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The formula for a 45-45-90 triangle is: legs are a, hypotenuse is a sqrt 2. 

Here is a picture for clarity: 

Yes, that's exactly what I was looking for! Thank you. 

But the number being multiplied by the square root stays the same (in this case 5)? and then actual numbers inside the square root gets divided by 2. 26/2 = 13. That part makes sense, just not the first part- could you clarify?

Just to be clear, you want to know what the legs are, right?

If so, then if the hypotenuse is a sqrt 2, then the legs are both a. 

in this case, the hypotenuse is 5 sqrt 26. so , the legs are 5 sqrt 13

If I'm wrong, please correct me.

JP

Because $2^{10} = 1024,$ and $1000^2 = 1,000,000,$ we can see that $(2^{10})^2 = 1024^2$ which is obviously greater than $1,000,000.$

If we have $2^{19},$ that is $2^10 \cdot 2^9 = 1024 \cdot 512$ which is obviously less than $1,000,000.$

Thus, $2^{19} < 1,000,000 < 2^{20}$

Note $8^{n} = 2^{3n}.$

Since we know that $2^{19} < 1,000,000$ and $2^{3n} < 1,000,000, n = \left \lfloor{\frac{19}{3}}\right \rfloor = 6.$

Thus, $8^6 < 1,000,000 < 8^7.$

We have the answer to be $19 - 6 = \boxed{13}$

Go and cheat somewhere else Kinda.

You are abusing the kind-hearted people of this forum and you are actively preventing yourself from learning anything.

2^19 is the higher power of 2 lower than 1000000. 8^6 is the highest power of 8 lower than 1000000. 

19-6=13

2^13

Yep    .... the  tan^-1   key   .....

Remember  that  the trig function gives the value for an angle.....the inverse  returns the angle for that value

answer is \(2/5+8/11=62/55\)

ahh okay- so on the scientific calculator would i have to input tan^ (-1?)

Just  take  the  tan inverse  of (3/2)

arctan (3/2)  ≈  56.3°  = x

(Make sure you're in degree mode.....)

lol yeah sorry 

You had it correct  the first time, Guest......

20 evens, 20 odds  from  0- 39  inclusive

2. when we expand (2x+1/2)^6, what is the coefficient of the x^4 term?

We  are looking for this term

C(6,2) (2x)^4  (1/2)^2  =

15  (16x^4) (1/4)   = 

60 x^4

The total  distance  traveled  when the  ball hits the  groud for  the  nth time is

6 +  6  ( 1 - (1/2)^(n-1) )   / (1/2)

So.....when it  touches  the  ground for  the  5th time

6  +  6 (1 - (1/2)^4)  / (1/2)  =

6 + 12  ( 1 - 1/16)   =

6 +  12  ( 15/16)   =

17.25   ft 

Ok, no problem.  The first step we take is to recognize the fact that the question is naturally split into two parts, so we let the narrow point in the diagram be labeled C.  

The number of paths from A to B is (paths from A to C)(paths from C to B), make sure you see why.  

With this, we need to find a way to calculate the number of paths from A to C (C to B is easy).  

First, we realize that to make a 12 step path, we can only go up and to the right.  This means that a path from A to C will go up exactly 3 times and to the right 5 times.  

This means that a path from A to C will consist of 8 options, 3 going up and 5 going right.  In this, we want to find the number of ways to insert 3 points to move up in an 8 step path (for example, on steps 1, 4, and 5, we move up), and the 5 spots to move right will naturally fill in.  To pick 3 points from the 8 step path, there are \(C(8, 3)\) ways, meaning 56 combinations.  From C to B, we use the same method and find 6 paths.  Therefore, from A to B, there are 56*6 = 336 paths.  There are many math competition questions that are like this, for more methods, explanations, and such, search up "number of paths from a to b" or "paths on a grid"

Hopefully, this answered your question, have a great day!

288 pairs of shoes into 3 closets means 96 shoes per closet.  

96 shoes for 4 shoe racks means 24 pairs per shoe rack.  

Hopefully, this answered your question, have a great day!

This is English language arts, not math, but the answer is 

1.  The sun's gravity holds the planets in place. It provides them with heat and light.

2.  It takes Earth 365 days to orbit the sun. Jupiter takes 12 years!

3.  All of the planets in our solar system revolve around one star-our sun.

Each of the other options have little to do with the fact that the sun is the object in the center of the solar system.