### Linear Programming

Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x

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Solve the following system of simultaneous equations: 6x1 + 4x2 = 40 2x1 + 3x2 = 20 x1 = ??? put your answer in the form x or x.x

1. Find the slope of the line that passes through the points (2, 3) and (5, 8). 2. Find the equation of the line that passes through the points (3, -2) and (4, -2). 3. Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x + 3y = 6 and passing through (-3, 5). 4. Solve the

I need to know how to graph the following inequalities: 3x + y = or <5 x-y= or <2 y= or >5 Solve the system by graphing: x-y=2 3x-3y=6 3x-y=1 3x-y=2 Solve the system of linear inequalities by graphing: x-2y= or <4 x->1

Solve the following system of linear inequalities by graphing. 3x+4y is less than or equal to 12 x+3y is less than or equal to 6 x is greater than or equal to 0 y is greater than or equal to 0

1) f(x)=3x(2x-1). f(-1)= A)7 (B)11 (C)-6 (D) 9 2) The slope of the line through the points (3,4)and (-1,7) is A)4/3 (B) ¾ (C) -3/4 (D) 7/4 3)The line 6x + 9y=8 has slope A) -2/3 (B)-6 (C) 4/3 (D) 9 4)Select the line parallel to 6x +14y =20 A) 3x-7y=15(B) 7x-3y=8 (C) y=20/6x+14 (D)y= -3/7x+11/7 5) A revenue f

Please help with the following problems. Provide step by step calculations. Find the slope of each line that has a slope x=5y Find an equation in the form y=ms +b (where possible) for each line. Through (3,-5) parallel to y= 4 Graph each linear equation defined as follows; 3x - 5y =15 Solve each system of equat

Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them. Copy the questions to a Microsoft Word document and use an equation editor to enter the answers. Please answer the following questions

Note: For detailed description of the questions, please see the attached questions file. Below is the text that represents the brief description of the actual questions. Question (1) Given, f(x) = ( x + 2 )(2x - 3) , f (- 2 ) = ? Question (2) The equation of the line through (8 , 6 ) and (2 , - 4) is ... Question (3)

See attached file for full problem description. 24. Complete the ordered pairs so that each is a solution for the given equation. 3x + 4y = 12 46. Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula F = 9/5C + 32 . What is the Fahrenheit temperature that corresponds

Question Let (N, <) be the model with universe N and the "less than" relation. Show that Th(N, <) is decidable. Solution Reduce Th(AJ, <) to Th(fV, +), which we've already shown to be decidable. To do so, show how to convert a sentence 0, over the language of Th(A(, <), to a sentence 02 over the language of Th(AF, +) w

1. Solve the following systems of linear equations. Solve one using addition and one using substitution. State which method you are using for which system... a) 4x - 3y = 10 & y - 20 = -6x b) y = 3x + 6 & -6x + 2y = 12 2. You are buying coffee beans for your new business, "The Algebra Café." You

(See attached file for full problem description) 1. Graph f(x) = -2x + 2. 2. Rewrite the equation -x - 10y = 50 as a function of x. 3. Given f(x) = 5x2 - 3x + 1, find f(-2). A) -13 B) 15 C) -25 D) 27 4. Given f(x) = 4x - 5, find f(a - 1). A) 4a - 9 B) 4a - 6 C) a - 2 D) a - 9 5. Graph the inequality.

Step by step process in solving the following question. Using matrix algebra techniques, find a general solution of the system: x'=3x-4y y'=4x-7y

1) Given one point on the graph (-3, -5) and the slope, m = -2, develop an equation in the slope-intercept format Lecture). 2) Given one point on the graph (- 2/3, 2/5) and the slope, m = - 3, develop an equation in the slope-intercept format(Lecture). 3) Given the following two points, (- 4, - 2) & (-1, - 5),develop an

Solve the following linear system using Gaussian elimination. Show work. 2y + z = 4 x+ y +z = 6 2x + y + z = 7 Solve the following linear system for x using Cramer's rule. Show work. 4x - y + z = -5 2x + 2y + 3z = 10 5x - 2y + 6z = 1

1. You are given the following system of linear equations: 3x - 2y + z = 2 -x + y = 3 -2y + 6 = -1 Provide a coefficient matrix corresponding to the system of linear equations. What is the inverse of this matrix? What is the transpose of this matrix? Find the determinant for this matrix. Calculate the following

Please see the attached file for the fully formatted problems.

Matrices are the most common and popular way to solve systems of equations. Provide an example of a matrix that can be solved using Gaussian elimination. Show specifically how row operations can be used to solve the matrix. State the solution. Substitute the solution back into the equation to verify the solution. O

Let G be a group, and let H be a subgroup of G. Prove that H is a normal subgroup if and only if H can be expressed as the union of conjugacy classes of G.

10. Let A = a11 a12 a13 Show that A has rank 2 if and only if one or more of a21 a22 a23 the determinants a11 a12 a11 a13 a12 a13 a21 a22 a21 a23 a22 a23 are non zero. 14. Use the result in Exercise 10 to show that the set of points (x, y, z) in R3 for which the matrix

4. The Volta Battery Company manufactures AA, A. C, and D batteries in each of four plants. The daily production (in 1000's) for the four plants is given the following table: [TABLE] (a) The vectors that represent the production at the various plants are not linearly independent. Show this and find a dependency equation. (b)

Please see the attached file for complete description 1. Solve the system by graphing. x + y = 4 -x + y = 2 2. Determine which two equations represent perpendicular lines. 3. Solve the system by graphing. 3x + y = 6 3x - y = 0 4. Graph the inequality y < -3 5. Solve the following system of linear inequalit

10. Find the coordinate vector of p relative to the basis S = {p1, p2, p3}. (a) p = 4 - 3x + x2; p1 = 1, p2 = x, p3 = x2 (b) p = 2 - x + x2; p1 = 1 + x, p2 = 1 + x2, p3 = x + x2 22. Find the standard basis vectors that can be added to the set {v1, v2} to produce a basis for R4. v1 = (1, -4, 2, -3), v2 = (-3, 8, -4,

Prove that there is no field of order 6. (You can not refer to the fact that all finite field are of prime-power order)

2. Which of the following sets of vectors in R3 are linearly dependent? a) (4, -1, 2), (-4, 10, 2) b) (-3, 0, 4), (5, -1, 2), (1, 1, 3) c) (8, -1, 3), (4, 0, 1) d) (-2, 0, 1), (3, 2, 5), (6, -1, 1), (7, 0, -2) 4. Which of the following sets of vectors in P2 are linearly dependent? a) 2 - x + 4x2, 3 + 6x + 2x2, 2

1. Leon drove 270 to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10mph faster than Leon, how fast did each of them drive? 2. A company specializing in magazine sales over the telephone found that in 2500 phone calls, 360 resulted in sales and were made by a male caller, and 480 resulted in sal

A) Find the inverse of: |2 1 1| |0 1 2| |2 2 1| b) Use it to solve the following system of equations: 2x1 + x2 + x3 = 4 x2 + 2x3 = 0 2x1 + 2x2 + x3 = 1.

Suppose the sales of a company are given by S(x) = $200x + $20,000 where x is measured in years and x = 0 corresponds to the year 1996. Find the predicted sales in the year 2002 assuming the trend continues.

See attached file for full problem description. Graph y = -1. Solve the system by addition or substitution. 3x + 6y = 0 x = Find the slope of the line passing through the points (-4, 10) and (-6, 5). Solve: 6x + 4(3x - 2) = 6x + 2 Graph 3x + y = 3. Let y vary directly with x, with

(1) Given a line containing the points (1, 4), (2, 7), and (3, 10) determine the slope-intercept form of the equation and provide one additional point on this line, and graph the function.