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Let  3^x   =   m

So

9^x   -  6*3^x     -  55    =  0

(3^2)^x   - 6*3^x   - 55   =  0

(3^x)^2  - 6* 3^x    - 55   =  0

m^2  - 6m   -  55   =  0

(m - 11) ( m + 5)   =  0

Only  the  first  factor  set to 0  and solved  for m  gives us our  answer

m - 11   =   0

m   = 11

So

3^x   = 11

So

x  =  log  11  /   log  3

you can subtract the two equations, like so:

4x+8y-(-10x+8y) = 40-(-44)

simplifying:

4x+8y+10x-8y = 40+44

14x = 84

x = 6

4(6)+8y = 40

24+8y = 40

8y = 40 - 24

8y = 16

y = 2

hope this helped! please correct me if i am wrong:)

since both of those are in the form y = mx + b, the slope would just be the "m" coefficient.

the slope of y = x + 3 would be 1, and the slope of y = -3x + 4 would be -3. 

hope this helped! please correct me if i am wrong:)

You're Right!!

Thanks!! :)

if you add the two equations together, you will get

-4x+5y+x-5y = 13-22

-3x = -9

x = 3

3 - 5y = -22

-5y = -25

y = 5

hope this helped! please correct me if i'm wrong:)

It  appears  that  the number of   "upright"  cards  in any tower  N   =  (N) (N + 1)

And  it appears  that  the  number  of "flat" cards   in any  tower N    = 2^(N - 1)  -  1 

So.....my  "guess"  is  that the  1000th tower should contain

(1000) ( 1001)   + 2^(1000 - 1)  - 1   ≈ 5.35 x 10³⁰⁰ cards     (  a whole  bunch   !!!! )

Domain and Range

Let

\(f(x) = \left\{ \begin{array}{cl} -x + 3 & \text{if } x \le 0, \\ 2x - 5 & \text{if } x > 0. \end{array} \right. \)

Hallo clairepow!

\(f(x)=-x+3\\ Domain =\mathbb R|-∞< x \leq 0\\ Range=\mathbb R|3 \le y<∞\)

\(f(x)=2x+5\\ Domain =\mathbb R|0< x <∞\\ Range=\mathbb R|-5< y<∞\)

  !

True that

The sum of the interior angles of any polygon with n sides is (n – 2) • 180^o  

So in this 4-sided figure, the sum of the four interior angles is 360^o  

Add 'em up:    (6x + 10^o) + (x + 37^o) + (7x – 9^o) + (56^o)  =  360^o  

Rearrange       6x + x + 7x  +  10^o + 37^o – 9^o + 56^o     =  360^o   

Combine                                                     14x + 94^o  =  360^o 

                                                                     14x  =  266^o  

                                                                         x  =  19^o  

                                           Angle T = 19^o + 37^o  =  56^o  

_.

Since we do not know if the opposite sides are parallel or not  (even though they LOOK like they are...) we'll have to find the value of 'x' and then compute angle T

The interior angles summed = 360

6x +10     +     x+37     +      56      + 7x-9 = 360

14x + 94 = 360

x = 19

Angle T = x + 37 = 19 + 37 = 56 ^o

 I like your idea.....but....let's forget the memorizing.....I'd just rather  eat pie.....

#pi cram session

We could eat pie while we memorize lol

Correct, catmg  !!!

Just need to memorize 69996 more digits, easy peasy. 

=^._.^=

It looks like ABC needs to be multiplied by 2.5 to get to DEF. 25/10 = 2.5 or 40/15 = 2.5 or 50/20 = 2.5. 

So I think K = 2.5. :))

=^._.^=

LOL!!!!

Well.......we're gonna' have to  go  some to  beat this  guy  :

https://www.guinnessworldrecords.com/world-records/most-pi-places-memorised

you serious?

Hmmm, my memory is not the best, so I just know the standard 3.1415

I have friends you know hundreds of digits tho. 

=^._.^=

Oops, I've forgotten about the Y, thanks for the reminder. :))

=^._.^=

I think it starts with '3'......cannot remember for sure....

Yeah..I see what you mean..let  me  think  about this

If x  = 4

Log ₃ ( 1)   = 0

So  if x  >  4

log  ₄  ( x)   >   1

So  log₃  ( x > 1)   will  be  >   0

So  log ₂  (something >  0)   will exist

So...I think you are correct   macar0ni    ....   (4, inf)   !!!

THX for  pointing this one out to  me       ......just proves I shouldn't be too  hasty with my answers without thinking them through  !!!!

n/3   + 15   >   n/2   + 1      multiply through by 6 to get

2n + 90 > 3n + 6

84 > n

n< 84       so   2  thru 83    is   82 numbers

Thanks for translating. :)))

=^._.^=

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