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fg(x) = 2(cx+5) + c

= 2cx+10+c                           [1 mark]

fg(x) = 6x+d. fg(x) = 2cx+10+c

6x = 2cx and d = 10+c          [2 marks]

3 = c and therefore d = 13    [3 marks...

Y= mX + c, 'X' is the horizontal value on the axis, the input value. The 'm' represents the gradient of the line, figured out by the change in y divided by the change in x. The 'c' value is the y intercep...

If you were to factorise this quadratic to find out its roots, you would get:

(x+1)(x+2)

which gives us roots of -1 and -2.

Remember that roots are where the graph crosses the x-axis,...

Use the product rule:

d/dx(fg) = f'g + fg'

f = x²    f' = 2x   g = sin(x)  g' = cos(x)

answer = 2xsin(x) + x²cos(x)

x² + 8x = (x + 4)² - 16, so x² + 8x - 5 = (x + 4)² - 16 - 5 = (x + 4)² - 21, so then (x + 4)² - 21 = 0 (x + 4)² = 21 -----> ...