CPhill

Second one....true statements

The graph represents a quadratic function

The equation of the graph could be wriiten as  y = x^2 + 2x  - 8

First one

True statement for  f(x)  =  l x l           The vertex is (0, 0)

True statement for the transformed function      The x intercepts are  (-7,0) and ( 3,0)

False statement for the transformed  function     The y intercept is (0, -5)

OK...thanks for that answer, guest.....I wasn't sure about mine  !!!

I don't  know  two interchangeable terms, but these are examples of  "proper fractions"   where the  numerator  [ top number]  is  less than the denominator  [ bottom number ]

I think this is correct.....but someone else might  know better than me !!!

On any  roll of one die...the chance of any number appearing is  (1/6)

So...the probability  of  any  particular arrangement showing up  by  rolling 10 dice is just   (1/6)^10  ≈  0.0000000165381717

Last one

P(A)  = 60 / 150 =   6/15  =  2/5

P(B) =  50 / 150  =  5 / 15  =  1/3

P(A and B) =  (2/5)(1/3) =  2 / 15

P(A l B)  =   P (A and B)                (2/15)

                  __________   =         _______   =       (2/15) * (3/1) =   6/15 =   2/5

                      P(B)                          (1/3)       

P(A l B )  = P(A)  is true.....the events are independent

I can do a couple of them.....

Flip a coin....roll a 6 sided die

P ( Heads  and < 6)  =   (1/2) * (5/6) =    5 / 12

The vertex  is  ( 4, 2)

We can start with this form

4p ( y - k)  = ( x - h)^2     where p  = 1  and ( h, k)  is the vertex

4p ( y - 2)  =  ( x - 4)^2   

4 ( y - 2)   = x^2 - 8x + 16

4y - 8  =  x^2 - 8x + 16

4y  =  x^2 - 8x + 24          divide both sides by 4

y = (1/4)x^2  - 2x + 6 

a = (1/4)      b  =  -2   and  c   =  6

And   their sum is     4 + 1/4   =    17  / 4  

Thanks, EP....here's a slightly easier way

2^x  = 7

2^(2x) =

 [ 2 ^x ] ^2  =

7^2   =

49

I think this is supposed to be

-5x - 3y  =  12

y = x - 12

Sub the second equation into the first for y and we have

-5x - 3 ( x - 12)  = 12  simplify

-5x  - 3x + 36  = 12     

-8x + 36  = 12    subtract  36 from both sides

-8x  =  - 24    divide both sides by -8

x  = 3

And    y  =    3 -  12  =  -9

So you are correct!!!!....    (3 , -9)  is the solution