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In a chess club, there are x boys and y girls. If 5 more boys and 8 more girls join, there would be half as many boys as girls. Show that y = 2x + 2

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

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How do I know if triangle ABC contains a right angle? (where AB=10cm, BC= 8cm, CA= 6cm)

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...

Answered by Sophia E. • Maths tutor

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A quadratic curve intersects the axes at (–3, 0), (3, 0) and (0, 18). Work out the equation of the curve

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...

Answered by Stanley S. • Maths tutor

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Solve the simultaneous equations: 12x - 4y = 12 and 3x + 2y = 12

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...

Answered by Lucca H. • Maths tutor

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Given point A: (5,9), point B: (d,15) and the gradient of line AB is 3... what is the value of d?

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

Answered by James C. • Maths tutor

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