math question help ~!!!!!

Test Preparation
1

<p>let the function p be defined by p x a x k 2 where a and k are positive constants for what value of x will the function p have its minimum value ??</p>

<p>-a
-k
0
a
k</p>

<p>answer (K)</p>

2

<p>another question <a href=“http://i40.■■■■■■■.com/f3wg0m.png[/url]”>http://i40.■■■■■■■.com/f3wg0m.png&lt;/a&gt;&lt;/p&gt;

3

<p>another one <a href=“http://i44.■■■■■■■.com/2d9xoxt.png[/url]”>http://i44.■■■■■■■.com/2d9xoxt.png&lt;/a&gt; </p>

<p>answer(D)</p>

4

<p>reply plzzzzz</p>

5

<p>I don’t know what you are asking in the first question (especially since I can’t tell the difference between x and the multiplication symbol), so I’m not doing that one.</p>

<p>As for the second one, just write out all of the numbers (in order) for each thing. This is basically asking you if you can read these types of graphs.</p>

<p>Numbers of hours studied: 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5 (Median = 2)
Number of hours slept: 4, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9 (Median = 7)</p>

<p>The difference between the medians is 5.</p>

6

<p>For the third one, I’ll show the algebraic way to do it (because you can solve this problem through guessing):</p>

<p>Because the giant square has a side length 8, we can say that the area of the square is 64. We see that the square is made up of 4 components: 2 squares (SI and SII) and two shaded rectangles (which are EXACTLY the same with the same dimensions as each rectangle have the two different sides against a square). So, we can say the area of the larger rectangle as a sum: S = SI + SII + 2(12). Due to the transitive property, the sum is now:</p>

<p>64 = SI + SII + 24 -----> 40 = SI + SII</p>

<p>Now, here is where you can start guessing here, and you should get 4 (2^2) for SI and 36 (6^2) for SII. </p>

<p>However, although unnecessary, here is the algebraic method:</p>

<p>Let’s have SI = a^2 and SII = b^2. We also have the shaded rectangles, with a side a and side b (from the picture). So, each shaded rectangle is ab, and due to the transitive property, ab = 12. We are going to solve for one of the variables (doesn’t matter which), so we’d get a = 12/b.</p>

<p>So now we have two equations: 40 = a^2 + b^2 and a = 12/b. Plugging the second equation into the first gives us:
40 = 144/b^2 + b^2
40b^2 = 144 + b^4
0 = b^4 - 40b^2 + 144</p>

<p>Now use the quadratic formula to solve for b^2 (Note that I did not use a calculator for this calculation, but it’s extremely recommended).
b^2 = [40±√(1600-4(1)(144))]/2
b^2 = [40±√(1600-576)]/2
b^2 = [40±√(1024)]/2
b^2 = (40±32)/2
b^2 = 20±16</p>

<p>You should get that result, which reduces to 36 or 4, exactly the same answers as you’d get if you guessed initially.</p>