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1.  y  = x^2 - 8x + 12

y - 12  =  x^2 - 8x           complete the square on x

y - 12  + 16  =   x^2 - 8x + 16      simplify

(y + 4)  = (x - 4)^2

We have the form  (4p)(y - k) = (x - h)^2

The vertex  =   (h, k) =   ( 4, - 4)

Axis of symmetry    x  = 4

p  = (1/4)

The focus  =  ( 4 , - 4 + p)  =  ( 4, - 4 + 1/4)  =  ( 4, -15/4)

The directrix  =  y = (k - p)  =   - 4 - 1/4   =   -17/4

Here's a graph : https://www.desmos.com/calculator/am3svgafgw

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1.  2N

2.  xy

(5A - 4) (B - 1) / 3  - AB  = 2A + B

(5A - 4) (B - 1) - 3AB  = 6A + 3B

5AB - 4B - 5A+ 4 - 3AB  = 6A + 3B

2AB - 7B - 11A + 4  =  0

B (  2A - 7)  = 11A - 4            or            

B  =   ( 11A - 4)                                     

         ________                                           

           (2A - 7)                                               

We have two possibilities

A     B

4    40

38   6

The max  candies is either

(5(4) - 4) ( 40-1)/3   =  16 * 13  =  208     or

(5(38) - 4) (6 - 1)/3    = 310

So.....310 candies

(25, 26, 31, 33, 51), (53, 54, 70, 71, 72)

1. Mean  = 48.6 

    Median  =  [51 + 53] / 2  = 104/ 2 = 52

    Q1   =  31

    Q3   =    70  

    Interquartile range  = 70 - 31  =  39

2 Standard deviation for a sample  = 18.8

3.        [ 60 - 48.6]

           _________   =  .606  =  z score

              18.8

The %  passing  ≈ .7291

1) 8 is the only number 48 can be divided equally by.

2) 3 spaces forward

4x - x^3            x ( 4 - x^2)            x ( 2 - x) ( 2 +x)

______  =       ___________ =    _____________

  q(x)                    q(x)                       q(x)

If we have a  "hole" at x = -2, then q(x) must have a  factor  of ( x + 2)

If we have a vertical asymptote at x = 1, then (x - 1)  must also be a factor

If we have no horizontal asymptote, the q(x) must be a second degree polynomial - the rational fuction has a s;ant asymptote

And  since   q(3) = -30....then we have that

-30 = a(3 + 2) (3 - 1)

-30  =a (5)(2)

-30 = 10a

a = -3

So....q(x)  = -3(x + 2)(x - 1) =  -3(x^2 + x - 2)  =  -3x^2 - 3x + 6

Here's a graph :  https://www.desmos.com/calculator/dz5hnv1yoa

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C.  because 20% of 25 is 5. 

c

You left out some information in your question....

See:

https://web2.0calc.com/questions/suppose-20-of-all-widgets-produced-at-a-factory-are-defective

Whichever scenraio gets closest to finding 20 %  defective is the closest to reality....

A  5/100 =  5%

B  5/50 = 10%

C 5/25 = 20%

D 5/20 = 25 %           C

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True!

The three lines all intersect at this point   2,5

v_f =v_o + at       a = -9.8 m/s^2

Vertical velocity is   5.42 m/s sin 65 = v_y = 4.912 m.s

  When velocity = 0   it is at the max height

0 = 4.912 - (9.8) t     t= 1/2 sec

No, Michael is incorrect......the second 25% is taken off of the reduced price....not the original price:

Manager's way:   495 - 20% = 396       396 - 25% =  $ 297

Michael's way      495 - 45% =  $ 272.25

If you mean 5% simple interest per year, then she will have $(175 + 12*(5/100)*175) after 12 years.

As follows:

Thanks!

Here are a couple of possibilities: