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The student should state that there are x blue balls. From this, they may determine that overall, the number of blue and green balls combined must be 4x, and hence the number of red balls is therefore '10...

(1) 5(3x - 2y) = 14 -2ax 15x - 10y = 14 - 2ax (2) 15x +2ax -10y = 14 15x + 2ax = 10y + 14
(3) x(15 + 2a) = 10y + 14 x = (10y + 14) / (15 + 2a)
To asking us to make x the subject of a fo...

(a) let A be (x1,y1) and B be (x2,y2), Gradient = m = (y2-y1)/(x2-x1) m = (4- -5)/(-1-2) = 9/(-3) = -3 Gradient = -3
(b) equation of a straight line line: y = mx + c => y1 = ...

Let's take for example the integral 5x²(x³-4)⁴dx. This is very difficult and not at all nice to expand in terms of x, so we can effectively "create" a new variab...

AB = B - A = (4,3,-6)- (2,0,-1) = (2 , 3 , -5)BC = C - B = (9,3,-4) - (4,3,-6) = (5, 0 , 2)
If perpendicular "AB dot BC" should equal zeroAB dot BC = (2,3,-5) dot (5,0,2) = (2x5) + (3x0) + ...