# ALGEBRA PROBLEMS

May 28th, 2015
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A beseige is held 5700 men who have provisions for 66 days. If the garrison losses 20 men each day, for how many days can the provision hold out?A man is 41 years old and his son is 9. In how many years will the father be three times as old

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ALGEBRABlock Diagram of the Number SystemDefinitions:Complex numbers numbers which take the form x + yi where x and y are real numbers.x is the real party is the imaginary parti is the imaginary unit which is equal to Examples: 2 + 3i, 3 4i, -2 + 5iRational number a number which can be expressed as the ratio of two integers such as , , 3, 0.25.Irrational number - a number which can not be expressed as the ratio of two integers such as , , , e.Integer any whole number which can be either negative, zero or positive such as 3, 0, 7.Natural numbers- are positive whole numbers including zero such as 0, 1, 2, 3, 4, . . . .Properties of Real Numbers1. Commutative property : Changing the order of terms/factors in addition/multiplication will not change the sum/product, i.e.a + b = b + a for addition &ab = ba for multiplication2. Associative property: Changing the grouping of terms/factors to be added/multiplied will not change the sum/product, i.e.a + (b + c) = (a + b) + c for additiona(bc) = (ab)c for multiplication3. Distributive property: a(b + c) = ab + ac4. Reflexive property: Any number is equal to itself, i.e. a = a.5. Symmetric property: If a = b, then b = a.6. Transitive property: If a = b and b = c, then a = c.Factors and Special Products1. Difference of two squares: 2. Sum of two cubes: 3. Difference of

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