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Haha, real funny

but, still, we are about to outnumber the new Wrap Day Trend, now lets outnumber the old one with 486 comments

and this post will officially be the longest one ever! 😈😈😈

alright, the troll has other bridges, theres one solution

B**w Them All Up!

ill go to the mines, where not only 7up, but also where my dynamite, tnt, and other explosives hide

then b**w up the bridges

then, NO MORE BRIDGE CROSSES!

then the Toll Bridge Patrol will have to be disbanned, and chaotic rate will increase

Tortoise A walks 52.0 feet per hour and Tortoise B walks 12 inches per minute. Which Tortoise travels faster? Explain. 

$$\frac{12 inces}{1 min} \\\\
= \frac{12*60inches}{60minutes}\\\\
= \frac{12*60inches}{60minutes}\\\\
= \frac{12*60inches}{1 hour}\\\\
= \frac{(12*60)/12 feet}{1 hour}\\\\
= \frac{60 feet}{1 hour}\\\\$$

so that is faster than 52 feet per hour.  :)

Yeah but he still have other toll bridges you would have to fly all the time to avoid them then how could you do anything on the ground?

I like 99 better. 100 have to many zeros. Of course maybe that is why you like them. Romans not have any zeros hahahaha

Since arctangent of 1/10 (in radians)=.09966865249........etc.  (1)

Then 8 x the above answer gives =.797349219929.....etc.        (2) 

Then since 1/4 of Pi=Pi/4=.785398163......etc.                         (3)

Then subtract (2) from (3) above

Then=.0119510565......etc. And this is the arcrangent.             (4)

Then we find the tangent of (4) above

Which is:0.01195162554520335317930497716049....etc.

Which is a rational fraction of: 1,758,719/147,153,121, Which is your answer!!!!!!.

What do you mean sometimes when i told you I only crossed the troll bridge once?

btw this is the 100th comment! Lets root for more comments here than the old Wrap Day!

$$-\sqrt{200}=-\sqrt{100*2}=-10\sqrt2$$

OK but that still not explaine how you can move around the kingdom with out him catching you some times.

4^5.5  =  4^{5 + .5}  =  4^{5 + 1/2}

    =  4⁵ x 4^1/2            (Adding exponents means multiplying bases.)

    =  4⁵ x √4               (A 1/2 exponent is a square root.)

    =  1024 x 2

    =  2048

Why don't you try & use any calculator with a X^Y key & get the answer?

4^5.5 =2048

If the original problem were entered slightly incorrectly:

  7^x + 7^{(x - 2)} + 7^{(x + 1)}  =  7·393

7^x + 7^x · 7^-2 + 7^x · 7¹  =  7·393

(1 + 7^-2 + 7) · 7^x  =  7·393

(1 + 1/49 + 7) · 7^x  =  7·393

(393/49) · 7^x  =  7·393

 7^x  = (7·393)·(49/393)

 7^x  = 7·49 = 7³

x = 3

Hi Zegroes  

2(r+2) + 5(1+5r)=63

2r+4    + 5+25r   =63

2r+25r   +4+ 5   =63

27r       +9          =63

                   27r  = 54

                    r    =  54/27

                    r    =  2

Also this one that i'm stuck on

-30+7b       =   4(1+6b)

-30+7b      =   4   +  24b

-30+7b-4   =   4   +  24b-4

-34 +7b      =   24b

-34 +7b -7b =   24b-7b

-34             =  17b

-34/17        =  17b/17

-2               =  b

             b =  -2

Reduce[-30 + 7 b = 4 (1 + 6 b), b]

-30+7b=4+24b

-30-4=24b-7b

-34=17

b=-34/17=-2

Problem #2:

im guessing this is simplification 

-30+7b=4(1+6b)

4*1=4

4*6b=24b

-30+7b=4+24b

This is really cool Geno. I not know how to do this until now.

Yeah, whihc never caught me cuz my plane is camaflouged 

only the Queen's 'elite' guards caught me, not the troll patrol 😈😈😈

Reduce[2 (2 + r) + 5 (1 + 5 r) = 63, r]

4+2r+5+25r=63

9+27r=63

27r=63-9=54

r=54/27=2

Problem #1:

$${\mathtt{2}}{\mathtt{\,\times\,}}\left({\mathtt{r}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}}{\mathtt{\,\times\,}}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{r}}\right) = {\mathtt{63}}$$

2*r=2r

2*2=4

5*1=5

5*5r=25r

2r+4+5+25r=63

2r+25r=27r

4+5=9

$${\mathtt{27}}{\mathtt{\,\times\,}}{\mathtt{r}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}} = {\mathtt{63}}$$

$${\mathtt{63}}{\mathtt{\,-\,}}{\mathtt{9}} = {\mathtt{54}}$$

$${\mathtt{27}}{\mathtt{\,\times\,}}{\mathtt{r}} = {\mathtt{54}}$$

54/27 and 27/27= 2

$${\mathtt{R}} = {\mathtt{2}}$$

OK so you fly in. That explain some things. I think the troll have some flying monkeys he use sometimes maybe he bring them in.

Since both logs are to the base 10, take both sides of the equation to the power of 10:

10^{log₁₀ (x^2 - 2x} )  =  10^{log₁₀ (2x + 12)}

Since 10^log₁₀ (Anything)  =  Anything

--->   x² - 2x  =  2x + 12

--->   x² - 4x - 12  =  0

--->   (x - 6)(x + 2)  =  0

--->   x = 6  or  x = -2

In problems like these, you need to check all the answers; they do work!

Could you just cross out the log₁₀ from both sides? -- So long as all of both sides are in log form, yes!

256 x 256  =  (250 + 6) x (250 + 6)

So, you must use FOIL:  F = First = 250 x 250,     O = Outside = 250 x 6

               I = Inside = 6 x 250,         L = Last = 6 x 6

You get:  (250 x 250)  +  (250 x 6)  +  (6 x 250)  +  (6 x 6)

     =  62500 + 1500 + 1500 + 36  =  65536

FOIL is an extended distributive property.

Really? He gave me a discount, and i didnt use it till a week ago

and yes, the troll bridge is just a one time job, cuz i was smart enough to fly my plane above the troll bridge

If you subtract successive y-terms (bottom up so that they are all positive):

150 - 50 = 100         300 - 150 = 150         500 - 300 = 200           750 - 500 = 250   1050 - 750 = 300

If these answers were all the same number, your formula would be a linear equation:  y = ax + b, but since they aren't, subtract the answers (again, subtract smaller from larger):

150 - 100 = 50     200 - 150 = 50     250 - 150 = 50     300 - 250 = 50

Since these answers are all the same and since it took two sets of subtractions, the formula will be quadratic:  ax² + bx + c = y

(1,50)  -->  x = 1, y = 50  -->  a(1)² + b(1) + c = 50   -->  a + b + c = 50

(2,150) -->  x = 2, y = 150 -->  a(2)² + b(2) + c = 150   -->  4a + 2b + c = 150

(3,300) -->  x = 3, y = 300 -->  a(3)² + b(3) + c = 300   -->  9a + 3b + c = 300

Now solve these for a, b, and c:

Combining the first two:  a + b + c = 50

                                       4a + 2b + c = 150

                   Subtracting:  3a + b = 100                (subtract bottom up)

Combining the last two:  4a + 2b + c = 150

                                        9a + 3b + c = 300

                   Subtracting:  5a + b = 150                 (subtract bottom up)

Combining these two answers:

                                     3a + b = 100

                                     5a + b = 150

                  Subtracting:  2a = 50   ===>   a = 25

Substituting back:  5(25) + b = 150   --->   b = 25

and finally, a + b + c = 50  --->   25 + 25 + c = 50   ===>   c = 0

So, the equation is:  ax² + bx + c = y   ===>   y = 25x² + 25x

Yeha I remember he give you the discount to get rid of you faster hahaha

You have to cross the bridge every time you come and go and he probaly have more than one bridge inside the kingdom so its not just a one time thing.

Bruh, i crossed the troll bridge a long time ago.....

remember? THE TROLL EVEN GAVE ME A DISCOUNT!!!!

Someone? please