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1 is not considered to be a prime number; the primes are 2, 3, 5, 7, 11, 13, ...

42 =  2 x 21

42 = 2 x 3 x 7

The prime factorization of 42 is 2 x 3 x 7.

If x represents her allowance:  (1/3)x  =  8

Multiplying by 3:                           x  =  24

Her weekly allowance is $24.00.

Equation:  x³  =  36x

This can be written as:  x³ - 36x = 0

Factoring:                 x(x² - 36)  =  0

Factoring again:  x(x - 6)(x + 6)  =  0

So, the answers are:  0, 6, and -6.

Braces, { and }, are used to represent a set of answers.

If the answers to a problem are the numbers 4 and 2, this answer can be expressed as       {4, 2}.

Also, {7} means that the answer is 7.

If there is no number between the braces, you have an "empty set", and there is no answer. So:  { } means that the problem does not have an answer.

9 * 1998  +  50^15/395  =  17982  +  1.160159  =  17983.160159

140/200  *  100 = 70%

140/200  = 70/100 = 70%

49^3/2  =  49 ^ (1 + 1/2) = 49^1  *  49^1/2  =  49  *  SQRT49  =  49 * 7  =  343

3/2  *  -5  = -15/2   =   - 7 1/2

Thanks Chris :)

Nice work and graphics, Melody......

Ahh TR That is a real girl, that is why she is so pretty. I not sure what cute means. My GF use cute for a lot of things including baby pigs, that's why I not know.

https://www.pinterest.com/jessyr13/creative-hair-color/

Btw, is that Anime on your profile pic?

it looks so cute

who knew anime was awesome?

7UP is alright

WAIT ITS NOT ALRIGHT!!!WHEN IT COMES TO LIME SODAS, SPRITE IS THE BEST!!

however, we cant invade each other, cuz if you didnt read my psa, it said royality was disbanned cuz of my stupid alt ego, and now i have entered Camelot territory as a temporarily citizen, but if I invade even someone outside of camelot, the queen would kick me out of Camelot, so I oretty much have to know what im doing

So pretty much i am staying in Camelot for a while to adapt to Servant life (remember, ive been a leader most of my life and cant remember the last time i had to serve)

So pretty much I cant do Operation Hot Sauce.....for now

I have no idea what you are talking about    

The members of a group of packaging designers of a gift shop are looking for a precise procedure to make an open rectangular box with a volume of 560 cu. units. from a 24 units by 18 units rectangular piece of material. The main problem is how to identify the side of identical squares to be cut from the four corners of the rectangular sheet so that such box can be made.Show a mathematical solution and illustration.

Let the side lengths of the identical squares be x 

The sides of the box will now be (24-2x), (18-2x) and x

$$\\Volume=x(24-2x)(18-2x)\\\\
560=x(24-2x)(18-2x)\\\\
560=4x(12-x)(9-x)\\\\
140=x(12-x)(9-x)\\\\
140=x(108-12x-9x+x^2)\\\\
140=x(x^2 -21x+108)\\\\
0=x^3 -21x^2+108x-140\\\\
0=(x-2)(x-5)(x-14)\\\\
x=2\;\;or\;\;5\;\;or\;\;14\\\\
18-2*14<0 $ so 14 is too big$\\\\\\$$

$$\\If \;\;x=2\\
Volume=2(24-4)(18-4)=2*20*14=560 \;\;good\\\\
If \;\;x=5\\
Volume=5(24-10)(18-10)=5*14*8=560 \;\;good\\\\$$

So the little cut out squares can have side length of either 2 units or 5 units.  

OK. First how do I know for sure you want a physics answer? Maybe you just want to karate chop your new BF to teach him a lesson. I don’t want to facilitate domestic violence.

hahahaha

140/1 + 10/15

140+1 and a half = 141 and a half

$$\\49^{3/2}\\\\
=\left(49^{1/2}\right)^3\\\\
=\left(\sqrt{49}\right)^3\\\\
=7^3\\\\
=343$$

a=sqrt(3)+1, b=sqrt(3)-1, ((a+bi)/(a-bi)+(b+ai)/(b-ai))^10

$$\\\left(\frac{(a+bi)}{(a-bi)}+\frac{(b+ai)}{(b-ai)}\right)^{10} \\\\
=\left(\frac{(a+bi)(a+bi)}{(a-bi)(a+bi)}+\frac{(b+ai)(b+ai)}{(b-ai)(b+ai)}\right)^{10} \\\\
=\left(\frac{a^2-b^2+2abi}{a^2+b^2}+\frac{b^2-a^2+2abi}{b^2+a^2}\right)^{10} \\\\
=\left(\frac{a^2-b^2+2abi+b^2-a^2+2abi}{a^2+b^2}\right)^{10} \\\\
=\left(\frac{4abi}{a^2+b^2}\right)^{10} \\\\
$We are given that $\;\;\;\ a=(\sqrt3+1)\qquadand\qquad b=(\sqrt3-1)\\\\
=\left(\frac{4(\sqrt3+1)(\sqrt3-1)i}{(\sqrt3+1)^2+(\sqrt3-1)^2}\right)^{10} \\\\$$

$$\\=\left(\frac{4(3-1)i}{(3+1+2\sqrt3)+(3+1-2\sqrt3)}\right)^{10} \\\\
=\left(\frac{4(2)i}{8}\right)^{10} \\\\
=i^{10} \\\\
=(i^2)^5 \\\\
=(-1)^5 \\\\
=-1$$

@@ End of Day Wrap  Sat 8/8/15     Sydney, Australia Time   8:42pm    ♪ ♫

Hi everyone,

We have had some terrific answers from TitaniumRomew, Rubenhh, Geno3141, CPhill, Alan Heureka, And Dragonlance.  Thank you  

I like your logic Dragonlance :)

Hayden had 212 gallons of water in his watering can. The seed packet said to use 14 of a gallon for peppers and 58 of a gallon for tomatoes. Hayden than used some of the water for lettuce. If Hayden had 34 gallons of water left over, about how much water did he use for lettuce?

$${\mathtt{212}}{\mathtt{\,-\,}}{\mathtt{14}}{\mathtt{\,-\,}}{\mathtt{58}}{\mathtt{\,-\,}}{\mathtt{34}} = {\mathtt{106}}$$

106 gallons.

I do not understand what you are asking.