Nice answer, geno.....

Another way to see this is that the 10th person plays 9 other people, the 9th person plays 8 other people (we've already counted the game against he/she played against the 10th person), the 8th person plays 7 other people, etc. Note that the 2nd person only has the 1st person left to play !!!!

So the sum of the first nine integers is just  [9 * 10 ] / 2   = 45 games.

I don't live with my mom in fact she is dead. maybe you should get to know people before you say stuff like that.

It would be 8 $${\mathtt{8}}{\mathtt{\,\times\,}}{\mathtt{3}} = {\mathtt{24}}$$

3(x-1)-(4x-5)=2(5x-1)-7    simplify both sides

3x - 3 - 4x + 5 = 10x - 2 - 7     combine like terms

-x + 2 = 10x - 9          add 9 to both sides and add x from both sides

11 = 11x                       divide both sides by 3

1 = x

The slope intercept form for a straight line has an equation:   y =mx + b

where  m  is the slope and  b  is the y-intercept.

For example:  y = -2x + 7 is a straight line that passes through the y-intercept (0,7) with a slope of -2.

That's impossible since triangles can be of different sizes.

-33/40

Can this fraction be simplefied? Lets find out!

First we factorize the numerator (top). We see that the digit sum is divisible with three. Therefore the whole number is divisible with three. 

33/3 = 11 

11 is a prime number, i.e. it has no other divisors other than one and itself.

The numerator on factorized form is therefore: 3*11

Lets factorize the denominator:

Since the last digit is 0, it must be divisible with 10 which equals 2*5

40/10 =4

The two last divisors must be 2 and 2.

OK, 40 on factorized form is: 2*2*2*5

We see that the numerator and denominator have no common divisors. Therefore -33/40 can't be simplefied. 

   Many ways to do this, this is one:

   [ -3x-y=-10 ]  (I)

+ [ 4x-4y=8 ]     (II)

= [x -5y = -2]     (III)

x = 5y-2    (IV)

substitute x with 5y-2 in the second equation:

4(5y-2) -4y =8

20y -8 -4y =8

16y =16

y=1

substitute y with 1 in (IV):

x= 5*1 -2

x= 3

Y=2(-2)-2

y = 3(-2)

y = -6

(3/5):(2/3)

Multiply the first fraction with the reciprocal of the other:

(3/5)(3/2)

Multiply the numerators (top) with each oter, and the denominators (bottom) with each other:

9/10

Recursively:  The first term is -1.

Each term after the first is found by taking the previous term times -8.

Thus, the recursive formula:  t(1) = -1

                                           t(n) = -8 · t(n-1)

If you mean  G(x)  =  x² + 4x:

(I'll use a 'y' instead of a 'G(x)'.)

Complete the square:     y + 4  =  x² + 4x + 4

Factor:                          y + 4  =  (x + 2)² 

Any equation in the form  y - k  =  (x - h)²  is a parabola with its vertex at (h, k);

therefore, for this equation, the vertex is at  (-2, -4).

You can set up a proportion:      number of people who buy           total number of people who have to buy

                                               ------------------------------    =    --------------------------------------------

                                                 number of people asked                      total number of people asked

                                                                                2 / 7  =  120 / x

Cross-multiplying:  2 · x = 7 · 120     --->     2x  =  840      -->     x  = 420

this is my method:

2a^2+2b^2+2c^2=2ac+2bc+2ac    (both side times two)

a^2+2ab+b^2+b^2+2bc+c^2+a^2+2ac+c^2=0

(a-b)^2+(b-c）^2+(a-c)^2=0

because the square of all real number always more than 0

so (a-b)^2=0 , (b-c)^2=0 ,(a-c)^2=0

so a=b=c

so this is a Equiatreral Triangle

Good job guys!

find the value of 5x-2y+3z when x=7,y=11 and z=-1. show your work

5x-2y+3z

5*7-2*11+3*(-1) Remember the order in arithmetics: 1. multiply and divide, 2. add and subtract

35-22+ (-3) Remember that +(-x) = -x

13-3 

10 

Enter it into your calculator as 10 ^ √12.

The answer is approximately  2911

Using the distributive property:

4 - x - 2 < -3x - 12    

Simplifying:

2 - x < -3x - 12

Adding 3x to both sides:

2 + 2x < -12

Subtracting 2:

2x < -14

Dividing by 2:

x < -7               

Each of the  10  will have to play  9  games each.

That would be  10 x 9  =  90  games; but ...

Each game would be counted twice: the game that Alan plays against Barb would be one of Alan's  9  but it would also be counted as one of Barb's  9  games. 

Therefore, we have to divide  90  by  2  to get a total of  45  games.

x can be any number except 0.

Sometimes, but not always, will 0^0 be 1.

My brother and I get $10.00 from our uncle. We spent $5.00 on candy. We will evenly split what's left. How much will each of us get?

My mother, my father and I drove for 10 hours. I drove the first five hours. My parents split the remaining driving time. How long did my mother drive?

2^(1/6)  ≈  1.12246...

It is an irrational number; it never terminates and it never repeats; therefore, there will be exact common fraction equivalent. 

0.9  =  9/10

First, find out how much you still owe after your down payment:

     773  -  88   =   685

Since you are going to make 5 equal payments, divide  685  by  5:

     685  ÷  5   =   137

Your monthly payment will be  $137.00.

Check:  does  5 x 137 + 88  =  773?  If so, we have the right answer; if not, we'll have to rework this...