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Simplifying we get x<=17

So the interval notation would be (-inf,17]

If we multiply all of them together we get a^3*b^3*c^3*d^3=27000.

The square root of that is a*b*c*d=30.

We can independently solve for each number with the above equations.

So a=1, b=3, c=5, and d=2.

1+3+5+2=11.

This is probably the question:

Let G be the center of the equilateral triangle XYZ. A dilation centered around G with scale factor -2/3 is applied to triangle XYZ to obtain triangle X’Y’Z’. Let A be the area of the region that is contained in both triangles XYZ and X’Y’Z‘. Find A/[XYZ].

And here's the answer:  https://web2.0calc.com/questions/help_54234#r3

[24! + 12!] = 2^10 * 3^5 * 5^2 * 7 * 11 * 821 * 11087 * 142302163

Say we have 48 giraffes and 40 apes

THen we would have 5 zebras

The GCD of these numbers is 1, so we cant simplify these numbers anymore

SO the zoo has 5 zebras

I think its 4, but i got 8

2002*2+444*-9

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.

Imagine there are only 4 characters: a, b, c, and  d

And we want to know how many strings of length 3 can be made with those 4 characters.

First let's list all of the strings that start with  'a' :

aaa

aab

aac

aad

aba

abb

abc

abd

aca

acb

acc

acd

ada

adb

adc

add

There are 4 groups of 4 which means there are  4 * 4 = 16 strings in the above list.

Now imagine if we kept the pattern going. We could copy and paste the above list and change all of the first characters in each string to "b". Then we could paste it again and change all of the first letters to "c", and again for "d". That would make 4 total groups: the first group all start with "a", second group all start with "b", the third all start with "c" and the fourth all start with "d".

So then there would be a total of  4 * 4 * 4 = 4³  =  64 strings  in the completed list.

So the total number of strings is  4³  , which is the number of different characters raised to the power of the length of the string.

I hope this helps explain a little bit where the  62⁷  comes from!

why am i so alone   

There is no stigma to being alone.  The Native Americans knew this long ago, some of them even incorporated the condition into their names.  Just some examples are Lone Horn, Lone Eagle, Lone Wolf, and Lone Shark.  And then, of course, there's The Lone Ranger.

_.

ab + cd = 13.

If it 1 has to make it, then we can find the probability of none making it and work from there. If the probability wanted is 3/4, then 1/4 is the chance they all don't make it. So (4/5)^x has to be less than .25.

The smallest number is 7

What is the area, in square units, of a square whose sides are the same length as the radius of a circle with a circumference of 12 units?

Hello Guest!

\(C=2\pi r\\ r= \dfrac{C}{2\pi}\\ r=\dfrac{12}{2\pi}\)

\(r=\dfrac{6}{\pi}\)

\(a=r\\ a=\dfrac{6}{\pi}\\ A=a^2\\ A= (\dfrac{6}{\pi})^2\)

\(A=\dfrac{36}{\pi^2}=3.648\)

The area of this square is 3.648 in square units.

  !

The distance from T to face ABC is 3*sqrt(5).

1+5y=x

x+y=97

x=97-y

1+5y=97-y

6y=96

y=16

x=81

81-16=65

Wow, that's a lot! Looks like bitly.com is going to stay in business for quite a while! Thanks for showing me how that works, I thought it might be calculated with permutations or something like 10+26+26=62

Then you need to calculate 62!, but that is just insanely big. And wrong lol. Thanks again!

Is this code for  the location of buried treasure  ???

Multiplying a polynomial by a (non-zero)  constant does not change its degree

So

degree 8   +   degree  9     =    degree 9

g(x)   = degree 9

I'm guessing that you wnat to know the  ratio of the  red area  to  the  area of the square  ???

If so 

One white area  has  a base  =  the side of the square  =  S

And the  height of one of these right triangles =  S/4

So....its area =   (1/2) S ( S/4) =  S^2 / 8

And   the toal white area  =  (4) S^2/8  =   S^2/2

So....red area  to square area  =   1/2

Nice logic, 4M     !!!!

OOPS....awful  error   !!!!!.....corrected   !!!!

Having 3 less quarters means he has 75 cents less so 230-75=1.55.

He has 1.85 now so he needs 185-155 30 cents more or 6 nickels, which would be half of Andrew nickels. So he has 12 nickels and 5 quarters.

That would mean Shelby has 6 nickels and 8 quarters, and .30+2 is 2.30.

So shelby has 6 nickels and 8 quarters

Call the side of the square, S

BH  =  sqrt (2) S  -  8  +  4  =    sqrt (2)S  - 4

BC  = 4

EH  = sqrt (2)S

EF = S

Using similar triangles

EH/ EF  =  BH / BC

sqrt (2) S  / S   = (sqrt (2)S  - 4)   / 4

sqrt (2) * 4   =  sqrt (2)S   - 4

4sqrt (2) + 4  = sqrt (2) S

S =  4 ( sqrt (2) + 1)  / sqrt (2)

S =   2sqrt(2) ( sqrt (2) + 1)  =     4 + 2sqrt (2)  = 4 + sqrt (8)

Area of  square  =    (4 + sqrt (8) )^2  =  16 + 8sqrt (8)  +  8    =   24 + 8sqrt(8)  = 

 24 + 16sqrt (2) ≈   46.63

The area of the trapezoid is 24*sqrt(2).

the number of unique characters   =   10 + 26 + 26   =   62

the number of unique strings of 7 such characters   =   62⁷   =   3 521 614 606 208

That's over 3 trillion!

Thanks!