PART III: REVIEW FOR THE WRITTEN EXAMINATION in .NET framework

Encoder PDF 417 in .NET framework PART III: REVIEW FOR THE WRITTEN EXAMINATION

PART III: REVIEW FOR THE WRITTEN EXAMINATION
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5x 5 x Examples: ___ = __ __ = 5 x 1 x (3 + 6x)(x 4) ______ _____ ____________ = 3 + 6x x 4 = x 4 1 3 + 6x 3 + 6x In the example above, 3 + 6x is a factor of (3 + 6x)(x 4) and therefore can be cancelled
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Negative Variables
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When working with an equation dealing with a negative variable ( x), you must change the equation in terms of (x) using multiplication or division Example: x = 5 Multiply both sides of the equation by 1 ( 1) ( x) = 5 ( 1) x = 5
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Note: If the term containing the variable in the algebraic equation has a negative coef cient (factors being multiplied), multiply both sides of the equation by the reciprocal (inversion) of the coef cient, which will also be negative
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1 Example: 2x = 8 Multiply both sides by __ 2 1 1 __ 2x = 8 __ 2 2 x = 4
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Addition and Subtraction of Fractions with Variables
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When adding and subtracting fractions with variables, treat the variables as if they were prime numbers (to nd the LCD) 3 x Example: ___ + __ The least common denominator is 50 50 2 3 3 ___ = ___ 50 50 x 25x + __ = ____ 2 50 3 + 25x _______ 50
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Multiplication of Fractions with Variables
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Multiply fractions with variables the same way you would multiply fractions without variables Multiply the numerators rst and then multiply the denominators 5 2x 10x 2 6x 12x 4x ___ ___ = ____ = ___ Examples: __ ___ = ____ 7 3 21 3y 7 21y 7y
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CHAP 7: MATHEMATICS
Division of Fractions with Variables
Dividing fractions with variables is similar to dividing fractions without variables Invert the second fraction and multiply the fractions 4 x Example: __ __ 5 9 4 x 4 9 36 __ __ = __ __ = ___ 5 9 5 x 5x
MONOMIALS AND POLYNOMIALS
A monomial is a single term that has no plus or minus sign between entries Examples of monomials are 3x; 22y2; 3xy2; 380xy2 But 4x + 2 and 6y2 3y are not monomials because they have a plus or minus sign between entries A polynomial is two or more monomials attached with plus signs and/or minus signs Examples: 4x + 2; 4y 3; 2x2 + 3x; 7x2 9x + 1
FACTORING
Expressing an algebraic expression as a product of certain factors is called factoring It generally involves nding one factor of a product and using it as a divisor to nd other factors Factoring is important in algebra and useful in simplifying expressions and solving equations
FOIL Method of Expanding Expressions under the Distributive Law
FOIL is a method of multiplying terms and subsequently adding or subtracting like terms to get a polynomial result Example: (x + 5) (3x 7) F F O I L First First Outer Outer Inner Inner Last Last 3x2 O I L (x + 5) (3x 7) = I (5) (3x) = 15x (5) ( 7) = 35 3x2 + 8x 35 L F x(3x) = 3x2 x( 7) = 7x O (x + 5) (3x 7) (x + 5) (3x 7) (x + 5) (3x 7) (x + 5) (3x 7) 7x + 15x 35 =
PART III: REVIEW FOR THE WRITTEN EXAMINATION
Example: (4x 8) (2x + 6) F O I L 8x2 + 24x 16x 48 = 8x2 + 8x 48
Note: The distributive laws allow us to execute the often easier task of completing two smaller multiplications and calculating the sum, rather than performing one multiplication involving large numbers
Arithmetic and Algebraic Equation Applications
COMPUTATION PROBLEMS (ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION)
Example: George rents a car for a day from a company charging $60 a day, plus a lateness fee of $10 an hour for cars not brought back on time If George returns the car the next day two hours late, how much would he be obligated to pay the rental company Answer: $60 for the day, plus $20 for two hour late fee = $80 Example: A beachcomber collects $4320 off the sand on Saturday and $2767 on Sunday How much more money did the searcher collect on Saturday compared to Sunday Answer: $4320 $2767 = $1553 Example: An EMT checks the pulse of a rescued re victim The victim s pulse count is 19 for the fteen seconds that the pulse was examined What is the number of beats per minute Answer: Since 15 seconds is 1/4 of a minute, multiply the pulse rate in 15 seconds by 4 to get the pulse rate per minute 19 4 = 76 Example: Four businesses share the cost of purchasing a building valued at $5,000,000 If all four businesses pay equal amounts, how much would each business have to pay Answer: $5,000,000 4 = $1,250,000
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