All Answers 355967 Answers

64^(x - 2)  =  256^(2x)       get the bases  the same     

(2^6)^(x - 2)  = (2^8)^(2x)         [  a^b)^c   =  a^(b * c) ]

2^( 6x - 12)   = 2^(16x)           

We  have the  bases  the same.....solve for  the exponents

6x  - 12  =   16x

-12  =  16x  -  6x

-12  = 10x

x  =  -12/10  =   - 6 / 5

I think x y and z can each be  1  or -1  

1 + 1 +1 = 3

-1 + 1 +1  =1

-1 -1 + 1  = -1

-1 -1 -1   = -3         4 values

a)

f(-1)  =  (-1)^3   +  5   = 4

So   g ( f(-1) )  =  g (4)   =  3(4)    = 12

b)  f^-1(x)

y = x^3  +  5

y  - 5   = x^3      take  the  cube root

∛ ( y -  5)   = x      "swap"   x  and  y

∛ ( x  - 5 )  =    y   =  f^-1(x)   = the inverse

Thanks Chris 

To be truthful, I have not finished it. 

I am not sure how easy or difficult it would be to show it is a maximum.  

(x-0)(x-1)=0          roots             = 0  and +1

x^2 -x  + 0              coefficients = -1   and  0 

-150   =   360   -150   =  210°

cos (210°)  =  -cos (30°)   =  -sqrt ( 3)   / 2

Thank you!

a1 = 1/4      r = 1/4

SUm =     a1/ (1-r) =     1/4   *   4/3    =   1/3  

y = (1) * x^2       a = 1     focus =   (0, 1/4a) = (1 , 1/4 )

Unit circle     do you know how to compute the sides of the triangle for -60 degrees?

   here is a good video ....starting at  7:50 into the video

https://www.youtube.com/watch?v=3GgO7Q_kg8Q

       sin -60 = - sqrt3 /2

https://www.sarthaks.com/183043/the-sum-of-first-20-terms-of-the-sequence-0-7-0-77-0-777-is

or

https://learn.careers360.com/engineering/question-try-this-the-sum-of-first-20-terms-of-the-sequence-07-0770777is/

or

https://doubtnut.com/question-answer/the-sum-of-first-20-terms-20-terms-of-the-sequence-070770777-is-53796460

have the solutions, the answere tho is option 4 which is \((7/81)(179 + 10^{-20})\)

Maybe this posting:  ??     I did not check answer....

https://web2.0calc.com/questions/the-quadratic-has-the-following-unexpected-property

Thanks a lot cat!!!

🐺🐺🐺

Still not sure what this multi-posted question is asking

   n =4 is not included in the definition of the funtion's domain 

       BUT   f(4)   would be 

                                              2⁴ = 16

Hi vockeyvockvock (your username is very fun to say)!

So, let's try visualizing this box scenerio. 

10000000

20000000

30000000

40000000

01000000

11000000

21000000

31000000

It becomes like counting in base 5. But, the numbers are reversed. (1, 2, 3, 4, 10, 11, 12, 13, 14, ...)

So we just need to convert 2010 into base 5 and sum the digits, 31020. (Normally, I'd put a link to a video explaining how to convert bases, but my posts keep getting flagged because of it.)

Now we just add the digits, 3+1+0+2+0 = 6. 

6 is our answer. :))))

=^._.^=

25x^2  - 4                   (5x - 2) ( 5x + 2)             5x +  2

__________     =    ________________  =   _________

5x^3  - 2x^2                x^2 ( 5x - 2)                      x^2

z^10 + 1/z^10 also works out to 1.

interest for first 6 months   then moves to second 6 month interest

   10000 (1 + .02)        

    [ 10000 (1 + .02)] (1 + .025) = $..............            note that Doc only gets 1/2 of the annual interest  for each 6 month deposit

FV = PV (1+ i)ⁿ         n is the number of periods    5 yr  x   4 = 20 periods

                                   i = decimal inteest PER PERIOD   = .044/4

                                  PV = present value = loan amount = 11200

                                  FV = futere value

FV = 11200 (  1 + .044/4)²⁰ = $ 13939.31                interest earned =  13939.31 - 11200 =..........

2.)  Same equation with different numbers:

        128500 =  PV (1 +.065/2 )¹⁶       Solve for PV

Note that  minor  arc DE  =  360   - 238   =  122

We  have   this

DCE   = (1/2)  ( measure of major arc DE   - measure of minor arc DE) 

DCE  =  (1/2)  ( 238  - 122)

DCE = (1/2) ( 116)

DCE  =  58°

10 =  .5  * 1.21^x      divide  both sides  by  . 5

10/.5     =  1.21^x

20  =   1.21^x      take  the log  of each side

log 20   = log 1.12^x            and  by a log  property we  can write

log 20   =x  * log 1.21       divide both sides  by   log 1.21

log 20  / log 1.21  =  x   ≈  15.7 years  =  16  years

So

1988  +  16   =     2004

.10x  + .20(120)  =  .18 ( x + 120)   simplify

.10x + 24  =  .18x  +  21.6

24  -  21.6  =  .18 x   - .10x

2.4   = .08x  

2.4  /  . 08   = x    = 30   grams  

Total  length of  one wall   = 246.75  + 900   =  1146.75

Total length of  the other  wall  = 246.75  +  3500   = 3746.75

Distance  between the  two wall ends using the Law of Cosines

distance  =  sqrt   (  1146.75^2  + 3746.75^2  - 2 ( 1146.75 * 3746.75) cos ( 125.2°) )  ≈ 4506 ft

The second digit must be even, so it must be one of 0, 2, 4, 6, or 8 However, it cannot be 6 or 8 since then the fourth digit could not be twice the second digit. Thus, there are  different possible combinations of second and fourth digits, as shown in the following table:\[
\begin{array}{|c|c|}\hline
\text{Second digit} & \text{Fourth digit} \\ \hline
0 & 0,1,2,3,4,5,6,7,8,9 \\ \hline
2 & 4,5,6,7,8,9 \\ \hline
4 & 8,9 \\ \hline
\end{array}
\]

The first digit can be any of the  nonzero digits, and the third digit can be any of the 10 digits. The answer is $18\times 9\times 10=\boxed{1620}.$

A = cost  of adult ticket

S =cost of student ticket

We have this system

1A  + 2S  =  18

1A  + 7 S  =  43      subtract the  first equation from  the second

5S  =  25

S =  5 (dollars)

1A  + 2(5)    =18

A  + 10  =  18

A  =  8  (dollars)