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In order to rationalise the denominator we need to get rid of the surd (square-root) on the bottom of the fraction.

To do this, we can multiply the denominator by sqrt(5).

But we must notice...

We want to determine whether a function has a tangent which is horizontal. To answer the question we need to know what a horizontal tangent to a function means. A tangent to a graph of a function is a lin...

To see where the graph is greater than zero, we start by finding where it meets zero. By factorising (x^2 - 7x - 18), we find it equals (x-9)(x+2). The expression equals zero at the points x = 9 and x = -...

Since y is equal to both 5-x and to x+1, we know that 5-x is equal to x+1. We can write 5-x=x+1. Take 1 away from each side: 4-x=x. Then add x to each side: 4=2x. Divide both sides by 2: 2=x. Now we have ...

Finding 51% of 400 is the same as finding 50% of 400, and 1% of 400, and adding them together. Finding 50% of a number is the same as finding half of the number, since half of 100% is 50%. Half of 400 is ...