Alan

rise over run

or difference in y values divided by difference in x values: (y2 - y1)/(x2 - x1)

Depends on the specific question!

I've found the images aren't always visible also!  It's usually a temporary glitch.

However, for lines to be parallel, the gradients must be the same.  If you express the line in the form y = m*x + c where m and c are constants then m must be the same for parallel lines.

The line x = 1/2 is just a vertical line at x = 1/2 (with an infinite slope!) 

1cm = 1/100 m

so 5.2 cm = 5.2/100 m = 0.052 m

This graph should help with the answer.

$$(2a)^{0.5}\times(3a)^{2.5}=2^{0.5}\times a^{0.5}\times3^{2.5}\times a^{2.5}$$

$$=2^{0.5}\times 3^{2.5}\times a^3$$

$$=(2\times 3)^{0.5}\times 3^2\times a^3$$

$$=9\sqrt{6}\times a^3$$

-3*(4 - 12) = -3*4 + 3*12  ("two minuses make a plus")

                 = -12 + 36

                 = 24

$$3\log{x}=\log{x^3}$$ using the property of logarithms that log(a^b) = b*log(a)

$$\log{x^2}+\log{x^3}= \log{x^5}$$ using the property that log(a*b) = log(a) + log(b)

Using these, and adding 10 to both sides of the original equation, we have

$$\log{x^5}=10$$

This means that

$$x^5=10^{10}$$

Take the fifth root of both sides

$$x=10^2$$

or $$x=100$$

The general equation for a quadratic is y = a*x² + b*x + c, so if you have 3 points, say (-1, 3), (2, 18) and (5, 69),  you can use the equations section of the calculator to solve for a, b and c as shown in the images below:

Well done!