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Is there a way to use P(this given this) on this question?

Is there an auxiliary line or something to solve this problem?

I tried using cases such as 2 Ts, 1 T and 0 Ts, but apparently, I got the wrong answer.

Note : 1  = log2(2)

2log₂ ( x + 5) = log₂(x - 9) + log₂(x + 53) + log₂(2)

log₂(x + 5)^2  = log₂(x - 9) + log₂(x + 53) + log₂(2)

log₂(x + 5)^2  =  log₂ [ (x - 9)(x + 53) * 2 ]        ....so...

(x + 5)^2  =  2(x - 9)(x + 53)

x^2 + 10x + 25  =  2 ( x^2 + 44x - 477)

x^2 + 10x + 25  = 2x^2 + 88x - 954

x^2 + 78x - 979 = 0

(x - 11) ( x + 89) = 0

Setting each factor to 0 and solving for x produces

x = 11  (accept)            or

x = -89  (reject as it doesn't give a real valued log  )

I tried setting the side length to a. Then, I used the length given and got an equation for the third small triangle. Then I got confused on how to solve that. Is there any other way?

I tried to graph all 3, but how would you know where they intersect, at one point ot two points without a calc?

Here's what I tried:

8 has to be in the middle

We can put the first number in 2 places: at the end or at the front

Then we can put the second number in 2 places, then the third, then the fourth, ... all the way to the 6th number

The 7th number has to be in the remaining spot.

So, I got 2^6= 64. How do you do this?

Thanks Chris :)

8^(x^2) * 4^x  =  2

[ 2^3 }^(x^2) * (2^2)^x  =  2^1

2^(3x^2) * 2^(2x)  = 2^1

2^( 3x^2 + 2x)  = 2^1         the bases are the same......solve for the exponents

3x^2 + 2x   = 1

3x^2 + 2x - 1  = 0

(3x - 1)(x +1) = 0

Setting both factors to 0   and solving for x produces  

x = 1 / 3    or   x   = -1

Thanks!!!!

Oh, I see. Thank you!!!!

3.8 / 24  =  19/120  ≈  15.8%

It's concerning the UPC (Universal Product Code) label found on most items in a grocery store....(also known as a "bar code" )........the bar code  is scanned at the register for the price...I think the "check digit" is used to detect fraud....

I'm sure that Australia probably uses some form of this

f(g(x)  =  f ( x - 2)

a(x - 2)^2 + b(x - 2) + c  = 

a (x^2 - 4x + 4)  + bx - 2b + c

ax^2 - 4ax  + 4a  + bx  -2b + c

ax^2 + (b - 4a) x + (4a - 2b + c)     =  2x^2 - 5x + 19

a = 2

b - 4(2)  = - 5

b = 3

4(2) - 2(3) + c = 19

2 + c  = 19

c = 17

a + b + c  =   22

there are only 5 cases, of course they all total to 36

1)    a, a+5,  twice as big as the first one

2)    a, a+5,  half as big as the first one

3)    a, a+5,  twice as big as the second one

4)    a, a+5,  half as big as the second one one

5)    a, a+5 =2a,  36-3a

What is this question about Chris?

Okay then. Thanks!!!

Thanks!!!

I didn't use a calculator.....the final square root is easy to evaluate....

Thanks!!!

Thanks!!!

You are correct....I missed that  !!!

 71404303885

Don't know much about this, but here is the algorithm

Add the digits in the odd-numbered positions (first, third, fifth, etc.) together and multiply the total by three: 
(7 + 4 + 4 + 0 + 8 + 5) X 3  =   (28) x 3 =  ( 84)

Add the digits in the even-numbered positions (second, fourth, sixth, etc.).
(1 + 0 + 3 + 3 + 8)  =  (15)

Add the two results together:
84 + 15  =  99

Now what single digit number makes the total a multiple of 10? That’s the check digit.
99 +  1   

1 is the check digit. The full UPC number is now   714043038851

Thanks!!!

Well, calc wasn't exactly allowed... Is there a way to do it without a calc?