geno3141

sqrt( 1096 )  =  sqrt( 4 · 2 · 137 )  =  sqrt(4) · sqrt(2·137)  =  2 sqrt(274)

Since 2 and 137 are prime numbers, 2·137  =  274  can't be removed from the square root.

Since BD bisects angle(ABC), angle(ABD)  =  angle(DBC).

                                                     ½y + 10  =  y + 4

Subtract ½y from both sides:                 10  =  ½y + 4

Subtract 4 from both sides:                      6  =  ½y

Multiply both sides by ½:                         12  =  y

So:  angle(ABD)  =  ½y + 10  =  ½(12) + 10  =  6 + 10  =  16

       angle(DBC)  =  y + 4  =  12 + 4  =  16

Angle(ABC)  =  angle(ABD)  +  angle(DBC)  =  16 + 16  =  32.

When adding a negative number to another negative number, your answer will be negative.

Examples:     - 6 + -4  =  -(6 + 4)  =  -10

                      -7 + -2  =  -(7 + 2)  =  -9

First:  find slope:  m  =  ( y₂ - y₁ ) / ( x₂ - x₁ )           x₁ = -4     y₁ = 5     x₂ = 1     y₂ = 0

                            m  =  ( 0 - 5 ) / ( 1 - -4 )

                            m  =  -5 / 5

                            m  =  -1

Use point-slope form:     y - y₁  =  m( x - x₁ )

                                       y - 5  =  -1( x - -4 )

                                       y - 5  =  -1( x + 4 )

                                       y - 5  =  -x - 4

                                            y  =  -x + 1

[Your English is fine!]

ElectricPavlov is correct.

One way to analyze the problem:  

     Each worker worked 10 eight-hour days for a total of 80 hours (10 x 8).

     Since there were four workers, they worked a total of 320 hours.

If you want to build the stage in 5 eight-hour days, each worker needs to work 40 hours (5 x 8).

The total number of hours needed is still 320 hours; since each worker works 40 hours, calculate  320 / 40 to get 8.

You will need 8 workers. 

Combination:     _nC_r  =  n! / [ (n - r)! · r! ]

If you assuming that only one number is chosen at a time, if there are  n  numbers, your answer will be  n!. 

There are several ways to work this problem; this is one way:

                                                              x² < 1

Subtract 1 from both sides:              x² - 1 < 0

Factor:                                  (x + 1)(x - 1)  < 0

Analysis:  If two numbers are multiplied together and their answer is negative (less than 0), then either the first number is

                positive and the second number is negative or the first number is negative and the second number is positive.

                For this problem, the two numbers are  x + 1  and  x - 1.

So: first number positive, second number negative     or    first number negative, second number positive

                      (x + 1) >  0   and  (x - 1) <  0                            (x + 1) < 0   and  (x - 1)  > 0

                       x + 1  >  0    and   x - 1  <  0                              x + 1  < 0   and    x - 1  >  0

                             x  >  -1   and        x  < 1                                     x  <  -1  and        x  >  1

                                    -1  <  x  <  1                                                   <this is impossible>

Thus:     -1  <  x  <  1

The formula for permutations is:  _nP_r  =  n! / (n - r)!

So:                  ₃₀P₂  =  30! / (30 - 2)!  =  30! / 28!

                                                           =  [ 30·29·28·27·26·...·4·3·2·1 ] / [ 28·27·26·...·4·3·2·1 ]

(which, after cancelling, becomes)     =  30·29  =  870

(1/6)²⁸  =  1 / 6, 140, 943, 214, 000, 000, 000, 000  (approx)

            =  1 in 6.14 x 10²¹  (approx)

However a septillion is 1 in 10²⁴, so (1/6)²⁸ misses a septillion by (about) a factor of 1,000.

(2w)² · (5w)²  =  (2xw) · (2w) · (5w) · (5w)  =  (2 · 2 · 5 · 5) · (w · w · w · w)  =  100w⁴