All Answers 355939 Answers

h(x) = f (g(x) =  3 (2x+8) + 4  = 6x +28

inverse is     (x-28)/6

If a number is congruent to n modulo n, then it is congruent to (n-n) modulo n, which means it is divisible by n.

Now, (using a calculator because I'm lazy) adding all of these numbers up, we get 

1 + 12 + 123 + 1234 + 12345 + 123456 + 1234567 + 12345678 + 123456789 + 1234567890 + 12345678901 + 123456789012 = 137174210008. 

Now n must be a factor of 137174210008, and n must be less than 9, so testing, we get that only 2,4, and 8 divide 137174210008 and are less than 9, so \(\boxed{n=\{2,4, or \space 8\}}\)

Hope this was helpful :)

Alternative solution:

Pair the numbers up as follows

We can see that there are 2010/2=1005 rows, and the sum of each row is 2011, which is equal to 1 modulo 2010, thus the answer is

1005*1 = 1005

Hope this helped :)

999 mod (9 - 1) ==7 - the 999 count would start from 1 to the left as number 993 (1), 994 (2), 995 (3), 996 (4), 997 (5), 998 (6) and 999 (7).

Add 'x' to both sides and add 5 to both sides to get

3x <= 17    divide by 3

x <= 17/3           <====== you can finish I hope .....

We can first factor the denominator as \(\frac{1}{(x)(x+2)}\). In order for this to be a terminating decimal, both \(x\) and \(x+2\) have to only have factors of 2 and/or 5. Testing small values of x, we find that \(x = \{2,8, etc.\}\). Looking at this, we can see that the second smallest integer value of x is \(\boxed{8}\)

That is correct

What is the remainder when 5^(301) is divided by 7?

Let's look for a pattern

5^1              5     mod7 = 5                5^(6n+1) = 5 mod 7

5^2              25     mod 7 = 4            5^(6n+2) = 4  mod 7

5^3            125   mod 7 = 6             5^(6n+3) = 6  mod 7

5^4            625  mod 7 = 2              5^(6n+4) = 2  mod 7

5^5            3125 mod 7 =3              5^(6n+5) = 3  mod 7

5^6           15625  mod 7 = 1           5^(6n) = 1  mod 7

7         78125 mod 7 = 5

8         390625 mod 7 =4

an so we have a pattern

301 = 1 mod 6  

so the remainder will be 5

Umm, this seems like homework in Chemistry, search the question up and you will see that.

Chegg costs money!

Fun Fact: A question from 2015.

Straight

Straight, that definitely was not helpful.

Hartelin was reporting a broken calculator feature.  

Maybe it has been fixed,  it is working alright now.

Hello Hartelin,

When I use x 

Example: x+1=3 = Error: timeout

IT GIVES Error: Timeout

WHY????

HELP PLEASE

That is coming because you type something nonsense or don't know how to do that equation.

Hmm, x+1=3 => x=2, they said by me, but actually, you can calculate this yourself.

But if "Error: timeout" comes, and you want to know the solution for e.g x than you can also use WolframAlpha (I don't want to make advertisement).

Hope that was helpful.^^

Straight

Hello Guest,

there is a calculator, namely: Remainder Calculator | The best Long Division Calculator (calculatored.com)

and the link https://www.calculatored.com/math/algebra/remainder-calculator.

I also got the remainder 5.

Hope that was helpful.^^

Straight

Of the three-digit integers greater than $500$, how many have two digits that are equal to each other and the remaining digit different from the other two

2 zeros :  4

1 zero : 5*2=10

the rest have no zeros

2 of 1,2,3,4      :    4*5 = 20

2 of 5,6,7,8,9   and one 1,2,3 or 4  :  5*4*2=40

2 of 5,6,7,8,9   and one 5,6,7,8,9  :  5*4*3=60

4+10+20+40+60 = 134

5^(301)  mod 7==5 - the remainder

1 + 2 + 3 + 4 +.........+ 2010 ==[2010 x 2011] / 2==2,021,055 mod 2010==1,005 - the remainder

Thank you very much...

You are very welcome :)

In right triangle ABC with B = 90 , we have 2 sin A = 5 cos A. What is tan A?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

2(sinA) = 5(cosA)

sinA = 2.5(cosA)

We know that  (sinA)² + (cosA)² = 1

x² + (x / 2.5)² = 1 

x = 0.92847669                (x = sinA)

cosA = x / 2.5 = 0.371390676

Angle A = 68.19859051º

tanA = sinA / cosA  

sum_(n=1)^2012 n^2009 = 2508173028 - these are the last 10 digits.

Thanks Melody youre the best 

sin b = cos c = 4/17

....and we sometimes se Q's  about     fluid dynamics     statics    dynamics   thermodynamics    mechanics of materials   electronics   etc   

500 should NOT be included....Q asks for numbers GREATER than 500 .....

We field all Q's      Math   Physics   Chemistry   Biology    etc ..... but technically it is a Math forum