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# Linear Algebra

### Algebra - Linear Inequalities

1. How do solving linear inequalities differ from solving linear equations? 2. What is the difference between identity, conditional, and inconsistent equations? Support your answer with an example of each. 3. What is the necessary condition for the following fraction to be valid? What value(s) of "x" that cannot be used

### Graphing [See the attached questions file.]

1. Which of the following graphs correctly describes the system and its solution? x + 4y = 12 y = -x A) B) C) D) None of these. 2. Which of the following systems of equations corresponds to the graph? A) C) B) D) 3. Solve the system of linear equations: 4x + 10y = -28 6x + 7y = 6 A) {(-2

### Discussion questions on systems of linear equations

Please provide an answer to the following questions below that contains 250 to 300 words each. 1.By looking at two linear equations, how can you tell that the corresponding lines are parallel, the same graph, or intersecting lines? How many solutions does each possibility have and why is that? Show examples for each possib

### Fueling Up - Motorists often complain about rising gas prices. Some motorists purchase fuel efficient vehicles and participate in trip reduction plans, such as carpooling and using alternative transportation. Other drivers try to drive only when necessary. ...2. Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was \$1.26 and in January 2006 the price of regular unleaded gasoline was \$2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points. Describe how you arrived at your answer. ...[See the attached questions file]

Fueling Up (1) & (2) Motorists often complain about rising gas prices. Some motorists purchase fuel efficient vehicles and participate in trip reduction plans, such as carpooling and using alternative transportation. Other drivers try to drive only when necessary. Application Practice Answer the following questions. U

### Develop and Solve a Linear Programming Model for this Problem. 1. Khan manufacturing produces two popular grades of commerical carpeting among its many other products. In the coming production period, Khan needs to decide how many rolls of ecah grade should be produced in order to maximize profit. Each roll of Grade A capret uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade B carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade A is \$200, the profit per unit of Grade B is \$160. In the coming production period, Khan manufacturing has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1700 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use.

Khan manufacturing produces two popular grades of commerical carpeting among its many other products. In the coming production period, Khan needs to decide how many rolls of ecah grade should be produced in order to maximize profit. Each roll of Grade A capret uses 50 units of synthetic fiber, requires 25 hours of production tim

### Linear Programming Case - The central police department

The central police department had recently been criticized in the local media for not responding to police calls in the downtown area rapidly enough. In several recent cases, alarms had sounded for break-ins, but by the time the police car arrived, the perpetrators had left, and in one instance a store owner had been shot. Sgt

### Set up a system of equations to model this scenario

Problem: A survey of 615 teenagers found that 44% of the boys and 35% of the girls would like to be taller. Altogether, 231 teenagers in the survey wished they were taller. 1) Set up a system of equations to model this scenario. 2) Use determinants and Cramer's rule to determine how many boys and how many girls were in the su

### Algebra - System of Linear Equations

1) In what fundamental way does the solution set of a system of linear equations differ from the solution set of a system of linear inequalities? Give examples. Discuss the important implications arising from this difference. 2) In your own words explain what is meant by a dependent system of linear equations. How does this dif

### Linear equations polynomial

1. Form each of the following: ? A linear equation in one variable ? A linear equation in two variables ? A quadratic equation ? A polynomial of three terms ? An exponential function ? A logarithmic function

### Systems of Linear Equations

Low-fat yogurt: Ziggy's Famous Yogurt blends regular yogurt that is 3% fat with it no-fat yogurt to obtain low-fat yogurt that is 1% fat. How many pounds of regular yogurt and how many pounds of no-fat yogurt should be mixed to obtain 60 pounds of low-fat yogurt?

### Clarification of Linear Equations

Super Bowl Contender: The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do play is 1. What is the probability that San Francisco plays in the

### Landscape Design - Solving Linear Equations

Note: Please view the attachment file. Landscape Design: Landscape designers often use coordinate geometry and algebra as they help their clients. In many regions, landscape design is a growing field. With the increasing popularity of do-it-yourself television shows, however, many homeowners are becoming amateur landscape

### linear relationship between population and size of habitat

3. To estimate animal populations, biologists count the total number of animals in a small section of a habitat. The total population of animals is directly proportional to the size of the habitat (in acres) polled. a. Write an equation using only one variable that could be used to solve for the constant of variation k.

### Truth Table

I need help with wether the symbolic form of the argument on the right is valid or invalid. q->r r->p _________ ~q->~p is this argument valid or invalid ?

### Word and Graph - 1. Why does the inequality sign change when both sides are multiplied or divided by a negative number? 2. Does this happen with equations? Why or why not? ... [See the attached Questions File.]

1. Why does the inequality sign change when both sides are multiplied or divided by a negative number? 2. Does this happen with equations? Why or why not? 3. Write an inequality for everyone to solve. In the equality, use both the multiplication and addition properties of inequalities. 4. How do you know if a value i

### Diverse Algebra Equations and Graphs 2

Algebra equations, word problems, and graphs (see attachment) 1. solve the following system of equations: x + 3y = 2 x = 6 - 3y 2. Determine the slope of the line shown in the right 3. Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 60 miles per hour and train B is traveli

### Graphical representation of linear equations - 1. Plot the graph of the equations 3x-8y=5 and 4x-2y=11 and interpret the result. ...

1. Plot the graph of the equations 3x-8y=5 and 4x-2y=11 and interpret the result. 2. Plot the graph of the equations 4x-6y=2 and 2x-3y=1 and interpret the result. 3. Plot the graph of the equations 10x-4y=3 and 5x-2y=6 and interpret the result. Show all graphs.

### Solving Systems of Equations and Inequalities

Please see the attached document for proper formatting of these questions. Thanks. ---------------------------------- Solve by graphing. Indicate whether each system is independent, inconsistent, or dependent. 1. y= 2x-1 x+y = 2 2. 3x - y = 4 3x - y = 0 Solve each system by substitution method.

### Graph and analyze linear functions - 1. How do we write the equation of a horizontal line? What would be an example? ...

1. How do we write the equation of a horizontal line? What would be an example? 2. How do we write the equation of a vertical line? What would be an example? 3. The points (3,9), (5,13), (15,33), (34,71), (678, 1359), and 1234,2471) all lie on M. The points (3,-9), (5,-11), (15,-21), (43,-40), (678, -684), and (1234, -124

### P and q compound statements

Give that p and q each represent a simple statement, write the indicated compound statement in its symbolic form. 1.p: This is a hammer q: This is a tool. If this is not a hammer , then this is not a tool. 2. p: The cone has three scoops . q. The cone costs \$1.85. The cone has three scoops if and only if the c

### The linear equation represents an estimate of the average cost of gas for year x starting in 1997

3. The linear equation represents an estimate of the average cost of gas for year x starting in 1997. The year 1997 would be represented by x = 1, for example, as it is the first year in the study. Similarly, 2005 would be year 9, or x = 9. a) What year would be represented by x = 4? b) What x-value represents the year 20

### Algebra - Diverse Function Problem

1. Find the slope, if it exists, of the line containing the pair of points (-2, -10) and (-13, -12). The slope m = ? Simplify your answer type an integer or a fraction, type N if the slope is undefined. 2 Use the intercepts to graph the equation x - 5 = y ... [See the attached Question File.]

### Algebra - Linear Programming for Maximizing

1. Maximize z = 4x1 + 2x2 Subject to -x1 - x2 &#8804; 12 3x1 - x2 &#8804; 15 x1 &#8805; 0, x2 &#8805; 0. 2. Maximize z = 5x1 + 4x2 + x3 Subject to -2x1 + x2 + 2x3 &#8804; 3 x1 - x2 + x3 &#8804; 1 x1 &#8805; 0, x2 &#8805; 0, x3 &#8805; 0.

### Gauss-Jordan Method

Use the Gauss-Jordan Method to solve each of the following systems of equations. 1. x + y = -1 y + z = 4 x + z = 1 2. 2x - y + z = 1 3x + y + z = 0 7x - y + 3z = 2 Please provide me the detailed steps on how to arrive at the answer to these problems. Thank you

### Substitution method:

Solve with substitution 9x+3y= -39 -3x + y = 29

### Solving system of equation by using elimination

Elimination method 4x - 8y = 3 4x - 8y = 4

### For most people, buying a house is a great investment that can offer security in an uncertain world, but buying a house is also a commitment.

Buying a Home For most people, buying a house is a great investment that can offer security in an uncertain world, but buying a house is also a commitment. Application Practice Answer the following questions. Click the white space below each question to maintain proper formatting. 1. Suppose you are in the marke

### Comparing Methods of Solving Systems of Linear Equations

Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method? Consider some of your responses by indicating pros and cons that you may not have considered or p

### What similarities and differences do you see between functions and linear equations?

What similarities and differences do you see between functions and linear equations? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for evaluation.

### Motorists often complain about rising gas prices.

1. Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: a) What does the number 3.03 represent? b) Find C(2) c) Find C(9) d) For the average motorist, name one value for g that would be inappropriat