...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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...A linear equation In this lesson you can learn how to solve a simplest equation with one unknown variable. I will start with the following example. Solve an equation 5x - 8 + 2x - 2 = 7x - 1 - 3x - 3 for the unknown variable x. The left side of the equation is an expression, which is to the left of the equal sign. The right side of the equation is an expression, which is to the right of the equal sign. In our case the left side of the equation is 5x - 8 + 2x - 2, while the right side is 7x - 1 - 3x - 3. Terms containing variable x are called variable terms; terms containing the numbers only are called constant terms, or simply constants. The equation under consideration is called a linear equation, because its both sides are linear polynomials. The solution of an equation is such a value of the variable x that turns the equation into a valid equality when this value is substituted to both sides. I am explaining below how to solve this linear equation, in other words, how to find the unknown value of the variable x. The first step you should do is to simplify both sides of the equation by collecting the common terms containing variable x and the common constant terms separately at each side of the equation. Let us do it. By collecting common terms with the variable x at the left side, you will get 5x + 2x = 7x. By collecting common constant terms at the left side you will get -8 - 2 = -10. Thus, now the left side is 7x - 10. Making similar calculations...
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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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...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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...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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...that had been tagged. In this example a proportion will be used to estimate the size of the bear population. The original bear population will be examined against the later observed population to make this determination. The ration for the original tagged population against the entire population is 50/x The ratio of bears recaptured tagged bears against entire sample 2/100 50 = 2 This is the proportion that will be used to solve the problem by solving for x X 100 Cross multiplying will be used to yield a solution. The extremes of our proportion are 50 and 100 and the means are 2 and x. 50 (100) = 2x 5000 = 2x Both sides are divided by 2 2 2 2 is canceled out on the right side of the equation leaving 5000/2=x, x=2500. This means that the estimated population of bears on the Keweenaw Peninsula is 2500. I have seen on many animal shows on televisions where scientist tag animals release them And come back at a later time and recapture a sample to study tagged populations for various reasons. I now see one way they are able to calculate and estimate populations...
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...Crystal Shanyse King Professor Starra Shermin: Algebra Course November 28th, 2014 M2 Linear Reflection & Report When a person looks in the mirror, they see a reflection of themselves. Reflections in math often involve us flipping something over a line called the line of reflection. We can create mirror images of certain figures by reflecting them over a given line. It’s so amazing to use math in a reflection of our everyday lives. As a child, we think that math is pointless and why are we learning it? We think that we’ll never use it in life. But as i have grown older and have become an adult, i’ve used math almost everyday of my life from the smallest to the biggest things. It’s very important to be attentive in class, especially when your learning about algebra, because you never know when you’ll have to use it. In this week’s small group discussion, i learned so much from my classmates. Some of my peers did a linear equation reflection on they’re personal health, losing weight, making baby food, giving medicine to a baby, paycheck vs. expenses, a pool party, shopping, personal business, and budgeting. All examples of linear equations in real life. The example i was most impressed with was making baby food and giving medicine to a little child. I do not have any children, nor have i watched any long enough to give them medicine or baby food. But i learned that as a young parent it can be pretty scary. You are always concerned about what your putting into your child’s mouth...
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...refrigerators. This will be shown on the graph as “x” axis and the number will be “p” for television for the “y” axis. The points on the graph are going to show on the graph as (0,330) and (110, 0) these numbers are given to determine on how the slope is going to be placed on the graph in which will be known as the slope form. (Part A.) p = y1-y2 / X1-x2 = 330 – 0 / 0-110 = -3/1 the slope is -3/1 or -3 Y – y1 = p(x – x1) Y – 330 = - 3 / 1(x-0) Y = - 3x/1 + 330 -3x/1 +330 = y expression switch by place the y on the right hand side -3x/-3 = y/-3 – 330/ -3 divide each equation by -3 and cancel out like terms -3y = 1x + 110 -3y + 1x < 110 330 – 0 = -3 This will be known as the Point Slope Form. 110 – 01 This would be the slope -3/1. (0,330) (110, 0) Having these calculations will give me the point slope form for the linear...
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...|Teachers: | |Karla Meinen and Andrew Geigas | |Accommodations by Dalton Cook | |Student: |Age: |Grade Level: | |“Junior” |15 |Freshman | |Subject: |D| |Algebra 1-2 |a| | |t| | |e| | |:| | | | | |W| | |e| | |e| | |k| | ...
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...Linear Functions Natasha D. Collins MTH/208 14 April 2011 John Rudin Linear Functions Question: Using the readings in Ch. 3 of the text, identify and explain at least one real-world application of algebraic concepts for one of the following areas: business, health and wellness, science, sports, and environmental sustainability. Do you think it is easier to relate this concept to one of these areas over any other? Explain why. I think the point slope method would be good in professional sports, because you can see the process of an athlete’s career. Question: Imagine that a line on a Cartesian graph is approximately the distance y in feet a person walks in x hours. What does the slope of this line represent? How is this graph useful? Provide another example for your colleagues to explain. Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4. Question: Can one line have two slopes? Explain how or why not. If the line is a straight line, meaning 180degrees, it can only have one slope. If it is a function (f(x) = or y=) then the line may have more than one, one, or an undefined slope. Find the first differential of the function and plug in your given x value to find the slope at any given point. Question: What is the difference between a scatter plot and a line graph? Provide...
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...diameter stayed the same, it would become very difficult to stay attached, especially when you consider that the length of a tapeworm is much larger than the width of the neck. 2. My hypothesis will be confirmed if the slope value (or scaling coefficient, α) of the linear equation of the graph of the log of the neck width versus the log of the rostellum diameter is equal to 1. This is because we are comparing two 1 dimensional features of the cestode, unlike Poulin who compared a 2 dimensional feature (surface area of body) to 1 dimensional features so isometry in his study would have been determined by a .5 slope. A 1:1 relationship means that the features being compared are growing at equal rates so the α = 1 and the relationship is defined as being isometric. If the body feature is growing faster than the body size, the α > 1, then the relationship is defined as being hyperallometric. Finally, if the body size is growing faster than the body feature size, then the α < 1, and the relationship is defined as being hypoallometric. 3. The reason we transform the raw data that was collected into log data is to show a linear relationship. Plotting the raw data could sometimes result in linear graphs, but could also show curvilinear, etc. To avoid this, we plot the log of the data, with the slope acting as the scaling coefficient, in order to determine the growth relationship between features....
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