Chapter 4 Solving Linear Equations 1. Definitions Linear Equation Solution Property of Equality 2. Solving Linear Equations Distributive Property Eliminating Fractions 3. Solving for One Variable in a Formula 4. Summary: Process for Solving Linear Equations 5. Worked out Solutions for Exercises 4.1 Definitions: Linear Equations: An equation is a statement that two expressions have the same value: [pic] Any number
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of -1. Straight Lines: Equation of a straight line is y = mx + c‚ where m = gradient‚ c = y-intercept. The equation of a line‚ if we know one point and the gradient is found using: (y - y1) = m(x - x1) (If given two points‚ find the gradient first‚ and then use the formula.) Two lines meet at the solution to their simultaneous equations. Note: When a line meets a curve there will be 0‚ 1‚ or two solutions. 1. Use substitution to solve the simultaneous equations 2. Rearrange them to form a quadratic equation
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of operations is a rule to clarify confusion that may occur in an equation that has multiple different operations. This rule of Order of Operations states we must solve a complex equation by complete the operations in this order: Parenthesis‚ Exponents‚ Multiplication‚ Division‚ Addition‚ and Subtraction. We can remember this by this mnemonic: Pink‚ Eyes‚ May‚ Doubt‚ Anyone’s‚ Style. *** This will happen if we take this equation and NOT follow the Order of Operation*** 4+ 2 x 3 = If I did not
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Straight Line Equations and Inequalities A: Linear Equations - Straight lines Please remember that when you are drawing graphs you should always label your axes and that y is always shown on the vertical axis. A linear equation between two variables x and y can be represented by y = a + bx where “a” and “b” are any two constants. For example‚ suppose we wish to plot the straight line If x = -2‚ say‚ then y = 3 + 2(-2) = 3 - 4 = -1 If x= -2 -1 -1 1 0 3 1 5 2 7 As you can see‚ we have plotted the
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1. Equations and Graphs In each of problems 1 - 4‚ find (a) an ordered pair that is a solution of the equation‚ (b) the intercepts of the graph‚ and (c) determine if the graph has symmetry. 1. 2. 3. 4. 5. Once a car is driven off of the dealership lot‚ it loses a significant amount of its resale value. The graph below shows the depreciated value of a BMW versus that of a Chevy after years. Which of the following statements is the best conclusion about the data? a. You should buy
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TEN EQUATIONS THAT CHANGED THE WIRLD The brightest minds in history have used mathematics to lay the foundation for how we measure and understand our universe. Time and time again‚ we have proved that it only takes one simple formula to alter the course of humanity. Here are ten equations that did just that. ISSAC NEWTON’S LAW OF UNIVERSAL GRAVITATION Newton’s law explains why planets move the way they do‚ and how gravity works‚ both on earth and throughout the universe. First published in the
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reason why the Drake Equation is not a successful science is because it would be impossible to calculate some of the elements in the equation. The elements would take too long to get an accurate sample to give a scientifically sound explanation. For instance how would you calculate fi (the fraction of intelligent life forms)‚ how do you define intelligent? Is intelligent like you and I‚ is it like a bird or a rat‚ could it be a plant? There is no way to truly determine what counts and doesn’t
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The Form of Structural Equation Models Structural equation modeling incorporates several different approaches or frameworks to representing these models. In one well-known framework (popularized by Karl Jöreskog‚ University of Uppsala)‚ the general structural equation model can be represented by three matrix equations: However‚ in applied work‚ structural equation models are most often represented graphically. Here is a graphical example of a structural equation model: For more information
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Transformation from Cylinder to Cartesian Coordinates Transformation from Cartesian to Cylindrical: Transformation from Spherical to Cartesian: The inverse transformation Differential Lengths‚ Surfaces and Volumes When integrating along lines‚ over surfaces‚ or throughout volumes‚ the ranges of the respective variables define the limits of the respective integrations. In order to evaluate these integrals‚ we must properly define the differential elements of length
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Chemical Reactions I. Purpose – The purpose of this lab was to observe different type of chemical reactions to write and balance chemical equations. II. Hypothesis: If you mix two chemicals together‚ then they will change color and/or bubble/fix. III. Procedure - Workstation 1: 1. Light the Bunsen Burner 2. Add 5 – 8 mL of HCL to a test tube that’s in the test tube rack 3. Drop a 2 – cm piece of Mg ribbon into the test tube 4. Record Observations 5. Clean Workstation
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