...Part 1 State whether the equation 3x^2 y = 6 is linear or nonlinear and explain your answer. My answer is that the equation is nonlinear because there are 2 different parallel lines that do not intersect with each other, the solution is x = 0 and y = 2/x^2. The Cartesian plane which is a two dimensional coordinate system. A horizontal number line forms the x-axis of the plane, and a vertical number line forms the y-axis. The axes intersect at their 0 points; this coordinate is called the origin. Every point in the plane can be defined by its x and y coordinate. The x-coordinate of a point is the point’s distance in the x direction from the y-axis. Similarly, the y-coordinate of a point is the point’s distance in the y direction from the x-axis. It is customary to use ordered pairs (x, y) to represent the coordinates of a point in the plane. The x-coordinate is the first coordinate, and the y-coordinate is the second coordinate. It is possible to use graphing to solve a system of linear equations. There are three possible situations for the graphs of lines in a system: the graphs are parallel lines, they are the same line, or the lines intersect at a unique point. If the lines are parallel, their graphs have no points in common and there is no solution to the system. Lines with the same slope and same y-intercept are not only parallel but also the same line. The graphs are the same line and the system has an infinite number of solutions. An equation states a balanced relationship...
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...Unit 6: Systems of Linear Equations and Inequalities SELECTED RESPONSE Identify the letter of the choice that best completes the statement or answers the question. 1. Identify the graph that represents the system of linear equations. [pic] |A. |[pic] |C. |[pic] | | | | | | |B. |[pic] |D. |[pic] | 2. The graph below shows the cost (c), in dollars, to rent a boat for h hours at two different boat companies. [pic] At what number of hours will the cost to rent a boat be the same at both companies? F. 4 G. 5 H. 8 J. 20 3. John and Patrice are each saving money to buy a car. John has $750 saved and will save an additional $30 a week. Patrice has $1,200 saved and will save an additional $20 a week. How many weeks will it take John and Patrice to save the same amount of money? A. 39 weeks B. 40 weeks C. 45 weeks D. 55 weeks 4. Choose the equation wherein you would isolate a variable easily so that substitution method can be used to solve the linear system. [pic] F. Equation 1 G. Equation 2 H. Neither Equation 1 nor Equation 2 J. Both Equation 1 and Equation 2 5. Solve the linear system. [pic] A. (5, 7) ...
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...One of the most important concepts that we learned in this course is formulating linear equations from everyday life problems that need solutions. With this concept under your belt you will always be able to find solutions in everday life. For example what if you have a new house interior to paint and you need to figure out how much paint you should purchase. Through this course we have attained the ability to determine the exact amount of paint needed to be purchased. What many fail to realize is that math is in our lives daily on multiple occasions. This course provided the comfort of being able to handle this daily math without worries. Out of all the concepts explained inequalities seem to be the least important to everyday life. Although they seem the least important does not mean they are useless. Someone somewhere is using these equations for a significant task. How do you think you will use the information you learned in this course in the future? Which concepts will be most important to you? Which will be least important? Explain your answers. I will continue to use basic mathematical (algebraic) calculations such as expenses versus income in applicable situations, estimation of materials based upon linear measurements and the calculation of expenses based upon the cost factor of those materials as I progress in my personal life. I do see myself for personal reasons, using simple graphs to get ideas or guidance on how my personal venture(s) in life is...
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...Week Three Linear Inequality Lynn Branham MAT221 Instructor Charlie Williams May 9, 2013 Introduction On Linear Inequalities Linear equations are special kinds of algebraic expressions that contains two variables. The value of one variable is dependent upon the other. The functions of inequalities are expressed as a line. The complexity of linear equations and linear equalities are sometimes compared concerning the complications of each. Unlike linear equations, linear inequalities incorporate the assessment of where to shade after a solution has been determined. Typically, two equations collaborate to compose a linear inequality. A linear equation will be made up of a combination of constants, a set of numbers and variables. The variables must be to the first power and cannot be squared or cubed. According to Michael Judge, the most common type of linear equation is in the form y = mx + b and describes a straight line (2010). In this case, the two variables are usually x and y and the constants are m and b which are numbers giving the slope and intercept of the line. Operations of Linear Equations Two equations and two variables are needed to find specific values. My variables are: c = # of classic maple rockers m = # modern rockers A classic maple requires 15 board feet of maple, and a total of...
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...Unit 2: Instructor Graded Assignment Equations In this and future Instructor Graded Assignments you will be asked to use the answers you found in the Unit 1 Assignment. Note: For these questions you need to cite a reliable source for information, which means you cannot use sites like Wikipedia, Ask.com®, and Yahoo® answers. If you do use those sites the instructor may award 0 points for your response. The Assignment problems must have the work shown at all times. The steps for solving the problems must be explained. Failure to do so could result in your submission being given a 0. If you have any questions about how much work to show, please contact your instructor. Assignments must be submitted as a Microsoft Word® document and uploaded to the Dropbox for Unit 2. Type all answers directly in this Assignment below the question it applies to. All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit. Finding the National Average Price for Gas These first few questions will require you to use the internet to search for the national average price for gas. Remember to use a scholarly site for information. List the website(s) you visited here: http://fuelgaugereport.aaa.com/todays-gas-prices/.com 1. (2 points): What was the average price of a gallon of gas 1 year from when your business math class started? A month ago the national average gas price was 2.035 2. (5 points): You have $50 on hand and need to buy gas. How many gallons...
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...before they are needed so they are not caught in a lurch. Our regression analysis looks at comparing two factors only, an independent variable and dependent variable (Murembya, 2013). Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.018314784 R Square 0.000335431 The portion of the relations explained Adjusted R Square -0.009865228 by the line 0.00033% of relation is Standard Error 1.197079687 Linear. Observations 100 ANOVA df SS MS F Significance F Regression 1 0.04712176 0.047122 0.032883 0.856477174 Residual 98 140.4339782 1.433 Total 99 140.4811 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 4.731133588 1.580971255 2.992549 0.003501 1.593747586 7.86852 Intrinsic -slope 0.055997338 0.308801708 0.181338 0.856477 -0.5568096 0.668804 Line equation is benefits =4.73 + 0.0559 (intrinsic) Intercept- t-stat HO: Coefficients is zero. Intrinsic t-stat is zero...
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...independent variable 3. On a graph of two variables, X and Y, ceteris paribus means that: Other variables not shown are held constant 4. There are two sets of (x,y) points on a straight line in a two-variable graph with y on the vertical axis and x on the horizontal axis. If one set of points was (0,6) and the other set (6,18), the linear equation for the line would be: y=6+2x 5. The slope of a straight line is the ratio of the: vertical to horizontal 6. If a linear relation is described by the equation was C = 35 - 5D, then the slope of the line would be: 7. If two variables are directly related they will always graph as: an upsloping line 8. When variables A and B are negatively correlated, it implies that: A and B may or may not be causally related 9. A relationship illustrated by an upsloping graph means that an: Decrease in the value of one variable causes the value of the other to decrease 10. There are two sets of (x,y) points on a straight line in a two-variable graph with y on the vertical axis and x on the horizontal axis. If one set of points was (0,75) and the other set of points was (75,25), the linear equation for the line would be: y=75-.66x 11. If you knew that the vertical intercept for a straight line was 150 and that the slope of the line was 4, then the dependent variable would be 250 when the value of the independent variable is: 25 12. If an inverse relationship exists between two variables, then: one variable...
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...it from both left and right side of the masses. The following list of equations, that will be written in a linear system of differential equations, represents the forces acting onto each mass: m_1 〖x_1〗^''=〖-k〗_1 x_1+k_2 (x_2-x_1 ) m_2 x_2^''=〖-k〗_2 (x_2-x_1 )+k_3 (x_3-x_2) m_3 x_3''=-k_3 (x_3-x_2 )-k_4 x_3 m_1 〖x_1〗^''=x_1 〖(-k〗_1-k_2)+x_2 (k_2) m_2 x_2^''= x_1 (k_2 )+x_2 (〖-k〗_2 〖-k〗_3 )+x_3 (k_3) m_3 x_3''= x_2 (k_3 )+x_3 (〖-k〗_3 〖-k〗_4) [■(x_1''@x_2''@x_3'')]= [■((〖-k〗_1 〖-k〗_2)/m_1 &k_2/m_1...
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...Algebra I Suggested Teaching Strategies The curriculum guide is a set of suggested teaching strategies designed to be only a starting point for innovative teaching. The teaching strategies are optional, not mandatory. A teaching strategy in this guide could be a task, activity, or suggested method that is part of an instructional unit. It should not be considered sufficient to teach the competency and the associated objective(s); the teaching strategy could be one small component of the unit. There may not be enough instructional time to utilize every strategy in the curriculum guide. The 2007 Mississippi Mathematics Framework Revised includes the Depthof-Knowledge (DOK) level for each objective. As closely as possible, each strategy addresses the DOK level specified for that objective or a higher level. Suggestions or techniques for increasing the level of thinking may be included in the strategy(ies). In addition, the process strands (problem solving, communication, connections, reasoning and proof, and representation) are included in the strategies. The purpose of the suggested teaching strategies is to assist school districts and teachers in the development of possible methods of organizing the competencies and objectives to be taught. Since the competencies and objectives require multiple assessment methods, some assessment ideas may be included in the strategy. October 2007 2007 Mississippi Mathematics Framework Revised Strategies Comp. 1 2 Obj. a g ...
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...Linear Functions Unit Plan Part 2 – EDCI 556 – Week 2 Darrell Dunnas Concordia University, Portland Linear Functions Unit Plan Part 2 Mr. Dunnas decides to change the graphing linear equations lesson into a problem-based lesson. This lesson is comprised of three components. Component number one is to write the equation in slope-intercept form (solve for y). Component number two is to find solutions (points) to graph via t-tables and slope-intercept form. Component number three is to graph the equation (connect the points that form a straight line). In mastering this lesson, all components must be addressed. In teaching, all learners how to graph linear equations, one must create a meaningful context for learning. First, the lesson must be aligned to the curriculum framework (Van de Walle, Karp, & Bay-Williams, 2013). Graphing linear equations is a concept found in the curriculum framework. Second, the lesson must address the needs of all students (Van de Walle, Karp, & Bay-Williams, 2013). The think-aloud strategy and graphing calculators will be used to graph linear equations and address the learning styles of all learners. Third, activities or tasks must be designed, selected, or adapted for instructional purposes (Van de Walle, Karp, & Bay-Williams, 2013). Lectures, handouts, videos, and cooperative learning activities will be used in teaching the lesson. Fourth, assessments must be designed to evaluate the lesson...
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... [pic] Figure 1. The intersections of five one-way streets The letters a, b, c, d, e, f, and g represent the number of cars moving between the intersections. To keep the traffic moving smoothly, the number of cars entering the intersection per hour must equal the number of cars leaving per hour. 1. Describe the situation. • In this traffic model the pictures illustrates that as cars go out in one direction there is a number of cars coming that are equivalent to the total number of cars going out. The traffic flows through B, C and d will remain a constant, and traffic that flows through the other intersection will change. 2. Create a system of linear equations using a, b, c, d, e, f, and g that models continually flowing traffic. 3. Solve the system of equations. Variables f and g should turn out to be independent. 4. Answer the following questions: a. List acceptable traffic flows for two different values of the independent variables. b. The traffic flow on Maple Street between I5 and I6 must be greater than what value to keep traffic moving? c. If g = 100, what is the maximum value for f? d. If g = 100, the flows represented by b, c, and d must be greater than what values? In this situation, what are the minimum values for a and e? e. This model has five one-way streets. What would...
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...1) Evaluate the expression. 5xy 6 y if x 3 & y 4 2) Evaluate the expression. 3x 2 2 xy if x 3 & y 4 3) Evaluate the expression. x 3 y y x if x 6 & y 2 4) Evaluate the expression. xy xx y if x 6 & y 2 5) Combine the like terms. 11x 5 y 7 y 4 x 6) Combine the like terms. 13x 2 7 x 8x 2 x Ocean Township HS Mathematics Department (Algebra 2 Summer Assignment) 1 7) Combine the like terms. 7 xy x 2 y 9 x 2 y 4 xy 8) Combine the like terms. 8x 2 12 x 3 3x 2 5x 3 9) Solve the linear equation. 2 x 9 25 10) Solve the linear equation. 11 20 3x 11) Solve the linear equation. x 7 11 3 12) Solve the linear equation. 2 x 6 x 24 13) Solve the linear equation. x 4 x 6 30 14) Solve the linear equation. 2x 4 11 15) Solve the linear equation. 53 x 25...
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...algebra: Linear and quadratic equations, Solving linear and quadratic equations, Application of equations: profit, pricing, savings, revenue, sales tax, investment, bond redemption, linear inequalities, applications of inequalities: profit, renting verses purchasing, leasing versus purchasing, revenue, current ratio, investment, Maple session on solving linear, quadratic and higher degree equations, solving inequalities II. Functions and Graphs: Introduction to functions, domain and range of a function, Applications: demand, supply and profit functions, demand and supply schedule, value of business, depreciation, Special functions: polynomial, rational, piecewise defined functions, Absolute value function, and evaluation of such functions. Combination of functions. Applications: cost, investment, sales, profit, business, Graphs of functions: linear, quadratic, piecewise defined functions, graphing of quadratic functions by finding vertex, Applications on graphs: inventory, debt payment, pricing, revenue and profit, demand and supply curves, Maple session on functions and graphs III. Lines and Systems: Equation of a straight line, slope and intercept of a line, parallel and perpendicular lines, Applications: price-quantity relationship, production levels, cost, revenue, demand and supply equations, isocost line, isoprofit line, depreciation, appreciation, systems of linear equations, solution of system of linear equations, nonlinear systems: one linear one quadratic...
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...not of the same length, their product is not defined. Example: [pic] The Product of a Row Vector and Matrix When the number of elements in row vector is the same as the number of rows in the second matrix then this matrix multiplication can be performed. Example: [pic] If the number of elements in row vector is NOT the same as the number of rows in the second matrix then their product is not defined. Example: [pic] Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine function defined on this...
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...LECTURE 3 LINEAR FUNCTIONS AND GRAPHS TYPES OF FUNCTIONS a. Constant Functions f(x) = a b. Linear Functions f(x) = a1x + a0 c. Quadratic Functions f(x) = a2x2 + a1x + a0 d. Polynomial Functions f(x) = anxn + an-1xn-1 + …+ a1x + a0 e. Rational Functions g ( x) f(x) = h( x ) APPLICATION FUNCTIONS a. Linear Demand Functions, p = f(q) p = price; q = quantity of a product b. Linear Supply Functions, p = f(q) p = price; q = quantity of a product c. Linear Cost Functions, C(q) = fixed cost + variable cost q = number of units produced d. Linear Revenue Functions, R(q) = p q q = number of units sold; p = price e. Linear Profit Functions, π(q) = R(q) – C(q) q = quantity of a product FORMING LINEAR EQUATIONS I. Standard form of Linear equation Ax + By = C where A,B, and C are constants (A & B not both 0) ===> is a straight line It is a first-degree equation – each variable in the equation is raised to the first power. e.g.: 2x + 5y = -5 2s – 4t = -1/2 FORMING LINEAR EQUATIONS II. Slope-Intercept form of Linear equation y = mx + b Example: y = 2x + 1 y = -3x + 2 FORMING LINEAR EQUATIONS III. Point-Slope form of Linear equation y – y1 = m (x – x1) Is an equation of a line with slope m that passes through (x1, y1) It enables us to find an equation for a line if given a) its slope and the coordinates of a point b) two coordinates of two points on the line SLOPE -Slope of two points (x1,y1) & (x2, y2) is given by ...
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