If the diameter of a circle is 142.8 millimeters, then what is the radius?

First of all we need both the denominators the same. 

We need to find the smallest number which both 5 and 2 can divide into - that is, the lowest common multiple of 5 and 2. This is 10. So we change the denominators into 10:

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Parallel lines will never meet, no matter how far they are extented. 

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Angles in a triangle add up to 180°

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Find the interior angle of a regular hexagon

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We know from the formula that the interior angles of a hexagon add up to 720°.

As a hexagon has six sides, each angle is equal to 720÷6=120

Finding the exterior angle

We know that the exterior angles of a regular polygon always add up to 360°, so the exterior angle of a regular hexagon is [image]

Calculate the exterior angle of a regular octagon, and write down the value of the interior angle.

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The exterior angle is [image]

The sum of the exterior and interior angles is 180°, so the interior angle is 180 - 45= 135°.

Exterior angles are each 30° (180° - 150°)

360÷30=12

Pythagoras Theorem

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1) 8²= 64  6²= 36  64 + 36= 100 

√100=10

2) 13²= 169 5²= 25  169-25=144

√144= 12

3) 10²= 100 7²= 49  100+49= 149

√149= 12.21 (2 decimal places)

Ratio and Proportion

There are 15 girls and 12 boys in a class. What is the ratio of girls to boys? Give your answer in its simplest form?

The ratio of girls to boys is 15:12

However, both sides of this ratio are divisible by 3

Dividing by 3 gives 5:4

5 and 4 have no common factors (apart from 1).

So the simplest form of the ratio is 5:4

This means there are 5 girls in the class for every 4 boys.