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This is a typical example of a 3 mark question on a GCSE higher paper. The first mark would be awarded for multiplying both sides of the equation by 2, and then expanding the brackets:10 - x =2(2x-6)10 - ...

For y = f(x)+4: the graph undergoes a translation of (0,4) For y = f(x-5): the graph undergoes a translation of (5,0) For y = -f(x+4): the graph is reflected w.r.t the x-axis and translated by (-4,0)*imag...

The ways to complete the first one is to realise that it involves a difference of two squares. If you were to see (X^2) with a constant (number), you know they have no factor in common, meaning the two te...

y² + 2xy dy/dx = 3cos(3x) + 1/y - x/y² dy/dx                   thereforedy/dx = (3cos(3x) + 1/y - y²​​​​​​) / (2xy + x/y²)

Perimeter= 72Ratios are 3:4:5In total, you can think of there being 3+4+5=12 "portions".This means that in the perimeter includes 12 portions. 72/12=6 so each portion is worth 6cm.
Now we c...