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Rule:  a₁  =  16          a_n  =  ½·a_{n - 1}  

a₁  =  16  =  2⁴

a₂  =    8  =  2³

a₃  =    4  =  2²

a₄  =    2  =  2¹ 

Notice that each answer can be written as a power of 2.

Also notice that the subscript of the term when added to the exponent results in 5.

Combining these two ideas:  a_n  =  2^{5 - n}

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Cool, thanks!

Can you explain, -10/13 as the slope? Oh wait, nevermind

Thanks guys! I appreciate it!

Yes.

Median is the middle number in the list when listed in ascending order   ..... if there are TWO numbers in the middle...it is the average of those two.

Vertex form of parabola

y = a (x- -2)^2 -3

  =  a ( x+2)^2 -3           sub in the point given to calculate 'a'

-2 = a (-5+2)^2 - 3

  a = 1/9

y = 1/9 (x+2)^2 -3     <======== expand this to find your answer   ( well....you really should be able to see the answer without expanding)

and how do i find the median

Find the median of the original set and multiply it by 26

or: 

multiply each of the original numbers by 26 and find the median of this new set of numbers.

0.6 x 3.50  +  1.8 x 2.50  =  6.60

Point  7,4     slope = 3/2

(y-4) = 3/2 ( x-7)    

x³ - x² - x  =  x(x² - x - 1)  =  x(0)  =  0

https://web2.0calc.com/questions/counting_47060

Carpenter rate = 1 job / 1

assistant rates =   1 job / (6/10)

All three    1 job / ( 1 + 6/10 + 6/10)  = 1 / 2.2 = 5/11

Another (but longer) method ( because I can never remember the equation for the minumum distance between a line and a point)

4x+3y+7=2x-y+5     re-arrange to y = -1/2 x -1/2

Now use distance formula

d^2   =  (x -3)^2  + (4 - (-1/2x-1/2))^2

             x^2 -6x + 9    +  1/4x^2 + 4.5 x + 20.25

  d^2        =  5/4 x^2 - 1.5 x + 29.25          <====== take derivative and set = 0

                  10/4 x -1.5 = 0

                       x = 0.6            <====== sub this value into the line equation to find y = - 0.8

NOW, use the distance formula between (0.6, -0.8)   and (3,4)

        d^2 = ( 3 - 0.6)² + (4- - 0.8)² 

         d^2 = 28.8

           d = sqrt (28.8)             ( which = same answer that chris found....)   

the question said this so i copied and pasted lol btw my first language is english :)

g ( x) =   x^2  - 11x  + 30

Let's  assume  that    f(x)   is of the form    x^2 + bx + c

Then

g (f(x)  =  [ x^2 + bx + c ] ^2  - 11 [ x^2 + bx + c ]  + 30  =  x^4  -14x^3  + 62x^2 -91x + 42

Simplify

x^4  + 2bx^3  +  (b^2 + 2c) x^2  + 2bcx  + c^2   - 11x^2 - 11bx -11c  + 30  =

x^4   -14x^3  + 62x^2  -91x + 42

x^4  + 2bx^3  + (2c + b^2 - 11)x^2  + ( 2bc - 11b)x   + [c^2 -11c + 30]   =

x^4  - 14x^3  + 62x^2  - 91x + 42

Equate  coefficients

2b =  -14

So   b =  -7

2c + b^2 - 11 = 62

2c + 49 - 11  = 62

2c + 38  = 62

2c = 24

c = 12

So

f (x)  =   x^2   - 7x   + 12

Check

g(f(x)   =

[ x^2 - 7x + 12 ] ^2   - 11 [ x^2 - 7x + 12 ] + 30   =

x^4 - 14 x^3 + 62 x^2 - 91 x + 42

Like this:

a/c  =  [ a/b ] / [ c/b ]  =  [ sqrt(10) / sqrt(21) ] / [ sqrt(15) / sqrt(14) ]

                                  =  [ sqrt(10) · sqrt(14) ] / [ sqrt(21) · sqrt(15) ] 

                                  =  [ sqrt(10) / sqrt(15) ] · [ sqrt(14) / sqrt(21) ]

                                  =  [ sqrt(2) / sqrt(3) ] · [ sqrt(2) / sqrt(3) ]

                                  =  2/3

*** deleted ***

Rearrange  the  equation   in  the form    Ax + By + C  =  0

2x + 4y + 2    =  0

We have  the following  for the distance from  (x, y)  to  the line   =

l Ax  + By + C l                         l 2 (3)  + 4 ( 4)  + 2  l               24               24

________________  =         ___________________   =    ______  =   ______  =

  sqrt [ A^2 + B^2]                     sqrt  [ 2^2 + 4^2 ]                 sqrt 20        2 sqt 5

12 / sqrt 5   =   

(12/5) sqrt (5)

See the graph here :  https://www.desmos.com/calculator/3dgerbkzta

The left-hand limit is 0.

The right-hand limit is -5.