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It is a square.....   the smaller one is   2 x 2  = 4      the larger is 3 x 3 = 9

   so the dilation went from   2 to 3     the scale factor is thus  1.5  = X

both of the other answers are wrong

can you say the answer

From symmetry, if it contains the point (2,0), which is (5-3, 0), then it also contains the point (5+3, 0) or (8, 0).  Hence you have three equations:

From (2, 0):    0 = a*2² + b*2 + c

From (5,3):     3 = a*5² + b*5 + c

From (8, 0):    0 = a*8² + b*8 + c

Use these three equations to find a, b and c.

"Because not all airline passengers show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 115 passengers. The probability that a passenger does not show up is 0.05, and the passengers behave independently. Round your answers to four decimal places (e.g. 98.7654).

a) What is the probability that every passenger who shows up can take the flight?

b) What is the probability that the flight departs with at least one empty seat?"

GCD = 1

Let x  be  the weight  of a sack of sugar

Let y  be  the weight  of  a sack of flour

We  have  these inequalities

2x + 3y ≤  40

y - 2x ≤ 5

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

The    max  weight  of a sack of flour  occurs  at the "corner point" of  the  feasible region  =   11.25  lbs

Each  pendant  cost  

[14.40  -  5.70 ]  /  3    =   2.9   =    $2.90

We  have    6!  /[3! * 2!]   =  60   distinguishable configurations

I  get that  there 12  configurations  where  no black bead is  next to the yellow one  : 

YRRBBB    RYRBBB   BBBRRY

YRBRBB    BRYRBB   BBRBRY

YRBBRB    BBRYRB   BRBBRY

YRBBBR    BBBRYR   RBBBRY

So ....the  probability is  12  / 60   =   1  / 5

Let  the  number  of dimes  = D

Then the numbers of quarters  =  72 - D

So....we  have this

Number of dimes * value each  +  Number of quarters * value each  =  total amount

D * .10  + (72 - D)* .25  =  10.80    simplify

.10D  + 18  - .25D  = 10.80

-.15D  +  18  = 10.80    subtract  18  from each side

-.15D  = -7.2    divide both sides by  -.15   

D  = 48   (dimes)

Let  the  first term of  the  arithmetic  series  =  a

Let  the third  term  =  a + 2d

Let  the ninth  term =  a + 8d

And we  know  that    a  + 6d  =  14    

The  second  term of  the  geometric  series  =   ar

The  thrid  term  of the geometric series  =  ar^2

So

a + 2d  =  ar     ⇒ 

 2d  = ar - a   ⇒   

2d  = a ( r - 1)

a + 8d  =  ar^2   ⇒ 

8d  = ar^2 - a  ⇒ 

8d  = a (r^2 - 1)  ⇒ 

8d  = a (r- 1) (r + 1)  ⇒ 

8d = (2d)(r + 1)  ⇒

8 = 2 (r + 1)  ⇒

4 = r + 1

So  r  =   3

And

2d  = a (3 - 1)

2d  = 2a

d  = a

So

a + 6d  =  14

a + 6a  = 14

7a  = 14

a  = 2      so     d  also  =  2

(a)  The twelveth term of the arithmetic series  =  a  + 11d  =   2 + 11(2)  =   24

(b)   The  sum of the first 12 terms  of the geometric series  is

S =   a  [  1 - r^12  ] [ 1  - r ]  =   2 [ 1 - 3^12] / [ 1  - 3 ]   =  [ 3^12 - 1  ]   = 531440

Hello William Tanudyaya!  Good for you for getting the answer.

Hello William Tanudyaya!  Let us know if you have any further quesitons.

Let  the wind  speed  =  S

Let  the  rate of  the plane in still air = 180  + S

So  with  the  wind  the plane's  rate   =  (180 + S + S)  =  (180 + 2S)

Against  the  wind  the plane's  rate = (180 + S  - S) =  (180)

And  Time * Rate  = Distance....so......equating distances we have  that

2 (180 + 2S) = 3 (180)   simplify

360 + 4S  = 540        subtract  360  from both sides

4S    =  180      divide  both sides  by  4

S =  45  (mph)  =  wind speed

180 + S =   180  + 45  =   225 (mph)  =  plane's rate  in still air 

f(x)  =  48sin(6x - pi/9)  + 48

We  can  write this  in a slightly  differenent  manner  :

f(x)  = 48 sin [ 6 ( x - pi/54) ]  +  48

Only  the  "6"  matters....this  tells  how many  periods there are  in 2 pi

So....if  there  are  6 periods in each  2pi sec.......then the period  is   2pi / 6 =    pi/3  sec  = the time for one revolution

(6 x 8 in²)  *   $ 2.25 / in²   = .......

6 x  8  =   48  sq in

48 x 2.25   =

$108

Wait would the domain be restricted to  [0,pi] and the interval would be (-pi/2,pi/2)?

The  function  is

f(x)  =  12sec (x)

See the graph here  :  https://www.desmos.com/calculator/buvlwdjr3z

Ok...thanx for that !   This looks like a cosine function doesn't it? 

BUT it is taller than a normal cosine function....usually the height of the wave goes from -1 to 1       which means amplitude is 1

    THIS wave goes from 8 to 72      so amplitude is   32     ( 1/2 of the height is amplitude)

32 cos x        so far

  Now,     note that the wave is shifted UP from it's normal midline of zero..... the midline of this wave is 40

32 cos x       + 40

The period is the amount of x axis this wave takes to make a complete cycle.....  Looks to be 100 seconds

32 cos (x pi/50)   + 40  

Check this out......I superimposed the above wave on YOUR graph !

https://www.desmos.com/calculator/ozfmq36yob

The original function has  the  form

f(x) = Asin (Bx)  + C

A=  the amplitude  = 10

C = the midline shift  =  4

B =  2pi / period    =  2pi  / 2  =  pi

Original  function  is

f(x)  = 10 sin (pi x)  +  4

If  this is  reflected  over  the x axis.....then  f(x)  becomes   -f(x)  =

-10sin (pi x)  -  4

See the  original grah and the reflected  graph here  :  https://www.desmos.com/calculator/gvwssl3gbf

I plotted the points ---> https://www.desmos.com/calculator/gkrhzfgh4l