Real Math Questions

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1

<p>Hey guys
I need help in these math questions :)</p>

<p>1) <a href="http://i43.tinypic.com/a27z8z.jpg%5B/url%5D"&gt;http://i43.tinypic.com/a27z8z.jpg&lt;/a&gt;&lt;/p>

<p>2) <a href="http://i43.tinypic.com/16m0eph.jpg%5B/url%5D"&gt;http://i43.tinypic.com/16m0eph.jpg&lt;/a&gt;&lt;/p>

<p>3) <a href="http://i42.tinypic.com/m8jhna.jpg%5B/url%5D"&gt;http://i42.tinypic.com/m8jhna.jpg&lt;/a&gt;&lt;/p>

<p>4) <a href="http://i40.tinypic.com/j9yreu.jpg%5B/url%5D"&gt;http://i40.tinypic.com/j9yreu.jpg&lt;/a&gt;&lt;/p>

<p>5) <a href="http://i42.tinypic.com/dg2kj6.jpg%5B/url%5D"&gt;http://i42.tinypic.com/dg2kj6.jpg&lt;/a&gt;&lt;/p>

<p>6) <a href="http://i39.tinypic.com/2uetrwo.jpg%5B/url%5D"&gt;http://i39.tinypic.com/2uetrwo.jpg&lt;/a&gt;&lt;/p>

<p>7) <a href="http://i42.tinypic.com/fonajl.jpg%5B/url%5D"&gt;http://i42.tinypic.com/fonajl.jpg&lt;/a&gt;&lt;/p>

<p>and thx in advance :)</p>

2

<p>For 1, draw a line segment from A to the midpoint of BC. Since the triangle is isosceles, this segment is the median and altitude. Thus we get two 3,4, 5 right triangles with base 3 and height 4. So the area of the big triangle is 1/2 b<em>h = 1/2</em>6*4 = 12.</p>

3

<p>1.) Because AB and AC are equal, the altitude you draw down from A will bisect BC. So you have a right triangle with one side 3 (half of 6) and a hypotenuse of 5. Use the Pythagorean theorem to find the height which is 4. (1/2)(6 x 4) = 12</p>

<p>2.) 243 = 3^5, so Y=3 and Z=5. When we plug in 3 for Y, we get X^-3=1/8. Solve for x and you get 2. Plug in values of X and Z for the equation X+Z and we get 7.</p>

<p>3.) I solved this by drawing a line perpendicular to the X axis starting at (1,0). Now we have a 30,60,90 triangle, with one leg of length 1. This leg is the longer leg because it is opposite from the 60 angle. So, using the properties of a 30,60,90 triangle, I found that the short leg will be of length 1/sqrt(3). So the slope is 1/sqrt(3), so the answer is C.</p>

<p>4.) Write a system of equations.
X+Y=25
X+5Y=65
Solving this gets X=15 and Y=10. So the answer is 15.</p>

<p>5.) Because X>90, BC has to be the longest side. Because of the triangle inequality theorem, we know that the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides. So all possible answers would be 8<BC<14. (It’s greater than 8 instead of 2 because we know it has to be the longest side.)</p>

<p>6.) I’m pretty sure this one is E. Sorry, someone else would be able to explain this one better than me.</p>

<p>7.) Probability = # of favorable outcomes / # of total outcomes
There are four favorable outcomes: (6,6,5); (6,5,6); (5,6,6); and (6,6,6). There are 216 total outcomes: (6 x 6 x 6). 4/216 reduces to 1/54, so this is B.</p>

<p>Let me know if I made a mistake somewhere.</p>

4

<p>For 2, we can make the negative exponent positive by taking the reciprocal. So x^y = 8. Thus x=2 and y=3. So z=5. Therefore x+z=7.</p>

5

<p>For 7, there are 6<em>6</em>6 = 216 total rolls. 6,6,6 will give 18. 5,5,6 or 5,6,5 or 6,5,5 will give 17. So there are 4/216 = 1/54 possibilities.</p>

6

<p>For 5, by the triangle rule, the third side is between 8-6=2, and 8+6=14. If it were a right triangle, then the hypotenuse would be 10 (6,8,10 is a multiple of the Pythagorean triple 3,4,5). Since the triangle is obtuse, the third side is bigger than 10. So pick any number between 10 and 14.</p>

7

<p>For 6, the maximum is the highest point on the graph, f(v). The minimum is the lowest point on the graph, f(t). So the difference is f(v)-f(t).</p>

8

<p>For 4, you can guess and check using your calculator. But if you want an algebraic solution:</p>

<p>x+5y=65
x+y=25</p>

<p>Subtracting gives 4y=40. So y=10 hardcover books. So there are 15 paperbacks.</p>