Quadratic Equations ax2 + bx + c = 0 Examples of Quadratic equations 1. x2 +2x – 8 = 0 2. x2 – 10x + 25 = 0 3. 3x2 + x - 2 = 0 Quadratic Formula If [pic] a x2 + b x + c = 0‚ then [pic] Finding the zeros of the quadratic functions - The zeros of a function are the input values which result in an output value of zero. One way of solving quadratic equations is using factoring Examples are the following: 1) x2 + 5x + 6 = 0 Set this equal to zero:
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1. What is the exact number of bits in a memory that contains 640M bits? 640 · 1024 = 655‚360 · 1024 = 671‚088‚640 bits. 2. How many bits are in 1 Tb? You are asked to figure out the exact result. Hint: Depending on the tool used to calculate this‚ you may need to use a trick to get the exact result. Note that 220 = 1‚000‚00010 + d‚ where d is the difference between 220 and 1‚000‚00010‚ and that 1T = (1‚000‚00010 + d)2 8 bits/byte => 8 · 1 trillion or 812 => 8‚000‚000‚000‚000 3. Convert the binary
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Tutorial 1: Review of Basic Concepts 1. Let[pic]. List the elements of A that belong to the given set. i. Nature numbers ii. Integers iii. Rational numbers 2. Let set M =[pic]. List the elements of M that belong to the given set. i. Whole numbers ii. Integers iii. Rational numbers 3. Multiply out the brackets: a) 7(x + 2y) – 2(3y – 5x) (b) 2x2 + y – z2 – 2(3x2 + 2y – z) (c) (2x – 5)(5 + 2x) (d) (9y - 8)(3y - 3) 4. Evaluate the following without
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Now it is your turn to plan the trajectories required to launch a spacecraft through a specific route in space. The launch area is identified on the map below. Select three points for your spacecraft to travel through and label them Point A‚ Point B‚ and Point C. A coordinate plane is shown with a point at 1‚ 2 labeled‚ Launch Area. Log the coordinates of the specific points in space to which your spacecraft will travel. Please remember to include the graph of your points and the lines connecting
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could be used in an accounting profession is combining like terms. Like terms are terms that have identical variables and exponents. Like terms must have exactly the same letter parts. Using like terms may not be exactly the same in accounting as in algebra‚ but it is the same concept. You can only add things to the same accounts; you cannot add a cash total balance to an insurance expense account. An example of combining like terms in accounting is having $600 spent on rent‚ $350 spent on supplies‚
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following relational database: employee(employee-name‚ street‚ city) works(employee-name‚ company-name‚ salary) company(company-name‚ city) manages(employee-name‚ manager-name) For each of the following queries‚ give an expression in relational algebra‚ tuple relational calculus‚ and domain relational calculus: a. Find the names of all employees who work for First Bank Corporation. b. Find the names and cities of residence of all employees who work for First Bank Corporation. c. Find
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On the side of his house‚ a man is going to build two enclosures. One enclosure for a garden and another enclosure to keep his dogs in so the dogs aren’t roaming around. It is illegal to have any dogs roaming around. He bought 180ft of fence to use and one side is already existing. Refer to the picture on the next page. Since there are three short sides and one long side‚ to set up the perimeter‚ the short sides will be x and the long side will be y. So the equation is 3x + y = 180. The 180 comes
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PROPORTION METHOD The proportion method is used in both of these expressions. A proportion is an equation that says that two ratios are equivalent. The use of cross multiplying is in use in both expressions as well. I believe the first expression (#56) uses the extreme-means property; the product of the means is equal to the product of the extremes. #56. To estimate the size of the bear population on the Keweenaw Peninsula‚ conservationists captured‚ tagged‚ and released 50 bears
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Summer 2010-3 CLASS NOTES CHAPTER 1 Section 1.1: Linear Equations Learning Objectives: 1. Solve a linear equation 2. Solve equations that lead to linear equations 3. Solve applied problems involving linear equations Examples: 1. [pic] [pic] 3. A total of $51‚000 is to be invested‚ some in bonds and some in certificates of deposit (CDs). If the amount invested in bonds is to exceed that in CDs by $3‚000‚ how much will be invested in each type
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CBSE TEST PAPER-01 MATHEMATICS (Class-10) Chapter 3 : Pair Linear Equations in Two Variables 1. 2. 3. 4. For which values of p does the pair of equations given below have unique solution? (2 marks) 4x + py + 8 = 0‚ 2x + 2y + 2 = 0 Solve graphically: 3x + 2y = 14x‚ x – 4y = 7 (3 marks) Two rails are represented by the equations x + 2y – 4 = 0 and 2x + 4y -12 = 0. Represent this situation geometrically. (3 marks) a b c On comparing the ratio 1 ‚ 1 and 1 find out whether the lines representing the
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