<p>From BB Test # 8. If you could explain how to solve them, I'd appreciate it. :) </p>
<p>Section 5, # 17.
2
If 'K' and 'H' are constants and X + kx + 7 is equivalent to (X +1) (X+H), what is the value of K?
(A) 0 (B) 1 (C) 7 (D) 8 (E) it cannot be determined by the information given</p>
<p>Section 8, #15</p>
<p>If n/n-1 * 1/n * n/n+1 = 5/k for positive integers 'n' and 'k', what is the value of 'k' ?
(A) 1 (B) 5 (C) 24 (D) 25 (E) 26</p>
<p>Thank you, I really appreciate it. :)</p>
<p>n/n-1 * 1/n * n/n+1 = 5/k
[n<em>1</em>n]/[(n-1)<em>n</em>(n+1)] = 5/k
[n]/[(n^2-1)] = 5/k</p>
<p>n = 5
n^2-1 = k
k = (5)^2 -1
k = 24</p>
<p>For the first problem, do you mean x^2 + kx + 7? If so, then you can do the following:</p>
<p>x^2 + kx + 7 = (x+1)(x+h)
x^2 + kx + 7 = x^2 + (h + 1)x + h</p>
<p>From this, you know that h = 7 because it is the only constant term. Moreover, you know that k = h + 1, or 8, since it is the only x term.</p>
<p>In the second problem, you can cancel out one n term in the numerator and denominator.</p>
<p>( n * n * 1 ) / [ ( n - 1 ) * ( n + 1 ) * n ] =
n / ( n^2 - 1)</p>
<p>You know that this is equal to 5 / k. So you can simply set n = 5 and find that n^2 - 1 is 5 * 5 - 1, or 24.</p>
<p>If 'K' and 'H' are constants and X + kx + 7 is equivalent to (X +1) (X+H), what is the value of K?
(A) 0 (B) 1 (C) 7 (D) 8 (E) it cannot be determined by the information given</p>
<p>Assuming that's supposed to be x^2 + kx + 7
x^2 + kx + 7 = (X +1)(X+H)
x^2 + kx + 7 = x^2 + (H + 1)x + 1H
H = 7
(H + 1) = k = 8</p>
<p>It's supposed to be Xsquared, if that's how you indicate it.</p>
<h1>1 x^2+kx+7=(x+1)(x+h)</h1>
<pre><code> x 1
\/
/\
x h
</code></pre>
<p>1*h=7<br>
1+7=k<br>
so,
h=7
k=8</p>
<h1>2 n/(n-1)<em>1/n</em>n/(n+1)=5/k</h1>
<pre><code> n/(n-1)(n+1)=5/k
</code></pre>
<p>so,n=5,(n+1)(n-1)=4*6=24=k
k=24</p>