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-28+29=1 it's just a matter trick of integers 

does olivia have facebook dam shes fit running 42 km

1 + 1/7   = 8/7

So

8/7 x 12  =  96/7

What if you use l'hospitals?

We can solve this by this "formula"

n(n-1)/ 2 = 66    multiply by 2 on each side

n(n-1) = 132   simplify and rearrange

n^2 - n - 132 = 0    factor

(n - 12) (n+11) = 0    and setting  each factor to 0, we have that n = 12 and n = -11

Reject the negative

n = 12 people

We can see this easily

The 12th person shakes 11 hands

The 11th person shakes 10 hands, etc.

So...... the sum of

11 + 10 + 9 +......+ 3 + 2 + 1  = 66

press the sine button, then put in parenthesis next to it 28, and close the parenthesis.   Divide your answer by three, then calculate the inverse function to get your answer.  Hope this works!

can you even solve that

Let  x  be the amount that the "other person" pays.

Then 1.5x is the amount of the "one person".

Together they pay $850.00:

--->   x + 1.5x  =  850

--->         2.5x  =  850

--->              x  =  $340.00

--->         1.5x  =  1.5 · 340  =  $510.00

1.4z - 6  =  2.9z + 9

Get all the variable to one side:  either subtract 1.4z from both sides or subtract 2.9 z from both sides; I'll subtract 1.4z from both sides:

       -6  =  1.5z + 9

Subtract 9 from both sides:

       -15  =  1.5z

Divide both sides by 1.5:

         Z  =  -10

$${\mathtt{1.002}} = {\frac{{\mathtt{501}}}{{\mathtt{500}}}}$$

We have that

h/sin(theta) = 20/ cos(theta) →  h = 20 tan(theta)

And

h/cos(theta) = 9/ sin(theta)   → h = 9cot(theta)

So

20tan(theta)  = 9cot (theta) →

tan^2(theta)  = 9/20

tan(theta) = (2/3)√5

Therefore

tan-1( (2/3)√5) = theta = about 56.15°

So the shorter side is given by

cos(56.15) = 9 / S      where S is the shorter side

S = 9/cos(56.15) = 16.155

And the longer side is given by

cos(90- 56.15) = 20/ L

L = 20/cos(33.84) =  24.08

Check

√[16.155^2 + 24.08^2] ≈ 29

Substitute the value for y in the first equation (y  =  -2x + 9) into the second equation:

5x  =  35 - 5y     --->     5x  =  35 - 5(-2x + 9)

                                    5x  =  35  + 10x - 45

                                    5x  =  10x - 10

Subtract 10x from both sides:

                                   -5x  =  -10

                                     x  =  2

Since  x  =  2     --->   y  =  -2x + 9     --->   y  =  -2(2)  + 9     --->   y  =  5

Let L represent the larger.

Let S represent the smaller.

"The larger is 1 less than 8 times the smaller"   --->   L  =  8S - 1

"Their sum is 179"   --->   L + S  =  179

Substitute:             --->   (8S - 1) + S  =  179

                             --->   9S - 1  =  179

                             --->   9S  =  180

                             --->   S  =  20

Since L + S = 179   --->   L + 20  =  179   --->   L  = 159

Since the smaller interior triangle is similar to the full triangle, this proportion can be created (where x is the length of the shorter leg):

9/x  = x/29

Cross multiply:  x·x  =  9·29     --->   x²  =  261     --->   x = √261

This is 28 factorial

$${\mathtt{28}}{!} = {\mathtt{304\,888\,344\,611\,713\,860\,501\,504\,000\,000}}$$

Use a proportion.

35.56                x

---------    =     -----          Cross multiply.            327.84x = 3,556                     =  10.846754514397267 %

327.84            100                                           ----------     ---------

                                                                        327.84     327.84

1) Mental math approach:

15 is 1/4 of 60, and 1/4 is 25%. So, 15 is 25% of 60.

2) Standard approach:

15 = x% *60

x% = 15/60 = 25%