CPhill

y =  ax^2   +  k

If  the  vertexx is  (0, -4),  then  k   = -4

And  the  point (3,7)  is on the parbola implies that

7 =  a (3)^2  -  4     add 4  to  both  sides

11  = a (9)    divide both sides  by  9

11/9  = a

So.....the  equation is

y = (11/9)x^2  -  4

The side of  the  square  =  diagonal / √2  =  [10√2] / √2 =   10 cm

So....the area  =  side^2  =   (10cm)^2  = 100  cm^2

3(2x + 4) -  2x   =  50

6x  +  12   - 2x   = 50

4x  + 12  = 50      subtract   12  from both sides

4x  = 38      divide both sides by  4

x  = 38/4 = 19/2  =   9. 5

(-2 +  4i) * i^3  =  -2i^3  +  4i^4  = -2 (-1)(i) + 4(1)  = 2i  + 4 = 4 + 2i ⇒  Note that  this lies in Quadrant l

So

-2 + 4i    lies  in  Quadrant ll

Clockwise

Quadrant  l

What about 2100   ???

a^b  =  b^a

Take  the log of each side

b log a =  a log b

(b/a)  = log b  / log a

[( 9a)  /a ] =  log b  /log a

9  = log b / log a

Which implies  that

log _a b  = 9

So

a^9  = b

a^9  =  9a

a^8  =  9      take  the  8th root of  each side

a =  9^(1/8) = (3^2)^(1/8)  =  3^(2/8)  =  3^(1/4)  =  ⁴√ 3 

This is what geno  found and I'm assuming that it is the  form you  want

So

m + n  =   7

Not sure  about this....but  here's  my rationale

We  know that  we  have  15  scores of 10

Since  the  mode is  7  we  need to have  16  scores of 7  (and no more than this )

The  median  is  9, so the 20 and 21st  scores  must be  9....to keep the average as small as possible

And the other  3  scores  need to be  as small as possible so let them  =1

We  have

1, 1, 1, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7 ,7, 7, 9 ,9, 9, 9, 9, 9,10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10

Median  = 9

Mode = 7

Mean   = 7.975  =  8

3)

f(x) * g(x)  =  degree  4  * degree 4  =   degree 8   

2) Suppose f is a polynomial such that f(0)=47, f(1)=32, f(2)=-13, and f(3)=16. What is the sum of the coefficients of f?

If f(0) =  47....then  the  constant term  must  be  47

And if  f(1)  = 32.....then the  sum of the coefficients and the  constant term  = 32

Therefore

sum of coefficients  + constant term =  32

sum of coefficients  + 47 =  32     subtract  47  from both sides

sum of coefficients =   -15