(sqrt(3)x-sqrt(3)y)(sqrt(3)x+sqrt(3)y)
If by 'rule' you mean 'function' then there are an infinite number of possible answers. However, here are some examples. (Let input be x and output y.) Linear Functions y = x + 6 y = 3x + 10 Polynomials y = 3x2 - x - 10 y = x4 + 2x3 + 3x2 - 2x - 12 Exponentials y = 0.5x
If you mean: x+y = 30 and the value of y is 15 then the value of x is also 15
The tangent to 2x3 - 3x2 - 8x + 9 at x = 2 is y = 4x - 11 The tangent to y = 2x3 - 3x2 - 8x + 9 at x = 2 has the same gradient as the curve at that point; to find the gradient, differentiate: dy/dx = 6x2 - 6x - 8 which at x = 2 is: gradient = 6 x 22 - 6 x 2 - 8 = 4 At x = 2, y = 2 x 23 - 3 x 22 - 8 x 2 + 9 = -3 The equation of a line through point (xo, yo) with gradient m is: y - yo = m(x - xo) Thus the equation of the tangent to the line at x = 2 is: y - -3 = 4(x - 2) ⇒ y = 4x - 11
Y = X - 16 X= Y + 16 X is the original value. Y is the new value of the original value - 16.
x = +/- sqrt(y/3)
The value of x is 2
72
3 * x * x * y
3x2-y=6 3x2-y=6
(3x + 3y)(x + y) or 3(x + y)2
In expressions such as "x-y", both "x" and "y" can have any value. The value of "x-y" will depend on what the value of "x" and the value of "y" are.
(sqrt(3)x-sqrt(3)y)(sqrt(3)x+sqrt(3)y)
Without an equality sign it can not be considered to be an equation and the - or + value of 9x has not been given
You can find the x-coordinate of it's vertex by taking it's derivative and solving for zero: y = -3x2 + 12x - 5 y' = -6x + 12 0 = -6x + 12 6x = 12 x = 2 Now that we have it's x coordinate, we can plug it back into the original equation to find it's y coordinate: y = -3x2 + 12x - 5 y = -3(2)2 + 12(2) + 5 y = -12 + 24 + 5 y = 17 So the vertex of the parabola y = -3x2 + 12x - 5 occurs at the point (2, 17).
x = -1y = 33x2 - y2 = 3 (-1)2 - (3)2 = 3 (1) - 9 = -6
3x2 - 2y2 = 9x2 + 4y2 - 12xy (subtract 3x2 and add 2y2 to both sides) 0 = 9x2 -3x2 + 4y2 + 2y2 - 12xy 0 = 6x2 + 6y2 - 12xy (divide by 6 to both sides) 0 = x2 + y2 - 12xy or x2 - 2xy + y2 = 0 (x - y)(x - y) = 0 x - y = 0 x = y