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\(x=\sqrt{420 - \sqrt{420 - \sqrt{420 - \sqrt{420 - \dotsb}}}}\\x^2=420-x\\x^2+x-420=0\\(x-20)(x+21)=0\\\boxed{x=20}\)

lol

There are 13 heads    so there is 13 animals total

x = turtles                     feet = 4x

13-x = penguins           feet = (2)(13-x)              summed = 34

4x +    2(13-x) = 34

2x = 8

x = 4   = turtles            13-4 = penguins = 9

Hey there!

We know that there is 360 degrees in a circle, so using this we know that the fraction for the blue portion will be:

\(\frac{360-48}{360}=\frac{312}{360}=\frac{13}{15}\)

Hope this helped :)

$1500  * {   1267 t / lb   *  2.2046 lb/ kg  *  1 kg /$ .88) }  = ~~ 4761184 tabs

Thanks!

JM is 1/4 of the entire circumference

1/4   *  pi * 16.4 = ..........   miles

The exponent of the prime factorization of the gcd of the 2 numbers will be the biggest power of that prime number that divides into both of the 2 giant numbers. Knowing that here is the prime factorization of the greatest common divisor of the 2 numbers:

\(2^23^35^57^711^{11}13^717^519^323^2\)

Therefore \(\boxed{11}\) is the answer.

Slope of given line , m,   = -1/8

   perpindicular slope = - 1/m   = 8        the only choice is the first one ....slope = 8

Thanks!

I took 2 numbers that only have 3 divisors which would be 4 and 9 when you square both of them and find the divisors you will see that each of them have 5 now lets take a 3rd number like 25 when you square it (625) you also find it has only 5 divisors so your answer should be 5.

89*6 = total score at beggining which is 534

has to get to 90*7 which is 630 points total

You take 630-534 which is 96.

So he has to get a 96.

1 block east then 5 blocks west = net   4 blocks west

2 blocks south and 4 more blocks south = 6 blocks south

She winds up   4 blocks west and 6 blocks south

Thanks.

I figured it out...

D is the answer because when you add up all the animal you get 22 and you see that there are 9 so it would be the number of to the total number of animals 

72 is the awnser
 i don't know how to explain it

5 glip / 2 glup   *   3 glup /2 glop   =  15 glip / 4 glop

15 glip / 4 glop   *   1 glop  = 15 glip / 4    = 15/4   glip

5 glips = 2 glups
2 glops = 3 glups

15 glips = 6 glups
4 glops = 6 glups

15 glips = 4 glops

15/4 glips = 1 glop
 

Please do not post questions multiple times    

 4(a+6) >= -5(a+3)   expand

4a + 24  >= -5a -15

9a ≥ -39

a≥ -39/9

a ≥ - 4 1/3

\(( − ∞ , − 744464 /45 )\)

I believe that a P vs NP problem is one where it's easy to see that an answer is wrong, but hard to find the right answer. 

According to Wikipedia, "The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are also in P. This is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, and to biology, philosophy[5] and cryptography (see P versus NP problem proof consequences). A common example of an NP problem not known to be in P is the Boolean satisfiability problem."

Hmm, I'm not sure I understand it fully, but I hope you get it. :))))

Please tell me when you do. 

Good luck. 

=^._.^=

Find the price per liter     $ / L

Marian   $5.50 / 2 L         = $ 2.75 per liter

Ivan       $ 2.95 / .75 liter  = $ 3.93 per liter

Thank you though!

thats wrong :(