<span><span> 5n2+10n+20</span> </span>Final result :<span> 5 • (n2 + 2n + 4)
</span>
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "n2" was replaced by "n^2".
Step by step solution :Skip Ad
<span>Step 1 :</span><span>Equation at the end of step 1 :</span><span> (5n2 + 10n) + 20
</span><span>Step 2 :</span><span>Step 3 :</span>Pulling out like terms :
<span> 3.1 </span> Pull out like factors :
<span> 5n2 + 10n + 20</span> = <span> 5 • (n2 + 2n + 4)</span>
Trying to factor by splitting the middle term
<span> 3.2 </span> Factoring <span> n2 + 2n + 4</span>
The first term is, <span> <span>n2</span> </span> its coefficient is <span> 1 </span>.
The middle term is, <span> +2n </span> its coefficient is <span> 2 </span>.
The last term, "the constant", is <span> +4 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 1</span> • 4 = 4</span>
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is <span> 2 </span>.
<span><span> -4 + -1 = -5</span><span> -2 + -2 = -4</span><span> -1 + -4 = -5</span><span> 1 + 4 = 5</span><span> 2 + 2 = 4</span><span> 4 + 1 = 5</span></span>
Answer: yes its just set up diffrently
Step-by-step explanation:
Count the number of multiples of 3, 4, and 12 in the range 1-2005:
⌊2005/3⌋ ≈ ⌊668.333⌋ = 668
⌊2005/4⌋ = ⌊501.25⌋ = 501
⌊2005/12⌋ ≈ ⌊167.083⌋ = 167
(⌊<em>x</em>⌋ means the "floor" of <em>x</em>, i.e. the largest integer smaller than <em>x</em>, so ⌊<em>a</em>/<em>b</em>⌋ is what you get when you divide <em>a</em> by <em>b</em> and ignore the remainder)
Then using the inclusion/exclusion principle, there are
668 + 501 - 2•167 = 835
numbers that are multiples of 3 or 4 but not 12. We subtract the number multiples of 12 twice because the sets of multiples of 3 and 4 both contain multiples of 12. Subtracting once removes the multiples of 3 <em>and</em> 4 that occur twice. Subtracting again removes them altogether.
If
, then we can write
and since this is continuous for all
, the limit as
will be
Answer:
1 7/8
Step-by-step explanation:
2 5/8
+1 7/8= 4 1/2
- 7=3+4
- 5+3=8
- 2 5/8 + 3/8= 3
- 3 + 1= 4
- 4 + 4/8= 4 4/8
- 4 4/8 = 4 1/2
