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√72  =

√(36 * 2) =

6√2

(x+[1+√2]) (x-[1-√2])  =

x^2 + x(1+√2) - x(1-√2) - (1+√2)(1-√2) =

x^2 + x + √(2)x - x + √(2)x - ( 1 - 2) =

x^2 + 2√(2)x + 1

Modula arithmetic is not a topic I have ever formally studied.  I do know that it gets very difficult quite quickly although the early problems aren't too bad.

Perhaps you can share your questions with us and we can learn and revise together.  😞

I shall take a look for some questions.

I wonder if this isn't supposed to be

x - 40%(x)  =  317.27    ???   that's the the way I'm going to interpret it......!!!

So we have

x - .40x = 317.27      ( remember 40% = .40  )

.60x  = 317.27      divide by .60

x = 317.27 / .60

x = about 528.78

Yes lol

I haven't finished with that other problem yet.  Alan is very sure he is right.  😯

Thanks, Melody....at least there weren't any "inverse functions" involved......LOL!!!!

Sorry it is too difficult to display  on my phone.

but

just expand it like a normal quadratic.

I got the same answer as you Chris.

There is an error in the question.

😕

I have not made a personal aquaintance with them.  Sorry   

Take a  look at this - it is a good starting point I think.  

Call the full ship, 27 + x, where x is the number of prisoners....and if (1/2)x escape, then the number of people on the ship now equals 27 + (1/2)x ...therefore

27 + (1/2)x  = .85(27 + x)

27  + (1/2)x = 22.95 + .85x

4.05  = .35x

x = about 11.57

Sorry...I can't get the numbers to work, here....!!!!   (???)

Abs (a - b) will be largest when at least one of the other terms is minimized....so, since absolute value is always ≥ 0, let's minimize the middle term by letting b = c

This gives us

abs ( a - b)   + abs(c - a)  = 20   but, since  b= c, we can write

abs ( a - b)   + abs(b - a)  = 20  and let's assume  that a > b  [we could also assume the opposite....it won't matter]

So we have, using the definition of absolute value:

a - b  + -(b - a)  = 20

a - b  + a - b = 20

2(a - b)  = 20

(a - b)  = 10

Which implies that

abs (a - b) = 10

And that's as large as  abs(a - b) can be

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As Melody would say.......that's what I think..!!!.....of course....any constructive criticism is welcome....!!!

Hmm, great question. If you use equal quantities of yellow and violet, that would mean 6 quarts divided by 2. In this tree we know that there is 3 quarts of yellow paint, while the violet paint is made of blue and red. 1/3 of violet 3 quarts is one US quart, so 1 quart of red paint was used. Then 2/3 of 3 quarts is 2 US quarts, so 2 quarts of blue paint.And because six quarts of brown paint was partially made from 2 quarts of blue paint 2/6=0.33333333333333333(so on) multiplied by 100 to fufill the percentage, 33.333333(so on)%.

So for question number 1, one quart of red paint. Number 2, two quarts of blue paint. Num 3, 33.333333%.

And the 6 quarts of brown paint was made by three quarts of yellow paint, one quart of red paint, and two quarts of blue paint.

Thx 4 the great question 

There's lots of people here that can help you. What do you need?

This is not an equation, and x can be any number. 

1/2(-p+23+-p+15)=6p-23

 You mean this, right?:

(1/2)[-p + 23 + (-p) + 15] = 6p - 23     calculate: -p - p, and 23 + 15:

(1/2)(38 - 2p) = 6p - 23                 Find the product on left side:

19 - p  = 6p - 23                      Add p + 23 on both sides:

42 = 7p                      Divide both sides by 7

p = 6

I remember about thirty digits, but no one will ever memorize all of the digits of pi. Maybe some one with a really, really, really, good memory might remember all the discovered digits,(wow that is alot of memory wasted) but never all the real digits.

Pi lovers unite!

There's alot of people who can help you here. Just what do you need help with?

2+2=4 because (1+1)+(1+1) or 1+1+1+1=4. There's also many ways to express this, but whatever way you express this, 2+2 is 4.

(x-2)/(x+4)-5/6=0     Add 5/6 to both sides:

(x - 2)/(x + 4) = 5/6      Multiply both sided by x + 4:

x - 2 = 5(x + 4)/6          

x - 2 = (5x + 20)/6 = 5x/6 + 10/3      

x - 5x/6 = 10/3 +2                Get common denominator (bottom) by x = 1x/1 = 6x/6:

6x/6 - 5x/6 = 10/3 + 6/3       

x/6 = 16/3                            Multiply both sides by 6 = 2*3:

x = (16*2*3)/3 = 16*2 = 32

Sadly, this problem leads to quite a messy decimal, 0.0015414258188825.

$${\frac{{\mathtt{25}}}{{\mathtt{20}}}} = {\frac{{\mathtt{5}}}{{\mathtt{4}}}} = {\mathtt{1.25}}$$

Double factorial (aka semifactorial) is a mathematical operation in which one multiplies "every other" natural number up to a given number. A more precise definition is:

$$n!!=\prod \limits_{i=0}^{k}(n-2i)= n(n-2)(n-4)(n-6)...$$

Where k = (n/2) - 1 

Or read more on the "Double Factorial" Wikipedia web page :)

20 goes one into 25 one single time, and leave a remainder of 5. 

25 mod 20 = 5

Where "mod" stands for modulo.