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Correction... 

The length of the side of a square is 7.534 cm. 

Where is the question "at the bottom"??

8.73  +  8.86 ==17.59 Liters of purple paint.

[17.59 / 4 ] - [0.23 / 4]==4.3975  -  0.0575 ==4.34 Liters of purple paint in each container.

Check: 4.34 x 4 ==17.36  +  0.23 [left over paint] ==17.59

A==Alex,   M==Michelle,   N==Nurul

A ==2M

2M + 1/3M + 5/7N ==859

N - 5/7N ==58, solve for M, N

N ==203 - tarts that Nurul had

M ==306 -tarts that Michelle had to start with.

306 - (1/3 * 306) ==306 - 102 ==204 - tarts Michelle had left.

Let his money==M

M - (M/2 + 100) ==M/2 - 100 - money left after day 1
1/3 * [M/2 - 100] ==[M - 200] / 6 - money left after day 2 

1/2*[M - 200] / 6 ==10, solve for M

[M - 200] / 12 ==10
[M - 200] ==10 * 12 ==120
M ==120 + 200 ==$320 - Money he brought to the trip.
                                                                    

5 + 7 + 11 + 13 ==36 mod 3 ==0

Compute the sum 1 + 4 + 7 + ... + 2005 + 2008.

It is an arithmetic progression

a=1   d=3     L=2008

Tn=a+(n-1)d

2008=1+(n-1)*3

2007/3 = n-1

669=n-1

n=670

sn=n/2(a+L)

Sn=670/2    *(1+2008)

Sn=335  *2009

Sn=673015

My first tip is to draw it.

Have you done that?

Also, when someone talks about the distance of a point to a line they are referring to the perpendicular distance.

There are 2 possible points Cs.

Graph it to see what I mean

Note that f(x) = 1 has exactly 6 solutions (draw a line through y = 1 and count how many times it cuts through the curve).

Also, f(x) = 2 has exactly 6 solutions (draw a line through y = 2 and count how many times it cuts through the curve).

Also, f(x) = ...

Continue in this way until the line through the integer value of y does not cut through the curve exactly 6 times.

Because you said there is one unit between lines, I've assumed the fine grid is numbered 1, 2 etc.  However, your labels give the coarse grid as  having labels 1, 2 etc, in which case, only the value f(x) = 1, is relevant.

We have \(z^{49}+z^{50}+z^{51}+z^{52}=z^{49}(1+z+z^2+z^3)\)

The term in parentheses factors as \(1+z+z^2+z^3=(z+1)(z^2+1)\)

So, if \(z^2+1=0\) then \(z^{49}+z^{50}+z^{51}+z^{52}=0\)

Hello Guest!

I guess

\(\sqrt[3]{6x-12}+4=12\ |-4\\ \sqrt[3]{6x-12}=12-4\ |\ ^3\\ 6x-12=8^3\ |\ +12\\ 6x=512+12\ |\ :6\\ \color{blue}x=87.\overline 3\)

The length of the side of a square is 7.542 cm.

Hello Guest!

\(\sqrt{\frac{7x-10}{9}}=4\ |\ ^2\cdot 9\\ 7x-9=4\cdot 9\ |\ +9\\ 7x=4\cdot 9+9\ |\ :7\\ x=\frac{45}{7}\)

\(\dfrac{\sqrt{7x}-10}{9}=4\ |\ \cdot 9\ +10\\ \sqrt{7x}=4\cdot 9+10\ |\ ^2\\ 7x=46^2\ |\ :7\\ x= \frac{2116}{7}=302\ \frac{2}{7}\)

Write again what you mean, please.

  !

Let's say smaller leg is X

The longer leg is x+8

Hypo is x+14 

a^2 + b^2 = c

so x^2 + (x+8)^2 = (x+14)^2. 
Expand
x^2 + x^2 + 16x + 64 = x^2 + 28x + 196.
Minus x^2 from both sides

x^2 + 16x + 64 = 28x+196
Minus 16x 

x^2 + 64 = 12x + 196
Minus 64

x^2 = 12x + 132.
or
x^2-12x-132 = 0.

From there, hopefully you can solve 

So this is a common cause of adding numbers together with large numbers (IDK what its called)
Basically, the equation is: Add the First and last term. (in your case it's 2009). Then divide by 2, and multiply by a number of numbers in that said sequence. 
So how do we how many numbers there are in the sequence? We can use the Explicit function: F(x) = 1+3 (x-1), where f(1)=1. This means that 2008-1 = 2007/3 = 669. This means there are 70 terms. So we have 2009/2) x 70. Or 2009 x 35 which is equal to 70315. 
To double-check my work, I used Wolfram Alpha! 

Area = 2 * 13

Let tangent point on a circle be X

KX = sqrt(KT² - TX²)

KX = 2√8

Hint.  One will be between the numbers, and the other will be outside.

Draw the number line and figure it out.

area of trapezoid = (base1 + base2)*height / 2

(5+8)*4/2 = 26

I have not worked it out properly.  I just drew the pic.

Looks like about 7

Nice logic Textot!   

That makes your way nice and simple.    

tan(Y) = -E-    on my calculator  

The wrong question cannot have the right answer!!!