# Tutor profile: Madison T.

## Questions

### Subject: Geometry

The length of a rectangle is 3 less than 4 times the width. The perimeter is 34. Find the length and width.

To first start off, lets let x equal the width of the rectangle. We know that the length of the rectangle is 3 less than 4 times the width. 4 times the width can be written as 4x. However, the length is 3 LESS than 4 times the width. This can be written as 4x - 3. Lets use L to represent the length. We just found that L = 4x - 3 where x is the width The definition of the perimeter, is all of the sides of the object added together. Our shape is a rectangle which means that we have two shorter sides which are the width so we have 2x. We also have two longer sides which are the length so we have 2L. Therefore, we can write our perimter as P = 2x + 2L If you look above, we already solved for L so we can plug our value into our P equation. We were also given the value of P which we can plug in as well. We are left with 34 = 2x + 2(4x-3) Now lets solve for x. We need to distribute the 2 through our parenthesis and we get 34 = 2x + 8x - 6 We can combine like terms which leaves us with 40 = 10x x = 4 We stated earlier that x = width, therefore we just found our width value. We can then plug this into our L equation in order to find the length. L = 4(4) - 3 L = 13 Our answer is width = 4 length = 13

### Subject: Chemistry

Balance the following chemical equation Ca(OH)2 +H3PO4 --> Ca3(PO4)2 + H20

The first thing that I alway do when balancing chemical equations is, I write down how many of each element I have initially on each side. This would leave me with LEFT SIDE Ca = 1 O = 6 --> There is a 2 outside the parenthesis of OH which means that there are 2 O and 2 H molecules. If it was written as OH2 with no parenthesis, this would mean there is 1 O and 2 H molecules. Then, you must add the 4 O from H3PO4. H = 5 P = 1 RIGHT SIDE Ca = 3 P = 2 O = 9 --> You have to add the O molecules from (PO4)2 and H2O H = 2 Working from the first element down, we can see that the left side of the equation has 1 Ca while the right side has 3. In order to make them equal, we must put a coefficient of 3 in front of Ca(OH)2. This would leave us with... 3Ca(OH)2 + H3PO4 --> Ca3(PO4)2 + H2O Now, re calculate how many of each element you have on each side. LEFT SIDE Ca = 3 P = 1 O = 10 --> There were initially 2 O molecules in Ca(OH)2, however, since you added a coefficient of 3, you now have 6. Then add the 4 O molecules from H3PO4 H = 9 RIGHT SIDE Ca = 3 P = 2 O = 9 H = 2 Next, we want to make the amount of P on each side equal. We only have 1 P on the left side, while on the right side we have 2. To do this, we must multiply H3PO4 by 2. This leaves us with 3Ca(OH)2 + 2H3PO4 --> Ca3(PO4)2 + H2O LEFT SIDE Ca = 3 P = 2 O = 14 H = 12 RIGHT SIDE Ca = 3 P = 2 O = 9 H = 2 Finally, we need to make the amount of O and H on each side equal. We don't want to put a coefficient in front of Ca3(PO4)2 because that would mess up the amount of Ca and P elements that we just worked hard to make equal. This means, we must add a coefficient in front of H2O. Currently, we have 14 O on the left side and 9 O on the right side. We also have 12 H on the left side and 2 H on the right side. You can see that if you multiply H2O by 6, this would leave you with 12 H. If you then check the amount of O, you now have 14 on both sides. Therefore you have finished balancing your equation. The answer is... 3Ca(OH)2 + 2H3PO4 --> Ca3(PO4)2 + 6H2O

### Subject: Algebra

If 8x + 4 = 38, what does 12x(2) +2 = ?

The first step to solving this problem is finding the value of x. In order to solve for x, we need to isolate this term by itself on its own side of the equation. In order to do this, we need to subtract 4 from both sides. Remember, whatever we do to one side of the equation, we have to do to the other side of the equation as well. 8x + 4 (- 4) = 38 - 4 This would leave us with 8x = 34 Finally, we must get x alone. We can do this by dividing by 8. However, remember that we must do this to both sides. Therefore, we will end up with 8x/8 = 34/8 x = 4 Now that we have the value of x, we can plug it into the second equation in order to find the answer. This would leave us with 12(4)(2) + 2 = 98 Our final answer is 98!

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