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y - 1   = x    →  y = x + 1    (1)

x^2 + y^2 = 17   (2)

Subbing (1) into (2), we have

x^2 + ( x + 1)^2  = 17       simplify

x^2 + x^2 + 2x + 1  = 17

2x^2 + 2x - 16  = 0       divide through by 2

x^2 + x - 8  = 0

This will not factor.......using the quadratic formula, the two solutions for x are

[ -1 + sqrt(33)] / 2       and   [ -1 - sqrt(33)] / 2

And y = x + 1

So.....when x = [ -1 + sqrt(33)] / 2 , y = x + 1 =  [1 + sqrt(33)]/2

And, when x = [ -1 - sqrt(33)]/ 2 , y = x + 1 =   [1 - sqrt(33)] / 2

And the sum of all these solutions is

[ -1 + sqrt(33)] /2   +   [ -1 - sqrt(33)] / 2   +  [1 + sqrt(33)]/2 + [1 - sqrt(33)] / 2  = (suprisingly, 0  !!! )

You can see why this is so from the following graph: https://www.desmos.com/calculator/8axms04lcy

The solution coorrdinates just "cancel" each other out when we sum them !!!!!! 

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.5 = 1/2

1/2x = x/2

SO

.98 * .5 = .98/2

.98/2 = .49

^ May want to do long division for this..

The sum of the first N positive integers is given by :

(N) (N + 1)  / 2    ........so we have....

(366) (367) / 2    =  67,161

The first guest was incorrect, listen to what cphil said.

If the base is negative...

Say -1

-1^2 = 1

1>-1

This happens with all negative numbers squared, or put to the power of an even number.  <3

The common ratio is given by the ratio of the following two terms :

a_{n+ 1} / a_n  

So.....we have

  -3 / 9   = -1/3 = the common ratio    ......verify for yourself that this ratio is consistent with the rest of the terms  

As cphil was explaining the innequality is:

If lawns = x

x>=7

no you aren't 

21-(-20)

21+20

41

Hi Aditya,

The address that you have provided is not correct. :(

Did you check it for yourself?

Anyway I am starting to feel sorry for you - you must be getting very frustrated by now.

[Aditya has been PMing me with this question for the better part of a day. ]

Here is your question

People can answer it here I guess.

if n belongs to natural numbers then the highest integer m such that 2^m divides (3^2n)9-8n-9

if n belongs to natural numbers then the highest integer m such that

2^m        divides     3^(2n+2)  -8n -9

I have looked at this question and have not made any immediate progress.

I am too busy to look properly now.

I will however draw attention to your question, so that other mathematicians will pay attention to it.

-----------------------------------------------------------------------

I have called for more help here:

-1/3

In f(n)...

f(n) = -1/3x OR

f(n) = x/3

NOTE, IF THE LAST NUMBER WAS 1, WITH SIMPLE RATIOS THE NEXT NUMBER IS THE ANSWER!

120  + 30x >= 310     subtract 120 from both sides

30x >= 190     divide both sides by 30

x >= 6 + 1/3 yards

So......6 yards won't be quite enough.......he needs to mow 7

No prob......

Thanks so much!

150 / 8  =  75 / 4   =  18 + 3/4

sorry dont awnser that

Sure !!!......consider....

(1/2)^2  = 1/4       and  1/4 < 1/2

In fact, if the base is  > 0 but < 1, this will always happen.....!!!!

3x - y = 6       (1)

xy =  24 →  y = 24/x    (2)

So.....  substituting (2) into (1), we have

3x - 24/x = 6    multiply through by x

3x^2 - 24 = 6x      re-arrange

3x^2 - 6x -24  = 0       divide through by 3

x^2 - 2x - 8  = 0     factor

( x - 4) ( x + 2)  = 0       and setting each factor to 0, we have

x = 4   and x = -2

So.... y = 24/4  = 6      or.... y = 24/-2  = -12

And we have   (4, 6)  and ( -2, -12)

And the sum of these  is just     10 + -14   = -4

thats not even the question

i told you to go the link

x^2 = x * x

x^3 = x * x * x

x^4 = x * x * x * x

x^n = x * x * x... (n times)

the square root is the reverse of the square

3^2 = 3 * 3 = 9

4^2 = 4 * 4 = 16

5^2 = 5 * 5 = 25

sqrt(9) = 3 because 3^2 = 9

sqrt(16) = 4 because 4^2 = 16

sqrt(25) = 5 because 5^2 = 25

technically, sqrt(9) = +/- 3 because 3 * 3 = 9 and -3 * -3 = 9

the cube root is the reverse of the cube (a cube is x^3 = x * x * x)

cbrt(27)  = 3 because 3^3 = 3 * 3 * 3 = 27

cbrt(64) = 4 because 4^3 = 4 * 4 * 4 = 64

cbrt(125) = 5 because 5^3 = 5 * 5 * 5 = 125

good how are you doing

yeah if the exponent or base is negative

you have to think what cubed equals 27 and 3 cubed equals 27. hope this helps 

21/19

3^2n +2 = k

3^2n = k-2

log_3(k-2)=2n

1/2(log_3(k-2)) = n

k is whatever the expression is equal to initally. you didn't say it was equal to anything at first

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