<li>The tables above show the different colors and sizes of T-shirts that are available at Independence High School. How many different combinations of color and size are possible?</li>
</ol>
<p>p. 521</p>
<p>For this one, can i have a solution shown through plugging in?</p>
<li>A list of numbers consists of p positive and n negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of n/p?</li>
</ol>
<p>p. 521
14. For how many ordered pairs of positive integers (x, y) is 2x+3y < 6 ?</p>
<p>p. 533</p>
<li>|10 -K|=3
|K-5|=8</li>
</ol>
<p>What is the value of k that satisifies both equations above?</p>
<p>–</p>
<p>Also, I have a question regarding special right triangles. Suppose a triangle is a 45-45-90, and the hypotenuse is already given as 7. Would I change it to 7 sqrt 2? would the other sides be 7?</p>
<p>Would I even encounter a problem like that? Thanks a ton.</p>
<p>I don't have the book... but for p.521, the answer's probably 1, by using guess and check (1,1)</p>
<p>p.533.</p>
<p>Okay, so the absolute value sign makes the negatives turn into positives.</p>
<p>For example, |-5| = 5. And |7| = 7.</p>
<p>Simple enough.</p>
<p>So if |10 - K| = 3, k can either be 13 or 7.</p>
<p>And if |K - 5| = 8, K can either be 13 or -3.</p>
<p>What is the value of K that satisfies both equations above?</p>
<p>13.</p>
<p>Triangle question: Well, why would you change the hypotenuse when it's already given? It makes no sense to me.</p>
<p>In a 45-45-90 triangle, the hypotenuse is sqrt 2 times the length of the side. So going backwards, the length of each side is 7/sqrt2.</p>
<p>Why does this rule work?</p>
<p>Well, according to the Pythagorean Theorem, a squared + b squared = c squared. In 45-45-90 triangles, a and b are the same, so a^2 + b^2 = 2a^2.</p>
<p>p. 521
I thought it would be 5 bc you can have: (0,0),(0,1),(1,0),(1,1), (2,0)
Please correct me if I am missing something in the question. The answer is D. </p>
<p>p. 533
The answer is 13 bc
|10 -K|=3 has the same solutions as 10 - k = 3 and 10 - k = -3. Solve these two equations and you get k = 7 and 13.
|K-5|=8 has the same solutions as k-5 = 8 and k-5 = -8. Solve these two equations and you get k = -3 and 13.
Since 13 is present in both answers, it is 13. </p>
<p>p. 519
The answer is obtained by multiplying the number color choices by the size choices. 3 * 4 = 12. B is the answer. </p>
<p>And regarding your question about triangles:
If the hypotenuse is 7, you cannot change it to 7sqrt2. I understand why you want to do this since the sides of that special triangle are expressed in ratios based on sqrt2.</p>
<p>Think about it like this:
Hypotenuse: leg: leg
7: x : x
The formula for the sides of that special triangle is:
Ksqrt2: K : K</p>
<p>7 = K sqrt2, so K = 7/sqrt2. K (or x) is now the leg of the special triangle. </p>
<p>And although you may not see a problem directly asking you to do this on the SAT, it is safe to say many questions regarding triangles on the SAT are based on special triangles so finding the measures of the legs is something you need to be able to do.</p>