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Firt line SHOULD read

27^x  = 9^x+1

27x=9x+1

(3^3x) = 3^2(x+1)    equate the exponents

3x = 2x+2

x = 2

27x=9x+1

Hello Guest!

\(27x=9x+1 \)        |\(-9x\)

\(27x-9x=1 \)       

\(18x=1\)                 |  /18 

\(x=\frac{1}{18}\)

proof

\(27\cdot \frac{1}{18}=9\cdot \frac{1}{18}+1\\ \frac{27}{18}=\frac{9}{18}+\frac{18}{18}\\ \frac{27}{18}=\frac{27}{18}\)

  !

I'll come back if I get the right answer. 

And the answer is     a = 6 units  

what is 3 divided by 3/4 because someone said it was four and it was the wrong answer   

It is 4.  Whoever said it was not 4 is is the one that's wrong.  Check to make sure you copied the question correctly. 

_.

 80t - 16t^2  = height

36 = 80t- 16.1 t^2

-16t^2 +80t-36 = 0    Quadratic formula   shows t =  0.5 sec onds for 36 ft height on the way UP

                                                                            t =  4.5 seconds for 36 ft height on the way back down

x mod 4== 3

x mod 5== 2

x mod 6== 1

Using CRT + MMI

60m  +  7, where m=0, 1, 2, 3..........etc.

So, the smallest x == 7

See:

https://web2.0calc.com/questions/anybody-wanna-help

This is related and the solution can be applied here. 

OMG thank u sooo much different guest but a similar question. So if the "-11" was a "-6", it would be -3, -2, -6, -1, 1, 3, 2, 6?

The ratio is 1pi : 4pi  or 1/4

I think that your answer is not correct.

According to your calculations is as follows:

4 * tan∠FBC = 6.315789474

6.315789474 / tan∠EBD = 9.972299169     ( 4 + a )

AX and CZ are not congruent!!!

We need to look for the correct answer.

a = 6 units  

The quadratic -x^2 + 12x - 4 can be written in the form a(x + b)^2 + c, where a, b, and c are constants. What is a+b+c?

Hello Guest!

\(\color{BrickRed} -x^2 + 12x - 4\\ =a(x+b)^2+c\\ =a(x^2+2bx+b^2)+c\\ \color{BrickRed}=ax^2+2abx+ab^2+c\)

\(\color{blue}a=-1\\ 2ab=12\\ ab^2+c=-4\)

\(-2b=12\\ \color{blue}b=-6\)

\((-1)(-6)^2+c=-4\\ c=-4+36\)

\(c=32\color{blue}\)

\(a+b+c=(-1)+(-6)+(32)=25\)

  !

3 divided by 3/4

3 / (3/4)

3 * 4/3 = 4

Well..... on second look  A is incorrect   ALSO   ( though the note representations DO appear as though they were reflected vertially, but they are in the wrong order)

   so NONE of them are reflections, but I SUPPOSE  'C' would be the CLOSEST, though not really a reflection.   Sorry.  Bad Question!!

I still believe it should be A

If C were a reflection , the RIGHT side would look like this:

From A to B, the x coordinate increases by 12 and the y coordinate increases by 6.  If we continue on for 1/3 of this distance, we will add $1/3*12 = 4$ to the x coordinate and $1/3*6 =2$ to the y coordinate, to get $C = (14+4,4+2) = (18,6)$

The equation is missing......

dont cheat on your AOPS test lol

Sorry, I figured out the digits in the tens > digits in ones place. Here is the list where the digits in the hundreds > digits in the tens. The number DOES NOT change:

20648 , 20846 , 20864 , 24608 , 24806 , 24860 , 26408 , 26804 , 26840 , 28406 , 28604 , 28640 , 40628 , 40826 , 40862 , 42608 , 42806 , 42860 , 46208 , 46802 , 46820 , 48206 , 48602 , 48620 , 60428 , 60824 , 60842 , 62408 , 62804 , 62840 , 64208 , 64802 , 64820 , 68204 , 68402 , 68420 , 80426 , 80624 , 80642 , 82406 , 82604 , 82640 , 84206 , 84602 , 84620 , 86204 , 86402 , 86420 , Total =  48 permutations.

5! - 4! =96 permutations

20468 , 20486 , 20648 , 20684 , 20846 , 20864 , 24068 , 24086 , 24608 , 24680 , 24806 , 24860 , 26048 , 26084 , 26408 , 26480 , 26804 , 26840 , 28046 , 28064 , 28406 , 28460 , 28604 , 28640 , 40268 , 40286 , 40628 , 40682 , 40826 , 40862 , 42068 , 42086 , 42608 , 42680 , 42806 , 42860 , 46028 , 46082 , 46208 , 46280 , 46802 , 46820 , 48026 , 48062 , 48206 , 48260 , 48602 , 48620 , 60248 , 60284 , 60428 , 60482 , 60824 , 60842 , 62048 , 62084 , 62408 , 62480 , 62804 , 62840 , 64028 , 64082 , 64208 , 64280 , 64802 , 64820 , 68024 , 68042 , 68204 , 68240 , 68402 , 68420 , 80246 , 80264 , 80426 , 80462 , 80624 , 80642 , 82046 , 82064 , 82406 , 82460 , 82604 , 82640 , 84026 , 84062 , 84206 , 84260 , 84602 , 84620 , 86024 , 86042 , 86204 , 86240 , 86402 , 86420 , Total =  96 permutations.

20486 , 20684 , 20864 , 24086 , 24680 , 24860 , 26084 , 26480 , 26840 , 28064 , 28460 , 28640 , 40286 , 40682 , 40862 , 42086 , 42680 , 42860 , 46082 , 46280 , 46820 , 48062 , 48260 , 48620 , 60284 , 60482 , 60842 , 62084 , 62480 , 62840 , 64082 , 64280 , 64820 , 68042 , 68240 , 68420 , 80264 , 80462 , 80642 , 82064 , 82460 , 82640 , 84062 , 84260 , 84620 , 86042 , 86240 , 86420 , Total =  48 permutations.

Probability = 48 / 96 = 1 / 2

The ratio of the radii is 1/2, so the ratios of the areas is also 1/2.

The expected value of the sum is 5.

(2*sqrt(22))^2 =(2*sqrt(6))^2 + S^2, solve for S

a. S = 8 - the 3rd side

b.  8 / sqrt(88) =0.852802865 sine of the larger angle.

d.  Arcsine(0.852802865) = 58.52 Degrees - measure of the larger angle.

c. (58.52 / 180)  x  pi =1.0213 Radians - measure of the larger angle.

It was C

a=100; c=100*a % 991; if(c==1, goto3, goto4);printc, a; a++;if(a<1000, goto1, 0)

x = 882

[100*882] mod 991 ==1