<p>Can any one help me with these problems by providing a good explanation. </p>
<p>Thanks</p>
<p>(x-8)(x-k) = x^2 - 5kx + m</p>
<p>In the equation above, k and m are constants. If the equation is true for all values of x , what is the value of m?</p>
<p>A)8
B)16
C)24
D)32
E)40</p>
<hr>
<p>Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?</p>
<p>For the first one, just look at the answer choices and substitute them each. Just think about multiplying two binomials. FOIL(first, outer, inner, last) the terms. I just plugged in the answer choices and eventually 16 came out to be the answer. IF M was 16, then -8 * something=16(since M is the L in FOIL, it means the last term, of which -8 and k are the last). So then k=2. So then you get x^2-10x+16, and I believe that works out. </p>
<p>As for the 2nd one, I'm not so sure, but I just drew 6 dots and I could draw 5 lines from each dot to the other 5, and I got 30. I don't think that's right since it seems too easy.</p>
<p>I started out drawing the six dots, and drew five lines from the first dot. However, if I drew five from the second dot, it was coincident with one of the lines from the first dot. So the answer is 5+4+3+2+1.</p>
<p>topasz, do you mind explaining what you just said? I've seen the "!" from the Barron's 2400 book for # of combinations of n objects taken r at a time. One is n!/(n-r)! The other is n!/(n-r)!r!. I don't really understand those formulas, but please explain the !s.</p>
<p>Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?</p>
<p>Without the "combinations" formula.
There are 6 choices for the first point to draw the line through, 5 choices are left for the second point to connect with the first one, 6x5=30 altogether.
Since we counted each line twice (AB and BA, for example), the answer is 30/2=15.</p>
<p>I have not seen a CB SAT question yet where you would need nCr with r>2.</p>
<p>What if we choose different numbers for x and k?
Let x=10 and k=0, then
(10-8)(10) = 10^2 + m
20=100 + m
m=-80
That means for x=10, k=0 and m=-80
the equation
(x-8)(x-k) = x^2 - 5kx + m
is true, but it's not necessarily true for all values of x - and it's not.</p>
<p>In the equation above, k and m are constants. If the equation is true for all values of x , what is the value of m?<a href="x-8">/quote</a>(x-k) = x^2 - 5kx + m
x^2 -(k+8)x + 8k = x^2 - 5kx + m
5k=k+8 and m=8k
k=2 and m=16.</p>
<p>(x-8)(x-2) = x^2-10x+16 for all x. Try them all.:D</p>
<p>the first term of the sequence above is 2, and every term after the first term is -2 times the preceding term. how many of the first 50 terms of this sequence are less than 100?</p>