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# Linear Algebra

### Algebra

Sue is offered a new job selling furniture where she makes a base pay of $1500 a month plus commission. According to a current employee, she should be able to earn $30,000 in sales monthly. To maintain her standard of living she must make $3000 total monthly. What commission rate must she earn to maintain her standard of livi

### Graphing Equations and Inequalities

Plot (- 1, 4) on the coordinate axes; I cannot insert the letter X which belongs on the side of the graph just like the letter Y is above. Y The numbers are 1through 10; also a negative 1-10;

### Linear Equation Word Problems

Please see the attached file for the fully formatted problems. 1. Translate the sentence to an equation and solve it. Six less than eight times a number is equal to that number added to one. 2. The length of a rectangular mailing label is 3 centimeters less than twice the width. The perimeter is 54 centimeters. Find the d

### Exponential Functions : Population Growth

The U.S. Census Bureau International Database gives the population of the ten most- populated countries in the year 2000 and population predictions for 2050 for these countries: Chinahad 1.2 billion people in 2000 and is predicted to have a population of 1.3 billion in 2050. The U.S. had a population of 284 million in 2000 with

### Calculations for solving systems of equations

Please help with the following problems. Provide step by step calculations. 3. Solve for X, Y, and Z in the following systems of three equations: a. X + 2Y + Z = 6 X + Y = 4 3X + Y + Z = 8 b. 10X + Y + Z = 12 8X + 2Y +Z = 11 20X - 10Y - 2Z = 8 c. 22X + 5Y + 7Z = 12 10X + 3Y + 2Z = 5

### Linear Equations: Slopes and Intercepts

PLEASE SEE ATTACHED FILE FOR FULLY FORMATTED QUESTIONS 1. Find the slope of the line. ANSWER: 2. Find the slope of the line that goes through the pair of points: (2, 5), (6, 10). 3. Graph the line through (2, 3) with slope . 4. Draw L1 through (-2, 1) with slope , and draw L2 through (-2, 1) with sl

### Algebra - Linear equations.

Please explain and answer questions. Thanks 1. Equations of Lines in Slope-Intercept Form Find the slope and y-intercept for each line. 3x + 5y + 10 = 0 2. Write each equation in slope-intercept form y- 5 = - ¾ (x+1) 3. Interest rates. A credit manager rates each applicant for a car loan on a scale of

### Linear Equations

Please help with the following problems. There are three methods to solving Linear Systems with two Equations. They are the Graph method, the Elimination method, and the Substitution method. When would you use each method? What makes each method better than the other methods?

### Solving Systems of Linear Equations and Word Problems

1.) Solving Systems by Graphing and Substitution Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate? 2.) Ticket sa

### Solving Systems of Linear Equations

Solve each step by graphing y = -2/3x 2x+3y = 5 Answer: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent x= y + 3 3x - 2y =4 Answer: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent 2x -

### Graphing Linear Equations

Please see the attached file for the fully formatted problems. 1. a) Determine if the ordered pair (2, ¼) is a solution of the equation (1/8)x + 3y = 1 b) Explain why or why not the pair is a solution. 2. a)Graph or describe fully the graph of the equation y = (2/3)x + 1. b) Show the table method with values for x o

### Basic Algebra : Mean, Median, Mode and Linear Equations

Fiona kept the following records of her phone bills for 12 months: $42, $37, $51, $41, $58, $44, $42, $35, $53, $58, $46, $57 Find the median of Fiona's monthly phone bills. (a) Find the mean of the following set of numbers. 12, 16, 19, 22, 28, 30 (b) Find the mode of the following set of numbers. 11, 1

### Algebra: Linear equations..

Please see the attached file for the fully formatted problems. 1.) x - x = 5 2 3 2.) 0.5b + 3.4 = 0.2b + 12.4 3.) -3 - 4(t - 5) = 2(t + 3) +11 4.) 0.08x + 0.5(x + 100) = 73.2

### Systems of Linear Equations Word Problems

Problem 1. Investments. William opened two investment accounts for his grandson's college fund. The first year, these investments, which totaled $18,000, yielded $831 in simple interest. Part of the money was invested at 5.5% and the rest at 4%. How much was invested at each rate? Problem 2. "Arctic Antifreeze" is

### Graphing and Systems of Equations Word Problems - MTH208

10. solve the system by graphing y=2x+1 X+y=-2 The graphs of the following systems are given in (a) through (d). Match each system with the correct graph. a-d graph lines intersect at the following points a. (-3,2) b. (-3,-2) c. (3,-2) d. (2,3) 21. 5x+4y=7 x-3y=9 22. 3x-5y=-9 5x-6y=-8 23. 4x-5y=-2 3y-x=-3 24.

### Linear Programming, Matrix and Set Operations, Gaussian Elimination and Systems of Equations and Inequlaities

Please see the attached files for the fully formatted problems. 8. (6 pts) There is a jar containing nickels and quarters. Suppose there are 89 coins in the jar, and the total value is $19.45. We would like to find out how many nickels and how many quarters are in the jar. Let x = number of nickels and y = number of q

### Comparing Linear Functions and Equations and Domain and Range

(1)- What similarities and differences do you see between functions and linear equations that you studied in Chapter 3? . Are all linear equations functions? · Is there an instance in which a linear equation is not a function? Support your answer. · Create an equation of a nonlinear func

### Solving Linear Systems of Equations and Inequaities (9 Problems)

1. (5 pts) The equation of the horizontal line passing through (1, -5) is _______ A. x = 1 B. y = 1 C. x = -5 D. y = -5 2. (5 pts) The standard form of the inequality x - 4y 12 is _______ A. y> - ¼ x + 3 B. 4y < x - 12 C. y< ¼ x - 3 D. y> ¼ x - 3 3. (5 pts) Which of the fo

### Price optimization, understanding monopoly pricing decisions and implications when a monopolist produces additional complementary products.

Part 1: What Price Should Apple Charge for the IPod? The IPod is a computer console designed and manufactured by Apple. This console currently dominates the computer market, selling more than its competitors. Assume that the following facts are true: ? The demand for IPod consoles can be approximated by the linear equati

### Algebra, Factions and Rational Expressions

Section 6.1: Rational Expression Which numbers cannot be used in place of the variable in each rational expression? 18. 2y+1 y² - y- 6 Section 6.2: Multiplication and Division Perform the indicated operation 24. 3 * 2a+ 2 a² + a 6 Section 6.3: Finding the Least Common Denominator

### Algebra (15 Problems) : Solve Systems of Equations by Graphing and Systems of Inequalities

On three consecutive passes, a football team gains 9 years, loses 35 yards, and gains 33 years. What number represents the total net yardage? -The total net yardage is ____ yards. .Find the indicated outputs for f(x)=4x squared-4x f(0)=__ f(-1)=__ f(2)=__ Soybean meal is 12% protein; cornmeal is 6% protein. How many p

### Algebra: operations with polynomials

Section 5.1 Greatest Common Factor for Monomials Find the greatest common factor for each group of monomials. 40. 16x²z, 40xz², 72x³ Section 5.2 Factoring a Difference of Two Squares Factor each polynomial. 16. 9a² - 64b² Section 5.3 Factoring with Two Variables Factor each polynomial. 64. h²- 9hs + 9s²

### Systems of Equations: Independent, Dependent or Inconsistent

See the attached file. Solving by Substitution Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent. 36.) y= - 3x + 19 y= 2x -1 38.) Y= -4x -7 Y= 3x 42.) Y= x + 4 3y -5x =6 56.) 2x -y =4 2x -y =3 Solve each system by the substitution method.

### Matrices : Linear Programing and Systems of Equations

The Mundo Candy Company types of chocolate candy: Cheery Cherry, Mucho Mocha, and Almond Delight. The company produces its products in San Diego Mexico City, and Managua using two main ingredients: chocolate and sugar. a. Each kilogram of Cheery Cherry requires .5 kg of sugar and .2 kg of chocolate; each kilogram of Mucho Moch

### Some graphing and various equation problems

1.) The national cost "C" in billions of dollars for dental services can be modeled by the linear equation: C = 2.85n+ 30.52 where n is the number of years since 1990 (Health Care Financing Administration, www.hcfa.gov). a) Find and interpret the C-intercept for the line. Put n = 0, we will get C = 30.52 C-interc

### Important information about Mathematics - Algebra - Linear Programming

Graphs and work done in Excel can be copied and pasted into the cells. Page # Prob. # Problem and Solution: 196 4 a. Add slack variables or subtract surplus variables. b. Set up the initial simplex tableau. 6 a. Add slack variables or subtract surplus variables. b. Set up the initial simpl

### 20 Problems : Graphing and Solving Systems of Equations and Inequalities and Writing Linear Equations from Word Problems

The graphs of the following systems are given in (a) through (d). Match each system with the correct graph. 21. 5x + 4y = 7 x - 3y = 9 MATCHES: 22. 3x - 5y = -9 5x - 6y = -8 MATCHES: 23. 4x - 5y = - 2 3y - x = - 3 MATCHES: 24. 4x + 5y = - 2 4y - x = 11 MATCHES: A. B.

### Linear Transformations, Matrices, Projections, Reflections, Kernels, Vector Space, Rank and Nullity (11 Problems)

Please see the attached file for the fully formatted problems. 1 Prove that the solution space of AX = 0, where A is a m x n matrix, is a vector space. 2 Are the vectors x3 - 1, x2 - x and x linearly independent in P3 ? Why ? 3 Determine whether or not the function T : Mmn --> Mmn dened by T(A) = A + B, where B is a mix

### Business : Formulate and Solve Systems of Equations for a Real-World Problem

The financial institution has asked your firm to place some spot advertisements. The financial institution wants you to find the best allocation of ads between 2 of the local media outlets. The company you have chosen to handle the transaction has estimated the average number of potential new customers reached per spot annou