a comma after each item. Semicolons are the punctuation mark for the completion of a thought. In the example above "I bought a screwdriver, nails, and a hammer from the hardware store" since we're done talking about the hardware store, we can put a semicolon after hardware store. Finally, we must always capitalize proper nouns like "I" and "Ikea."

### Subject: Algebra

Find the distance between (-2,4) and (6,8).

If we're allowed to have a graph, I recommend drawing our coordinate points. Then draw a straight line connecting those points. The label that line C. Then with that line creates a triangle. Your picture should look similar, but not exactly like the picture in this link: http://www.bbc.co.uk/staticarchive/35c5cfc8617443f14ae861de121690c14b44dc0e.gif Label the line parallel to the Y Axis: A and the line parallel to the X Axis: B. This will help us create a visual later on. First we must label our coordinate points. If we choose (-2,4) to be (x1, y1) and (6,8) to be (x2, y2), we then can subtract our x coordinates and y coordinates together. Our labels should look something like this ( -2 {x1}, 4 {y1} ) ; ( 6 {x2}, 8{y2} ). We always subtract Y2 by Y1 aka (Y2 - Y1) and X2 by X1 aka (X2- X1). Let's start with the x coordinates. In this case, (6 - -2) = 8. Whenever we subtract a negative, it becomes positive, therefore the distance between the X coordinates (or our B line) is 8. Now let's do the Y coordinates. (8 - 4) = 4, so the distance for the y coordinates (or our A-line) is 4. Now we can use Pythagorean Theorem. Since we know the distance for the x coordinates is 8 and the y coordinates are 4, we now can square both the 4 and the 8 then add them together. We are basically plugging our numbers into this formula: a^2 + b^2 = c^2. 4^2 = 16 and 8^2 is 64. 64 + 16 = 80. If we want to find C than we must take the square root of 80, which is 8.94. We can make an educated guess that this is accurate because C will always be bigger than A and B.

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