All Answers 356000 Answers

Undefined....not allowed.....error

you cannot divide by zero

From 1 to 100 ==20 "9s"

From 100 to 600==100 "9s"

20 + 100 ==120 "9s", which includes counting repeats such as 99, 199, 299, 399, 499, 599.

ABC, DEF==692,307 

692307 x 4== 2,769,228

307692 x 9==2,769,228

Angle ECG = 33 degrees.

Casework!

1) Put all 4 balls into 1 box - 2 ways

2) Put 3 balls into 1 box, 1 ball into other box - 8 ways

3) Put 2 balls in both boxes - 12 ways

Total = 2 + 8 + 12 = 22.

thaks

See below:

These answers are equivalent, as shown below:

\(\frac{15}{4 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \boxed{\frac{15\sqrt{2}}{8}}\)

This process is called rationalizing the denominator.

\(\frac{30 + 19i}{2+5i} = \frac{30 + 19i}{2+5i} \cdot \frac{2-5i}{2-5i} = \frac{60+38i-150i+95}{4+25} = \boxed{\frac{155}{29} - \frac{112i}{29}}\)

a + b = 29.

There are C(6,3) = 20 ways.

The smallest positive integer n that works is 13.

Multiplying a polynomial by a constant does not change the degree       f+ ag   will be   6th degree

L * W = 192        W = 192/L

L + L  + W + W = 64

2L + 2 (192/L) = 64

2 L^2 - 64 L + 384 = 0     Quadratic Formula shows L = 24    or 8            L = 24      W = 8

20% means ==20 / 100 ==0.20

300 miles  x  1.20 ==360 miles can be covered by the new train in the same amount of time.

f(x)  =                x^3 + 3x ^2 + 4x - 7 

g(x) = -7x^4 + 5x^3 +    x^2         - 7

I am guessing it is 3 + 1 = 4?

This is the second time you posted this and you got the same response both time.

Most of the answerers here will ignore a string of questions in the same post like this.

There is strictly a one post = one question policy.

I am blocking both your threads. 

I do not want people to do all your homework for you.

I've done this one before somewhere ... so has Heureka.

I'll start you off (although there may be an easier way)

3 + x == 2^2 (mod 3^3)

3 + x == 4 + 3^3K

x == 1 + 3^3K

this would also mean that

x == 1 + 3K

5 + x == 3^2 (mod 5^3)

5 + x == 9 +  5^5L 

 x == 4 +  5^3L 

x == 4+ 5L

x == -1 + 5L

7 + x == 4^2 (mod 7^3)

7 + x == 16 + 7^3M

x == 9 + 7M

x == 2 +7M

First I solved  1+3K = -1+5L      and got   x= -1 mod 15

Then I solved    x=1+15a  with  x = 2+7M  and got   x=79+105b

So I got an answer of 79 but I could easily have made a careless error.

I use the Euclidean Algorithm to solve the diophantine equations.  

Find a.

Hello Guest!

\(f(x)=\frac{y_2-y_1}{x_2-x_1}\cdot(x-x_1)+y_1\\ f(x)=\frac{-5-11}{4-1}\cdot(x-1)+11\\ f(x)=-\frac{16}{3}x+\frac{16}{3}+11\\ \color{blue}y=-\frac{16}{3}x+\frac{49}{3}\ |\ \cdot 3\\ 3y=-16x+49\\ 3y+16x=49\ |\ /49\\ \frac{3}{49}y+\frac{16}{49}x=1\\ \color{blue}\frac{y}{b}+\frac{x}{a}=1\)

\(a=\dfrac{49}{16}\)

  !

Don't be rude Proyaop, it gets you nowhere.  

Besides I think you are better than that.

When someone tries to help you, you say thank you! (And you do not take points off them!)

Do you still want help?  You didn't state, one way or the other.

It was 5 :(

thanks asinus and thx for the reminder melody :D

\(\sqrt{2}+\sqrt{3}+\left(\frac{1}{2\sqrt{2}+3\sqrt{3}}\right)\)

\(\sqrt{2}+\sqrt{3}+\frac{1}{2\sqrt{2}+3\sqrt{3}}\)

\(\frac{\sqrt{2}\left(2\sqrt{2}+3\sqrt{3}\right)}{2\sqrt{2}+3\sqrt{3}}+\sqrt{3}+\frac{1}{2\sqrt{2}+3\sqrt{3}}\)

\(\frac{\sqrt{2}\left(2\sqrt{2}+3\sqrt{3}\right)}{2\sqrt{2}+3\sqrt{3}}+\frac{\sqrt{3}\left(2\sqrt{2}+3\sqrt{3}\right)}{2\sqrt{2}+3\sqrt{3}}+\frac{1}{2\sqrt{2}+3\sqrt{3}}\)

\(\frac{\sqrt{2}\left(2\sqrt{2}+3\sqrt{3}\right)+\sqrt{3}\left(2\sqrt{2}+3\sqrt{3}\right)+1}{2\sqrt{2}+3\sqrt{3}}\)

\(\frac{14+5\sqrt{6}}{2\sqrt{2}+3\sqrt{3}}\)

\(-\frac{-17\sqrt{2}-22\sqrt{3}}{19}\)

\(\frac{17\sqrt{2}+22\sqrt{3}}{19}\)

17+19+22=58, just the same as proyaop's answer!

\(\frac{1}{\sqrt{2}}+\frac{3}{\sqrt{8}}+\frac{5}{\sqrt{32}}\)

\(\frac{1}{\sqrt{2}}+\frac{3}{2\sqrt{2}}+\frac{5}{4\sqrt{2}} \)

\(\frac{4}{4\sqrt{2}}+\frac{6}{4\sqrt{2}}+\frac{5}{4\sqrt{2}}\)

\(\frac{15}{4\sqrt{2}}\)

hmm........ we got different answers

Appreciate the help! 

Wow! This is really a neat solution!