Two more difficult math questions...

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<h1>13: The graph of a quadratic function and the graph of a linear function in the xy plane can intersect in at most how many points?</h1>

<h1>14: If the length of LM is 7 and the length of MN is 8, which of the following could be the length of LN?</h1>

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<p>Answer choices:</p>

<p>13:</p>

<p>1
2
3
4
More than 4</p>

<p>14:
23
22
17
16
14</p>

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<p>bump10char</p>

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<p>have u try drawing out the graphs? it’s easy to see the correct answer, but you can approach it algebraically as well.</p>

<p>for the LMN problem, have you considered different combinations of where L,M, and N could be? For example, it could be M-----7—L-1-N? or L----7-----M------------8-----N?
It’s really when you sketch it</p>

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<p>for #13, think about solving it algebraically. if you have a quadratic, and you set it equal to a linear expression (such as x^2=x) the most number of answers that you can get for x is two, which means that the answer is two. (its basically a quadratic equation)
for #14, think about the extreme positions you could place the two lines, where the third line (LN) is longest and shortest. Basically, 8+7=15, and 8-7=1, so 1<LN<15, therefore, the only possible answer choice that works is 14.</p>

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<p>13) 2 </p>

<p>Think about a parabola… –> U now think of a line… –> /
The ‘/’ can only cross the ‘U’ at most at 2 points.</p>

<p>14) 14</p>

<p>LN is equal to LN= MN + MN
LN = 8 + 7</p>

<p>LN isn’t a line so it is less than that. only option less than 15 is 14.</p>

<p>P.S. I didn’t think these were that hard. Anyone else?</p>

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<p>They’re difficult for me because I didn’t understand the wording and am unfamiliar with quadratics.</p>

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<p>I’m going to bump this thread because I still don’t understand number 14. Why is it less than 15? How can you draw a line with LMN in the lengths given to equal 14?</p>

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<p>if the two lines are at an angle other than 180 degrees, it will be between 1 and 15</p>

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<p>But it’s a line. Shouldn’t it be straight? (sorry I never took geometry… so I’m clueless -_-)</p>

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<p>LN is still a line. Picture it as the third leg of a triangle so LM and MN would still be straight lines as well LN</p>

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<p>

</p>

<p>Triangle rule:</p>

<p>The length of the third side of a triangle must fall between the sum of the other two sides and the difference of the other two sides. </p>

<p>In 15, LM is 7 and the length of MN is 8. LM and MN are two sides of the triangle. LN is the third side of the triangle. The length of LN, therefore, must fall between 8 minus 7, which is 1, and 8 plus 7, which is 15. </p>

<p>LN therefore can be any number from 1 to 15, non-inclusive. </p>

<p>1<LN<15. </p>

<p>The only choice that falls between 1 and 15 is E or 14.</p>

<p>* Quadrilateral rule:*</p>

<p>While we’re at it, it is worth mentioning that the sum of the lengths of three sides of a quadrilateral must be greater than the length of the fourth side.</p>