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Slope  between  the two points  =  [ 5 - - 3 ]  /  [ 4 - 2 ]   =   8/2  =  4

Equation of the line  using ( 4, 5)

y = 4 ( x - 4)  +  5

y = 4x  - 16 + 5

y =  4x  - 11         rearrange  as

4x  - y  =  11

the answer is 70

The common  difference  is   10 - -8  =   18

We need to  evaluate  this

10  -  18 ( 17 - 2)   =

10  - 18 * 15  =

10  -  270  =

-260    =  2nd term

Welcome.....

We  can  find  the 10 th   term   as

500000 (5/2)^(4)   =   

19531250

k(x) = x^2 - 4x + 1.

Thanks!

Second one

We need  to solve  this

-6t^2 + 43t  =  77         rearrange  as

6t^2  - 43t + 77  =  0        factor

(3t  - 11) (2t - 7)  =  0

Both factors  set to  and  solved for t  gives

3t - 11  =  0                             2t - 7  =  0

3t =  11                                    2t  =  7

t = 11/3  ≈ 3,66 sec                  t = 7/2  =  3.5  sec

y = x^2 - 8x  -  33

We  want  to  solve  this

x^2  - 8x  -  33  =  0        factor

(x  - 11) ( x + 3)  =  0

The  first  factor set to 0  is what we need

x - 11  =  0

x  = 11     =     the  minimum  units needed to break even 

We  want  to  solve   this

25  +  4 ( n - 1)    >  120         simplify

25  +  4n - 4  >   120

21  + 4n  >  120

4n  >  120  -  21

4n >  99

n >  99/4

n >  24.75

She will  exceed  120  sit-ups  on  June 25th

The commo difference is    9

The  27th term is  given by

1  +  9 ( 27 - 1)  

1 +  9 * 26   =

235

IInside each  conference,  the number of  games played  = 

4 [ 7 + 6 + 5 + 4 + 3 + 2  + 1] =  4 * 28  =    112  games

Between  the  conferences   2* ( 8 * 8)   =   128  games are played

So  the total games played =  

2 * 112  +  128   = 

352

We  have  the folllowing  system

a3^3 + b 3^2  + c3 + d  =  2

a4^3 + b4^2 + c4 +  d  =  4

a5^3 + b5^2  + c5  + d  = -2

a6^3 + b6^2  + c6 +  d  =  8               simplify

27a  +  9b  +  3c + d  =  2

64a  +  16b  +  4c + d  = 4

125a  + 25b + 5c + d  =  -2

216a + 36b  +  6c + d  =  8

This  is a little lengthy to solve  (but  not impossible)...so....I will use a CAS  to solve

a  = 4     b   = -52    c  = 218   d  =  -292

f(0)  =  d =   -292

Set  the equations equal

2x^2  +  7x  - 4   =  x^2  + 4x  +  6              subtract  the  right side from  the  left

x^2  +  3x  - 10   = 0        factor  as

(x + 5)  ( x - 2)  =   0

Set  each  factor  to 0  and solve  for  x

x + 5  = 0               x - 2  =  0

x = -5   = a                    x = 2 = c

So

c -  a   =   2 - (-5)   =   7

Ohh, thank you. 

I accidentally forgot the 2. :))

=^._.^=

We got the same answer.

Yayyyyy :DDD

=^._.^=

Since 6 points in a circle determine a hexagon, and 3 points determine a triangle:

\({n \choose 6} = {n \choose 3}\\ \frac{n!}{6!(n-6)!}=\frac{n!}{3!(n-3)!}\\ 6!(n-6)!=3!(n-3)!\\ 4\cdot5\cdot6=(n-3)(n-4)(n-5)\\ \)

Notice that the terms on both sides form an arithmetic progression. If you set a term on the RHS to the corresponding term on the LHS, you get (I used the smallest term as an example):

\(4=n-5\\\boxed{n=9}\)

oh no I got sniped

Hello and welcome to web2.0calc :)))

(n)(n-1)(n-2)/3/2 is how many points of 3 you can select from n points (or number of triangles)

(n)(n-1)(n-2)(n-3)(n-4)(n-5)/6/5/4/3/2 is how many points of 6 you can choose from n points (number of hexagons)

(n)(n-1)(n-2)/3/2 = (n)(n-1)(n-2)(n-3)(n-4)(n-5)/6/5/4/3/2

1 = (n-3)(n-4)(n-5)/6/5/4

120 = (n-3)(n-4)(n-5)

n = 9

=^._.^=

thats wrong

one post = one question.

Do not post all your homework for other people to do for you.

If you want more explantion, always ask for it.

I mean you can say, "Thanks for the answer but can you show me how you got that please"

I like it when people ask me questions related to my answer. 

It means I actually have an audience and someone at the other end is actually trying to learn from me.

Multiply by the scale factor

P(2, 2)         P'(1, 1)

R(6, 2)         R'(3, 1)

Q(6, 5)        Q'(3, ⁵/₂)

A = (√3)/4 [2(sin15º * √48)]²