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Let:x = number of boysy = number of girlstherefore 2(x+5) = (y+8)2x + 10 = y - 8y = 2x + 2

When using Pythagoras' theorem, the hypotenuse squared should equal the square of the other two sides added together, so (a²=b²+c²). We also know that for Pythagoras' theo...

Using the equation y = ax² + bx + cCreate 3 separate equations:-a(3)² + b(3) + 18 = 0 -a(-3)² + b(-3) + 18 = 0
-9a+3b = -18-9a - 3b = -18
add the equations:-9a-9...

Method 1 for solving these equations would be to multiply equation 2 (3x + 2y = 12) by 4 so that the x coefficients are equal, this becomes (12y+8x=48). Then subtract equation 1 from equation 2: (12x+8y=4...

First use the gradient equation for a line: difference in y over difference in x:dy/dx = gradienttherefore: (15-9)/(d-5) = 315-9=3(d-5)6=3d-1521=3dtherefore d = 7