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Since the line of symmetry is x = 2, the x coordinate of the vertex  must = 2

And the x coordinate of the vertex is given by :   -b/2a.......so we have that

2  = -b/[2a]      →   -4a = b

And we have these  equations

1 =  a(1)^2   - 4a(1)  + c    →   1 =  -3a + c       (1)

-1 = a(4)^2   - 4a(4)  + c    →  -1 =  c      (2)

Subbing (2)  into (1)  we have that    1 =  -3a - 1   →  2 = -3a →  a = -2/3

Which means that b  = -4(-2/3)  = 8/3

So....the equation of the quadratic is :

y = (-2/3)x^2 + (8/3)x  - 1

And we know that

0 = (-2/3)(√n +2)^2  + (8/3)(√n + 2)  - 1          let √n + 2   = m.......and we have that

0  = (-2/3)m^2 + (8/3)m  - 1      multiply both sides by 3

0 = -2m^2  + 8m - 3     complete the square on m

3 - 8 = -2 (m^2 - 4m + 4)

-5 = -2 (m - 2)^2

5/2  = (m - 2)^2       take pos/neg square roots

±√[5/2]  = m - 2

±√[5/2] + 2  = m     back-substituting, we have

±√[5/2] + 2 = √n + 2   and since we want the larger root

√[5/2]   = √n

n = 5/2  = 2.5

Here's the graph :  https://www.desmos.com/calculator/102umpw19h

The larger root = ( √2.5  + 2 ,  0 )  ≈  ( 3.581, 0 )

\(\frac{4}{\sqrt{84}}\)

\(\frac{4}{\sqrt{4\times21}}\)

\(\frac{4}{\sqrt{4}\sqrt{21}}\)

\(\frac{4}{2\sqrt{21}}\)

\(\frac{4}{2\sqrt{21}}\frac{\times}{\times}\frac{\sqrt{21}}{\sqrt{21}}\)

\(\frac{4\sqrt{21}}{2\times21}\)

\(\frac{4\sqrt{21}}{42}\frac{÷}{÷}\frac{2}{2}\)

\(\frac{2\sqrt{21}}{21}\)

\(\frac{2\times 4.58257569495584...}{21}\)

\(\frac{9.16515138991168...}{21}\)

\(0.43643578047198476...\)

The total cost, C,  is given by :

C = 200.00 x

The answer is given by :

2² * 3 * 5   = 

4 * 3 * 5  =

60

We can find the radius by solving this :

9pi  = pi * r^2       divide both sides by pi

9 = r^2      take the square root of both sides

3 = r

So......the equation is :

( x - 0)^2   + ( y + 1)^2   = 9    which simplifies to

x^2  + ( y + 1)^2   = 9 

We need to find the midpoint of these two points......that will be the center of the circle......then, we can use the distance formula to find the distance between the center and one of the points.....this will give us the radius

Midpoint   =   [   ( 1 - 9 ) / 2  , ( -6 + 0) / 2 ]  =  [  -8/2 , -6/2]  =  [ -4, -3 ]  ......this is the center

Distance between   [-4, -3]   and  [-9, 0]  = radius  = √ ( [ -4 + 9]^2 + [-3 - 0]^2 )  =

√ [ 5^2  + (-3)^2 ]  = √ [25  + 9]  = √34

So the equation is :

( x + 4)²   + ( y + 3)²  =  34

We can use the distance formula ro find the radius

r = √  ( [ 7 - 3]^2  +  [ -5 -1 ]^2 )   =  √ [ 4^2 + (-6)^2  ]  = √ [16 + 36]  = √52

So......the equation  is

(x - 3)^2  + ( y + 5)^2  = 52

The radius  = 11  ...... so we have

(x - 7)²  + ( y + 9)²  = 121

The vertex is (-4,4)   and p  =  3

The equation  is

4(3)(y - 4)  = (x + 4)²

12 (y - 4)  = (x + 4)²

Since  the "x" term  is squared  and both the x and y terms are positive.......this parabola opens upward

In the form  (x - h)²  = 4p (y - k)

The vertex, (h,k)  will be (-4, 3)     and  p  can be found by subtracting the y coordinate of the vertex  from the y coordinate of the focus   =  [9  - 3]    = 6

So we have

(x + 4)²  =  4 (6)(y - 3)

(x + 4)² = 24(y - 3)    which is the same as

24(y - 3) = (x + 4)²

The form is given by:

(x - h)²   = 4p (y - k) 

The vertex is given by (h,k)   = (3,2)

And.....we have  a parabola with its focus that will lie 2 units below the vertex.......so p = -2

So we have

(x - 3)²  = 4(-2)(y - 2)

(x - 3)²   = -8(y - 2)  which is the same as

-8(y -2)  = (x - 3)²

P(2 yellow)   =

3/9   * 2/8  =

1/3  *  1/4   =

1/12

P ( first is blue and second is white) =

5/16   *   5/15   =

5/16  *   1/3   =

5/48

thank you so much mam, got it. :)

P (odd and D)  =

P(odd) * P(D)  =

3/5   * 1/4   =

3/20

P(not getting a yellow gumball)  = 

1 - P(of getting a yellow gumball)   =

1 - 1/7   =

6/7

Probability that both are under-filled  =

(3/100)²  = 

9 / 10,000 

(1/2) * (1/2)   =  1/4

The probability is given by :

P(getting  < 5 on the die) * P(tails on the coin)  =

(4/6)    *   (1/2)   =

4/12  =

1/3

P (white or <3)  = P(white)  + P(<3)  - P(white and  <3)

                               3/10     +    2/10    -   1/10     =

                                         4/10   =  

                                          2/5

P( t or m)  = P(t)   + P(m)   - P(t and m) 

                     2/11  + 2/11  -  0/11  =

                             4/11   =  "A"

Yep.......we try to......!!!!

4 / √84  =

4 / √ [ 4 * 21 ]   =

4 /  [ 2 √21  ]   =

2 / √21

Assume that a set of data has a mean of  m  and a standard deviation of  s.

Then, to find the  z-score  of any value  x,  use the formula:  z-score  =  (x - m) / s.