Alan

See my reply at http://web2.0calc.com/questions/consider-the-arithmetic-sequence-presented-in-the-table-below_1#r1

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Here is my interpretation:

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The question might have meant 4+(1/4) - (1+(2/3))

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-7*(-8) = 56

-7 + (-8) = -15

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The quickest way here is just to substitute each set of coordinates into both equations to see which set makes both equations true.

Alternatively:

Multiply first equation by 5:           -35x + 10y^2 = -50      (1)

Multiply second equation by 7:     -35x - 14y  = -154        (2)

Subtract (2) from (1) term by term   0 + 10y^2 + 14y = 104  or, dividing by 2:  5y^2 + 7y = 52

Write this as:  5y^2 + 7y - 52 = 0  

Solving this we get y = -4 and y = 13/5

Looking at the [possible solution sets provided we can see that it is y = -4 that we want.

Plug this into -5x - 2y = -22 to get -5x + 8 = -22  or 5x = 30  so x = 6.

Solution is (6, -4)

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A general circle equation is:  (x - x_c)^2 + (y - y_c)^2 = r^2 

where (x_c, y_c) are the centre coordinates and r is the radius.

Compare this with your equation to find the relevant values.

Correct.

At 3 m/s she takes 2700/3 seconds (or 15 minutes) to run 2.7km.

At the same speed for another 5 minutes she travels a further 3*5*60 = 900 metres (or 0.9 km)

Her total distance so far is 2.7 + 0.9 = 3.6 km 

This is two-thirds of the length of the jogging track which is therefore 3.6*3/2 km long (or 5.4 km)

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Not sure exactly what you mean.  Can you provide a specific example?

1.  g(x) = 5x               f(x) = 8x - 2

f(g(x)) = 8*g(x) - 2  so   f(g(x)) = 8*5x - 2  or f(g(x)) = 40x - 2

g(f(x)) = 5*(f(x))   so  g(f(x)) = 5*(8x - 2)  or g(f(x)) = 40x - 10

Now you try 2.