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There are 8 choices for the first digit, then 10 for the second, third, and fourth, then 1 for the rest.  So there are 8*10*10*10 = 8000 possible telephone numbers.

The graph of (x - 3)^2 + (y - 5)^2 = 16     This is a circle    centre (3,5) radius 4

is reflected over the line y = x + 2.            

I will find the perpendicular distance of y=x+2 to (3,5)

x-y+2=9       (3,5)

\(d=\frac{|3*1+5*-1+2|}{\sqrt{1^2+1^2}}=0\)

So the line goes through the centre of the circle.

So you are refecting the circle over a diameter.  So what does this mean?

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The new graph is the graph of the equation x^2 + Bx + y^2 + Dy + F = 0  for some constants B, D, and F. 

Find B + D + F.

I take half of Jeremy's money and divide it into 7 equal piles. Six of these piles b**w away in the wind, but from the seventh pile, I take 2 dollars and hand Jeremy the rest, which is 8 dollars. How much money, in dollars, did Jeremy begin with?

Work backwards !

7th pile is   8+2=10  

So what now?

No, I didn't assume n1 = n2.  The conclusion holds for each pair of terms separately.  

This means 2*k - 3 = -21

Can you now rearrange this to find k?

Yes indeed option d is too obvious, option c would be the right one since you arrived at the answer by only taking n₁ = n₂ (= n) commonly right? 

Thank you so much!

As follows:

The quoted answer d) is rather strange, since the question specifies that the n's are positive integers!. 

What you have done is to find the vertical height of the platform from ground to top.  Now you have that and the 110' you can use Pythagoras' theorem to find the length of the zip line.

"He charges 1 euro cent for the first meter, but then the price is to be increased by 50% from meter to meter."

Let's take this into account as an GP such that

       GP = 1, 1.5, 2.25,... and so on

⇒ a = 1     and      r = 1.5 

Length of the well is 37 m i.e. the no. of terms in the GP is 37. 

Now, in order to calculate the total amount, we find the sum of 37 terms in the GP

         ∵ \({S}_{n}={a(r^n-1)\over r-1}\)

        ⇒ \({S}_{37} = {1((1.5)^{37}-1)\over 1.5-1} ≈ 6552491.2\)

Thus he has to pay 6,552,491.2 euro cents. 

Thanks Amy  

BigBoi, next time you ask a repost question can you please give the address of the original post.

It is better that all the answers are together even if some are not good.   

In order to find the no. of possible sequences, you find the no. of ways 1, 2, 2, 3, 3 and 3 can be arranged. 

So, no. of digits = 6

      no. of 2's = 2

      no. of 3's = 3

Possible no. of rolls \(={6!\over 2!×3!}=60\)

Hope you got it. 

Is it okay if I answer? 

Spikers = 5, Setters = 4 and 1 either way.

Each 2-person team should have 1 setter and 1 spiker. 

Case 1 : If spikers = 6 and setters = 4                 Case 2 : If spikers = 5 and setters = 5

Then no. of ways \(={^6} C_{1}×{^4}C_{1}\)                         Then no. of ways \(={^5} C_{1}×{^5}C_{1}\)

In order to get total no. of ways, add the respective values you get in both cases. 

We want the discriminant to be positive:

m^2 - 4 > 0

m^2 > 4

The solution is (-inf,-2) U (2,inf).

ΔABC ~ ΔACD        BD = CD = 2          ∠B = ∠CAB =  β  

CD / AC = AC / BC

2 * 4 = (AC)²

AC = √8

sinβ / 2 = sin49 / √8

Angle B ≈ 32.253º

Nice solution. :))

=^._.^=

3  ( x^2 - 6x  +  4)       complete  the  square on x

3  ( x^2  - 6x  +  9  + 4  - 9)

3  [ (x - 3)^2  -  5  ]

3 ( x - 3)^2  -  15

(a, h , k)  =  ( 3 , 3  ,  - 15)

a + h +  k  =   -9

x  +  1/y  =   1

3 +  1/y  =  1

1/y = -2

y  =  -1/2

y + 2/z   = 1

-1/2  + 2/z   = 1

2/z  =  3/2

z/2  =  2/3

z  =  4/3

xyz  =  (3) (-1/2) (4/3)  =  -2

B  = A + 4

C =  A - 2

D =  A  + 6

So

A  +  B   +  C +  D   =  36

A + A + 4  + A - 2   + A + 6  =   36

4A  +  8   =  36

4A  =  36 - 8

4A  = 28

A = 7

B = 11

C = 5

D = 13

You can take it  from  here......

2 log ( a - 2b)  = log a  + log b    .....using a  coulpe of log properties

log (a - 2b)^2  =  log (ab)              which implies  that

( a -  2b)^2    =  ab

a^2  - 4ab + 4b^2   = ab

a^2  - 5ab  + 4b^2 =   0         factor as

(a  - 4b)  ( a - b)  =   0                       

a - 4b   =  0                  or             a -   b =   0

a = 4b                                           a =  b                      

a/b =  4                                        a/b =  1

Assuming a, b    are positive   ......

The second  solution either makes     (a -2b)   negative  and  we  can't take the  log of a  negative

So

a/b =   4

yeah it seems to be glitched -- but i somehow managed to see the image by clicking around LOL

the exterior angles of a polygon ALWAYS add up to $  180^\circ $

since we know that, we can write the sum of all that we are given and write it all equal to $ 180^\circ $

$ \large[ (5x+4)+(4x+9)+(9x-6)+(4x+1)+(7x+4)=180 \large]^\circ $

$(5x+4+4x+9+9x-6+4x+1+7x+4=180)^\circ $

$ ( 29x+12=180)^\circ $

$ ( 29x=168)^\circ  $

$ \boxed{ (x=\frac{168}{29}})^\circ  $ which we can say just about $ \boxed{5.8^\circ}  $

The smallest f(x) * g(x) can be is -15. (-5*3 or 5*-3)

The largest f(x) * g(x) can be is 15. (5*3 or -5*-3)

=^._.^=

i would use this formula:

$ BD=\frac{2\times a\times b}{a+b}\sin(120) $

:D

I can't see the image. 

=^._.^=

x =  180   -  44  -  57  =   180   - 101  =    79°