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A. deductible

Just add the amounts on lines 4,5 and 6 together, NSS

That will be your answer

1. The tangent to the circle x^2 - 2x + y^2 = 15 at(1,4)

Implicitly differentiating the function, we can find the slope of a tangent line to the circle

2x - 2 + 2yy'  = 0     

y'  =  [2 - 2x ] / [2y]

y' = [1 - x] / y

At (1,4)....the slope is

[1 - 1 ] / 4  = 0

So...the equation of the tangent line at (1,4) is

y = 4

Here's the graph : https://www.desmos.com/calculator/uqvstutnla

\(3\sqrt{10} = \sqrt{3^2}\times\sqrt{10}= \sqrt{9}\times\sqrt{10}= \sqrt{9\times10} =\sqrt{90}\)

 The number under the radical sign is \(90\)

Hope this helps!

me to

to many reasons to count

currently, my life sucks... how about you

But he/she says "by selecting 3 vertices of a regular octagon". So, shouldn't the number of distinct triangles be:

8C3 = 56 ???

On the left side....Let's simplify under the radical, first

b^2             c

_____  -    ___       multiplyy the second fraction by 4a  on top and bottom

4a^2          a 

b^2            4ac

____    -  ____          and this gives us

4a^2        4a^2

[ b^2  - 4ac ]  

__________       taking the square root    of top and bottom  we have

    4a^2

√ [ b^2 - 4ac ]

____________

 √ [ 4a^2 ]

√ [ b^2  - 4ac ] 

____________

       2a

So...combine tis with the first fraction on the left and we end up with

-b               √ [ b^2  - 4ac ] 

__    ±       ____________        which gives us

2a                   2a

-b   ±  √ [ b^2  - 4ac ] 

________________       =    [the right side ]

        2a

EDIT 

Like the guest says  8C3    =  56  !!!

Dang

You said how are you not what is your name. To ask what is your name it would be Com`o te llamas?

The polynomial is f(x)= 0x^7 + 8x^6 + x^5 +5x^4 + 2x^3 + 0x^2 + 0x + 2 (08152002)

so \(f(x)=8x^6 + x^5 +5x^4 + 2x^3 + 2\)

BTW we have the same day birthday but im in 1999

Hope this helps!

Why did you upload your question vertically? It is very difficult to read!!!!.

Made a good impresion to my girlfriend's mother while wearing my dad's army attire

Melody....I just read about the proof of this....roughly, it goes 

Let  n = p^a  where p is a prime factor

Then...the  divisors of  n  = p^a   are

 1, p, p^2, p^3, p^4.......p^a

So...the number of divisors   =  (a + 1)

So

p^a * q^b    where p, q are prime factors

has

(a + 1)  (b + 1)   divisors

Do not delete you questions!

You can add a post saying that you have found the answer  BUT do not delete your original question.

It is very rude.

Someone could have been working on it!

Hi guest answerer,

of the numbers from 1 to 15, 12 has the most factors so having b=12 sounds resonable.

n=15 also makes sense to me.

so maybe 12^15 is correct

BUT why do you say this has 496 factors?

They are all correct....!!!!

5+5^2+5^3=5+25+125=155 words

Thanks guest, i have edited it. I hope it is right now.  :)

\(1\rightarrow2\rightarrow4\rightarrow8\rightarrow16\)

And Backwards,

\(16\rightarrow8\rightarrow4\rightarrow2\rightarrow1\)

Also There Is A Fun Question,

Can You Solve It?

\(\frac{1}{2}*\int_{5}^{10}-\lim_{x\rightarrow 50}{100}_{10}=x=6\)