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Tiggsy has given some brilliant answers here. 

I am very glad that you found this one   

Thanks Tiggsy and thanks Iamhappy.         

Please just one question per post.

Also, when reposting please include the link to the original post and ask people to answer on the original thread.

Thanks.

ok, what did you get for     a,b,c   and      g(x)?

In France, the cost of one kilogram of apricots is € 3.38 .

In the UK, the cost of one kilogram of apricots is ￡ 4.39 .

￡1 = €1.04 .

Calculate the difference between these prices.

Give your answer in pounds (￡)

Hello Guest!

\(\Delta C=\frac{￡ 4.39}{kg}-\frac{ €\ 3.38}{kg}\cdot \frac{\ ￡\ 1\ }{€\ 1.04}\)

\(\Delta C=\frac{￡\ 1.14}{kg}\)

The apricots are more expensive in the UK \(\frac{￡\ 1.14}{kg}\) than in France.

  !

Oh ok

Hi Melody!

thank you so much for your response! 

the link does work (thankfully) and I tried to play around, but I was still stuck.

A monic polynomial is one where  the lead coefficient on the x^2 term is 1

We have the form    f(x)  =   x^2  + bx + c

If (0)  = 4   then c  =4

And we have that   f(1)  =  10   .....which means that

(1)^2  + b(1) + 4 = 10

5 + b =  10

b  = 5

So

f(x)  = 1x^2 + 5x  + 4

n=25, 142, 311, 649

n =649 - The largest such "n"

If  f(x) + g(x)  is degree 1.....then g(x)   must  be (for example)  7x^4 - 3x^3   (a 4th degree polynomial)

Other answers are possible  but g(x)  must still be degree 4

Jamie and Marshall can sit  2 ways  in any two  seats  and they can sit in seats   12, 23, 34, 45, 56  (5 ways)

The other student can  be arranged in 4!  ways for each of these

So.... the total possible  arrangements are    2 * 5 * 4!  =  10 * 24  =   240

Right, thankss!!!

Has to be a plus

7 - sqrt (129)  is a negative

And the rate of the  boat in still water  is always positive

I figured it out, thank you! I did it by finding a, b, and c, then finding g(x) which was (4^16-3^16)/2

OK

Take out the lowest common factor beteen  - 8  and  12.....to make matters simple....I'll use 4 in this example

Take out  the lowest common factoe  between x^2 and x^4  = x^2

Take our the lowest common factor  between y^4 and y  =  y

Take out the lowest common factor between z^3 and z^3  = z^3

On the outside of the parentheses we will just write  these in order   =    4x^2yz^3

To find out what goes in the parentheses  we just  fivide each  term in the original problem by 4x^2y z^3

So   -8x^2y^4z^3                            And    12x^4yz^3    

      ___________  =   -2y^3                      ________    =    3x^2                                          

        4x^2yz^3                                            4x^2 y z^3

Putting this all together  we get

4x^2yz^3  ( -2y^3 + 3x^2)

but cphill it would be + or -??

The largest n = 1

[120! / (60! * 60!) ] mod 7^1 =0

-8x^2y^4z^3  + 12x^4 yz^3    =

-4x^2 y z^3    ( 2y^3 - 3x^2)

Do you see how I did that, T4H???

Convert  speed in m/min to km /h

41 +2/3 m / min x 60 min  = 2500 m/ hr =  2.5 km / hr

Let R be the  rate of the boat in still water

[75% of 12  = 9]

And note  that   D /R  = Total time

Rate downstream  = R + 2.5        Rate upstream = R - 2.5

Distance downstream / Rate Downstream   +  Distance upstream/ Rate upstream  = Total time

12 / [ R + 2.5]   +  9 / [ R - 2.5 ]  =  6

(12 [ R-2.5] + 9 [ R + 2.5] )  / [  (R+ 2.5 ) (R -2.5)] = 6

[ 12 R  - 30  + 9R + 22.5]/ (R^2 - 6.25)  = 6

21R - 7.5  =  6 [ R^2 - 6.25 ]

21R - 7.5  = 6R^2 - 37.5       rearrange as

6R^2 - 21R  - 30  =  0        divide through by 3

2R^2  - 7R - 10  =  0 

Using the quadratic formula

R = (  7 +  sqrt [ ( 7^2 - (4)*(2) *( -10)] ) / ( 2 * 2)  =   ( 7 + sqrt ( 129)) / 4  ≈  4.6 km/h

109 mod d = 14

d =19,  95

Sum of d [19 + 95] =114