Even number are of the form 2n. The sum of this sequence is the average of the first and last terms times the number of terms.
So the first term is 2 and the 25th term is 50 so the sum is:
(2+50)(25/2)
52*12.5=650
The conjecture they wish you to make is that for n terms, the sum will be:
s=n(n+1)
And for 25 terms that would give you:
s=25*26=650
Answer:
The correct answer is "9√2 units".
Step-by-step explanation:
The given equations are:
⇒
...(equation 1)
⇒
...(equation 2)
According to the 2nd equation, we get
⇒ 
⇒ 
On substituting the value of "y" in the 1st equation, we get
⇒ 



On taking common, we get

On applying factorization, we get





or,


Now,
The points are:
(-7, 12) = (x₁, y₁)
(2, 3) = (x₂, y₂)
By using the distance formula, the length of chord will be:
= 
On substituting the values in the above formula, we get
= 
= 
= 
=
units
To answer your question: Rewrite <span>81<span>x2</span></span> as <span><span>(<span>9x</span>)</span>2</span>.<span><span><span>(<span>9x</span>)</span>2</span><span>−49</span></span>Rewrite 49 as <span>72</span>.<span><span><span>(<span>9x</span>)</span>2</span><span>−<span>72</span></span></span> Both terms are perfect squares, factor using the difference of squares formula, <span><span><span>a2</span><span>−<span>b2</span></span></span>=<span><span>(<span>a+b</span>)</span><span>(<span>a<span>−b</span></span>)</span></span></span> where <span>a=<span>9x</span></span> and <span>b=7</span>.<span><span>(<span><span>9x</span>+7</span>)</span><span>(<span><span>9x</span><span>−7</span></span><span>)</span></span></span>
Add 12 to each side
so it should be C>8