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2 is in the first category of x>0

  so   f(2) = ax+3           a(2) + 3 = 5     then      a = 1

0 is in the second category of x = 0

then f(0)  would be    ab = 5       a, we found is 1    then   b  = 5

-2 is in the third category x<0

  then f(-2) = bx+c  =-10                   b we found to be 5 

                     5(-2) +c = -10           so c =0 

a+b+c=1+5+0=6  

ah ok thank you hellospeedmind and ElectricPavlov! that helped me a lot :)

why don't you look at what guest posted on your last question? you don't have to write up the same exact question twice

16^2 is 256. divide 800 by 256 to get 3.125. Therefore, you need 3.125 16x16 tiles, but if you need a whole number then you need 4 16x16 tiles.

Since r is a root of x^3 + 2/5*x - 1 = 0, r^3 + 2/5*r - 1 = 0. Then the sum of the series is

\(\begin{align*} r^2 + \frac{4r - 2/5}{1 - r^3} &= r^2 + \frac{4r - 2/5}{2/5 \cdot r} \\ &= \frac{2/5 \cdot r^3 + 4r - 2/5}{2/5 \cdot r} \\ &= \frac{104/25 \cdot r}{2/5 \cdot r} \\ &= \boxed{\frac{52}{5}}. \end{align*}\)

Let P=(0,6), Q=(12,0), and R=(0,0). A line passing through the point (3,0) bisects the area of the triangle. Find the slope of this line.

 I will convert it to base 10 to start

2 +

3 x 4 +

2 x 4^2

1 x 4^3

0 x 4^4

3 x 4^5

0 x 4^6

2 x 4^7

1 x 4^8                           = 101486       divide by 8    remainder is 6

According to Wolfram Alpha, \(\frac{120301232_4}{8}\) is equal to \(\frac{50743}{4}\) in base 10, which means that the remainder is 6. Does that help?

https://www.wolframalpha.com/input/?i=%28120301232_4%29%2F8

1. The slope of line AB is -1/2.

2. The values of m are -2, 1/3, and 5/3.

3. The values of k are 1, 2, 10, and 11.

The centroid of triangle PQR is (4,3), so the slope of the line is (3 - 0)/(4 - 3) = 3.

Thank you for the explanation!

Expanding a little bit on Melody's answer...

You expand and get \(n^3 = (n^3-3n^2-3n+1)+(n^3-6n^2+12n+8)+(n^3-9n^2+27n-27)\).

Solve from here.

Hi Melody.  I don't know if this is related, but I'll pass it along for what it's worth.  Yesterday I tried to open the calculator, and got an image that looked like a caricature of a mall security punk and an announcement that I was blocked because the site would not admit anyone who is using AdBlock.  Well, fine, it's their site and they can do what they want, but the thing is, I'm not using AdBlock, nor any other ad blocker.  Today I tried again and did get into the calculator.   

_.

(2sqrt(5)*sqrt(3))^2+(1*2sqrt(15))^2 = 120

Using this website calculator.

another method: 

\(2\sqrt{5}=2*5^\frac{1}{2}\)

\(\sqrt{3}=3^\frac{1}{2}\)

So the first bracket can be written as:

\((2*5^\frac{1}{2}*3^\frac{1}{2})^2\)

Now using laws of exponentials, multiply each number by the exponent which is 2 so:

\(4*5*3\)=60 

So the first term is 60 (I.e. first bracket) 

Second bracket:

\((1*2\sqrt{15})^2=(1*2*15^\frac{1}{2})^2\)

same,

\(1*4*15\)=60

Add both,

\((4*5*3)+(1*4*15)=60+60=120\)

Hectictar just told me that another way to deal with this issue is to change the word  questions   in the address by to answers

That sounds like a neat alternative.  She is not sure if it always will work though.

Thanks Hectictar.  

Thanks guest. :)

Thanks Alan and guest.  

Some time maybe I will work out why mine is wrong.

It is always good to have the correct answer anyway.  

What would we do without your Monty Carlo simulations.  They really ae very useful !

Assuming for integers > -1 

~~~~~~~~~~~~~~~~~~~

a-b-c=0 

a=b=c

2s=a+b+c  

2s-a-b=c 

a-b-2s-a-b 

-2b-2s=0 

-2(b+s)=0 

b+s=0  

Indeed for that to be true a+b+c/2 MUST be 0 and b is zero 

Their sum is 0 simply.

The graph of y = x^2 - 3x + 6 hav intercept (0,6)

110 ft  : 5280 = 0.001893939...

Hi Sadaatkhan,

It is good to see you haviing a go ... but...

Your woking is not correct

(n-1)^3 is not n^3-1

100%   ==>    104g

  x        ==>        4g

x = 4*100%/104

x = 3.846 %