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In a chess club there are x boys and y girls. If ten more boys join and one more girl joins, there is an equal amount of boys and girls. Knowing that y = 2x+2, Calculate x and y. [4 marks]

There are x boys and y girls. So x = boys, y = girls. Ten boys join so x + 10 = boys, one girl joins so y + 1 = girls. These values are said to be equal, so we construct an equation with x and y. x + 10 = y ...
BL
6225 Views

Use the factor theorem to show that (x-1) is a factor of x^3 - 3x^2 -13x + 15

If (x-1) is a factor of x 3 - 3x 2 -13x + 15 then one of the solutions for x must be x = 1.(This is because, if (x-1) is a factor of this equation then it is true that x-1=0, because this is a point where th...
JB
5038 Views

A=(1,a;0,1/2) B=(1,-1;0,2) AB=I, calculate the value of a.

First notice I is the 2x2 identity matrix (1,0;0,1) now we can form an equation to solve for a, look for an entry where a is involved the (1,2) entry of I is 0 and calculated by 1(-1)+2a=0 now solving gives ...
DS
2578 Views

Point A lies on the curve y=3x^2+5x+2. The x-coordinate of A is 2. Find the equation of the tangent to the curve at the point A

First differentiate the function with respect to x, dy/dx=6x+5 this finds the gradient function now calculate the gradient at point A by inputing x=2 into the gradient function 6(2)+5=17. Now using y=mx+c wh...
DS
4713 Views

Find the tangent to the equation y=x^2 -2x +4 when x=2

When X=2 Y=2^2-2(2)+4=4 So the coordinates are (2,4)Differentiate Y so dy/dx = 2x-2Tangent Gradient when x=2 is 2(2)-2=2 so m=2We need to find the y intercept to get out tangent equationso y=2x+c , we sub in...
NN
2478 Views