geno3141

The formula for the sum of an arithmetic series is:  Sum  =  n(f + l)/2

n = number of terms = 28

f = first term = 25

l = last term =  not yet known

The formula for the last term of an arithmetic series is:  l = f + (n-1)d

f = first term = 25

n = number of terms = 28

d = common difference = 6

----->     l  =  25 + (28 - 1)·6  =  187

Sum  =  28(25 + 187)/2  =  answer ...

The divisors of 5 are 1 and 5. The divisors of 4 are 1, 2, and 4.

Including both the positive and negative possibilities:  1/1,  -1/1,  5/1,  -5/1,  1/2,  -1/2,  5/2,  -5/2,  1/4,  -1/4,  5/4,  -5/4

There are 12 possibilities.

At 6:30 the minute hand will be pointing directly at the six and the hour hand will be half-ways between the six and the seven.

The number of degrees between any two consecutive hours on a clock is 30^o.  [360^o / 12  =  15^o]

Therefore half-ways between the six and the seven is 15^o.  [30^o / 2  =  15^o]

This is not that difficult by finding and adding the individual terms; however, you can use the formula for the

sum of a finite geometric series:     Sum  =  a₁ · (1 - rⁿ) / (1 - r)

where  a₁ = 2  and  r = 2:                Sum  =  2 · (1 - 2⁹) / (1 - 2)  =  1022

 Compare this to:  2¹⁰  =  1024

x² + 10x + 25  =  4     --->     (x + 5)²  =  4

                                either     x + 5  =  2     or     x + 5  =  -2

                                                    x  =  -3    or           x  =  - 7

Choose the correct answer ...

I'm trying to interpret your question:

right triangle(ABC) with right angle(B) and hypotenuse(AC).

BD is an altitude.

Since AC = 27 and AD = 3, DC = 24

Use this relationship:  AD / BD  =  BD / DC

                                      3 / BD  =  BD / 24

                                          BD²  =  72

                                            BD  =  sqrt( 72 )

triangle(ADB) with also be a right triangle with hypotenuse AB.

use the Pythagorean Theorem:  AD² + BD²  =  AB²:

                 AB²  =  3² + ( sqrt(72) )²

                         .... 

(x + y)² + (x - y)²  =  (x² + 2xy + y²) + (x² - 2xy + y²)  =  2x² + 2y²

     =  2( sqrt(2006) )² + 2( sqrt(2007) )²

     =  2( 2006 ) + 2( 2007 )

     =  ....

Since twelve hungry teenagers can devour a very large pizza in 20 minutes, it takes 240 minutes (12 x 20) of chewing.

240 / 18  =  ...     number of teenagers  (you'll have to decide what to do with the fraction)

See your original post.

If you have no other way of approaching this problem, you can do it by listing all the possibilities:

PWW  =  (5/9)(4/9)(4/9)  =  ...

WPW  =  (4/9)(5/9)(4/9)  =  ...

WWP  =  (4/9)(4/9)(5/9)  =  ...

PPW  =  (5/9)(5/9)(4/9)  =  ...

PWP  =  (5/9)(4/9)(5/9)  =  ...

WPP  =  (4/9)(5/9)(5/9)  =  ...

PPP  =  (5/9)(5/9)(5/9)  =  ...

and adding all the results together.

This can also be done by using combinations but, if you forget the 'easy' way, don't give up!