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Equation of circle centered at (h,k) with radius r:

\[(x - h)^2 + (y - k)^2 = r^2.\]

$(AB)^2 = 18$

g(1) = 3*1 + 9 = 12.

Slope of  the line   =  ( -2 - 7)  / (3 - - 1)   =   -9 / 4

Using  (3,-2)....the  equation  of the  line  is

y  = -(9/4)  (x - 3) -  2   

When x  = - 6

y  = (-9/4) ( -6 - 3)  -  2   =  (-9/4)(-9)  - 2   =  81/4  - 8/4   =   73 / 4

Red is 5  out of  5+4 = 9     or 5/9 of the total

red =   5/9 * 450 = 250 ml        blue =  450 - 250 = 200 ml         take it frome here !

In  vertex  form  we  have  that

y  =a ( x + 4)^2  +  0

Since  ( 1, -75)  is  on the  graph, then

-75  = a ( 1 + 4)^2  +  0

-75  = a (5)^2

-75  = 25a

-75  / 25  =  a  =  - 3

Correct!! 4,8

horizontal line is   y=8

vertical line is x =4

they intersect at      4,8

put '6' in for height in the equation given    ( which is a dome shaped parablola due to the negative coeeficient of t²)

6 = -4.9 t^2 + 14t - .4

0 = - 4.9t^2 + 14t  - 6.4          now use Quadratic Formula to calculate the two 't values 

               ....the ball is above 6  between thes two values , so calculate the time between these two values of t

a = -4.9     b = 14      c = -6.4

\(t = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

Just leared some LaText btw!

slope = 9/-4

y = -9/4 x + a

7 = 9/4 + a

a = 7 - 9/4 = 19/4

$y = \frac{-9}{4} x + \frac{19}{4}$

$y = 13.5 + 4.75$

$y = 18.25$

Where they intersect , they are equal....

2x^2 - 7x + 1        =        8x^2 + 5x + 1       gather all terms to one side and simplify

6x^2 + 12x  = 0

6x ( x+2)  = 0        so the   'x' coordinates of the two points of intersection are   0   and  -2

                              use these values of 'x' in either of the equations to calculate the corresponding 'y' coordinates of the intersection points

Yes, I understand it now, thank you!

Thank You! I orginally put 2 but forgot they were pairs.

The green line in the image below represents f(c) = -1

    everywhere the line crosses the red graph is a value of c   that is   f(c) = -1     How many times does the line cross the red graph?

3. A line has a slope of -3/7 and its y-intercept is (0,18). What is its x-intercept?

Note  that  h(7)  =   5

So

h (h (7))  =  h (5)    =  -1

Does  that  make sense  ????

Lookat x = -2       now go vertical to intercept the graph  at  y= ~ 2/3      this is   f(-2)

Note  that  the point  (3.4) is  on  f

The  inverse  reverses  the coordinates....so  ( 4,3)  is on the  inverse

Which  implies  that  f^-1 (4)   =   3

Tank you manz

Thank you for your help! I got my answer now :)

(2x + 10)  ( x + 3)  <   (3x + 9) (x + 8)     simplify both  sides

2x^2 + 10x  + 3*2x  + 30   <  3x^2  + 9x + 24x  + 72

2x^2  + 16x  + 30  <  3x^2  + 33x  + 72        rearrange  as

x^2 + 17x + 42  >  0        factor  as

(x  +  14) ( x + 3)  >   0

Note  that     when 

x >  - 3   this  is  true

-14 < x < -3   it  is false

x < -14   it  is  true

So

(  - inf, -14 )  U  ( -3, inf)    are  the  intervals  that  make this true

This is the equation of a circle ......re write in standard form by 'completing the square' for x and y :

2 x^2 + 10x       + 2y^2 -6y  - 18 = 0      divide through by 2

x^2 + 5x            + y^2 -3y      = 9          complete the squares

(x+2.5)^2              + ( y-1.5)^2     = 9 + 6.25  + 2.25   <======== this equals radius ^2

                                                 17.5 = r^2           area of circle = pi r^2        area =   17.5 pi  units²

Let  Noah's pace in mph  =  N

Let  the distance  he  rides in 3  hrs =  D

So   3N  = D

And

Noah's pace  * 1.6  =   Grady's pace

So

Grady's  pace * time =  D + 15

(N * 1.6  )  *  3    =   D + 15

4.8 N  =  D + 15

4.8N  =   3N  + 15

4.8N - 3N  =   15

1.8N    = 15

N =  15 / 1.8   =  8.33 mph = Noah's pace

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