CPhill

Since CB is tangent to the circle at B, it  will have a negative reciprocal slope to radius AB

Slope AB  =   [ 4 -2] / [ 6 - 3 ] =    2/3

So.....the slope of BC  =    -3/2

Slope  

1)  Subtract the y values in some order      [ 69 - - 13 ]  =    82

2)  Subtract the x values in the same order  [ 23 - 95  ]  =   -72

3) Put  1  over  2  =     82 / - 72   (reduce)  =    41 / - 36   =    - 41 / 36      =   the slope

Remember that a function has to pass the vertical line test......that is,  if we draw any vertical line on a graph, it can only cut that graph at no more than one point

So

I and II  are functions ....any vertical line will  cut both graphs at only one point

II  and IV  are not ......a vertical line will cut both at two points

1/7   ÷  35/1           invert the second fraction and multiply

1/7  *  1 / 35    =

1 /  245

2x^2 - 7x + 6

(2x - 3) (x - 2)

No diagram shown......

The volume of the second prism  will be  [scale factor]^3 as large as the first prism....so......the volume will be :

300 (3.5)^3   = 12862.5 cm^3        

P.S. -  volume is always expressed in cubic units

His total order at the regular price  =  5 (15.40)  = £ 77

So....he gets a  6.5%  discount   =    93.5%  of the regular cost  =  .935

So.....the amount of the discount  =

77  -  .935 (77)   =  £ 5.005  =  £ 5.01   ( rounded )

He needs to purcahse  1200 - 450   =  750 L

A 7.5% discount  means that he pays  92.5%  of the normal price per litre  = .925

So.....the normal cost  -  discounted cost  = amount of the discount......so we have

81.5 ( 750)  -  .925 (81.5) (750)  = 4584.375p  ≈  £45.84

f(x)  =  6  means that we want to sub 6 for f(x) and solve for x.....so we have

6  = 5x - 9      add 9 to both sides

15  =  5x       divide both sides by 5

3  = x