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The U and inverted U symbols, ∪ and ∩, are mathematical symbols used to denote union or intersection, respectively. For example, when a rational algebraic equation is graphed, there may be some points where the equation is undefined. Visually, we see it as breaks or discontinuities. We use the ∪ symbol to express union. For example, {-∞,2)∪(4,+∞). That means that the graph passes at all x values except x=3.
The ∩ symbol is used for intersection of two lines, for instance. When equation A and equation B are graphed, they can intersect at points (x,y). It is therefore expressed as: A∩B = (x,y).
1. Consider right triangle ABK. The hypotenuse AB is 6 un. and the leg AK is 3 un. Since the leg is half of the hypotenuse, then the opposite to the leg angle is 30°. This means that m∠ABK=30°. Then m∠BAK=90°-30°=60°.
2. By the Pythagorean theorem,
3. Consider right triangle ABD. In this triangle AD is hypotenuse and m∠ADB=90°-m∠BAD=90°-60°=30°. Then the leg AB opposite to the angle 30° is half of the hypotenuse and AD=12 un.
4. The area of parallelogram is