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# Linear Algebra

### Systems of Linear Equations Word Problems

1- Joe wants to sell his horses for 500.00 each and his cows for 300.00 each for a total of 2100.00 for them all. How many horses and how many cows are Joe selling? 2- King's Service Station uses two kinds of cleaning solution containing acid and water. "Attack" is 2% acid and "Blast" is 6% acid. They want to mix the two to

### 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.

1- 30 morpho granadensis@\$4.15 per pupa 33 battus polydamus@\$1.50 per pupa What is the total cost 2- A Coast-Guard patrol boat travels 4 hr on a trip downstream with a 6-mph current. The return trip against the same current takes 5 hr. Find the speed of the boat in still water 3- Tim's student loans totaled \$15,500.

### 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

### Linear Equations - area under the graph

Please see the attachment for fully formatted question This question has to do with the dissolving of the CO2 into the water contained in basalt. The amount of water in a given volume of basalt varies with the depth in a way we can measure. We need to know how much carbon dioxide the water in a region can hold. Specificall

### 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

### Solving Systems of Linear Equations: Substitution and Addition

Solve the following systems by substitution. Determine whether the equations are independent, dependent or inconsistent 36. y = -3x + 19 y = 2x - 1 38. 4 = -4x - 7 y = 3x 42. y = x + 4 3y - 5x = 6 56. 2x - y = 4 2y = 4x - 6 70. x + 3y = 2 -x + y = 1 Section 7.2 Solve each system by addition. 8. x + y

### Creating a System of Linear Equations

Please create a system of linear equations from your own life. Keep in mind that a system of linear equations will consist of two equations using the same variables and the variables will represent the same thing for both equations, i.e., if you use X as a variable in the first equation and X represents a number of beers then yo

### Algebra - Writing and Solving Linear Eqns from Word Problems

After 2 minutes on a treadmill, Jenny has a heart rate of 82, after 3 minutes she has a heart of 86. Assume that there is a linear equation that gives her rate in h terms of time on the treadmill t. What is the equation and use it to predict her heart rate after 10 minutes on the treadmill.

### 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

### Eigenvalue problem

Consider the eigenvalue problem (see attached) with boundary conditions y(0)=0, y(1)+y'(1)=0 - Determine the general solution - Apply the boundary conditions to solve for the eigenvalues - Show that the eigenvalues are all positive, there are a countably infinite number of eigenvalues, all the eigenvalues are simple roots....

### 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 &#61619;&#61472;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

### College algebra study guide

MTH133 Unit 4 Group Project - A Name: Your group will develop four different population scenarios for a town. As a group, you will decide on the name of the town and the initial population. You will graph the function for each population scenario and use your model to make some decisions about the population. 1) 1) De

### 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

### Conjugacy Classes and Subgroups

(a) Write out the conjugacy classes explicitly in S_3 and S_4. (b) What are the conjugacy classes in A_4? (c) Since |A_4|=12, any subgroup of order 6 would be normal. Use (b) to show that A_4 has no subgroup of 6. Conclude that the converse to LaGrange's theorem is false. (d) Find a normal subgroup of order 4 in A_4

### Practical Application of Linear Equations

Walt made an extra \$12,000 last year from a part-time job. He invested part of the money at 7% and the rest at 9%. He made a total of \$970 in interest. How much invested at 7%? I think the answer is \$840 but I am not positive this is correct. Please help.

### 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

### Diophantine Equation

Let R be a PID. Consider the Diophantine equation ax+by=N where a,b and N are integers and a,b are nonzero. Suppose x_0, y_0 is a solution: ax_0+by_0=N. Prove that the full set of solutions to this equation is given by x = x_0 + (mb/gcd(a,b)) y = y_0 - (ma/gcd(a,b)) as m ranges over the integers.

### Determining a Number Based on Qualities

I am a number with the following properties: IF I am not a multiple of 4 then I am between 60 & 69. If I am a multiple of 3 I am between 50 & 59 If I am a multiple of 6 I am between 70 & 70 What number am I?

### 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

### Solving a linear equation and find the value of x

The questions are as follows: 1. Solve the following linear equation and so find the value of x: 3x + 4 = 5x - 10 2. Solve the following pair of simultaneous equations using either the method of elimination or substitution: (i) 5x = -3y + 11 (ii) y = 4x - 19 3. Determine whether the s

### Life span and linear equations

Some scientists believe there is a limit to how long humans can live.* One supporting argument is that during the last century, life expectancy from age 65 has increased more slowly than life expectancy from birth, so eventually these two will be equal, at which point, according to these scientists, life expectancy should i

### 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

### Linear Equations of Antifreeze Solution and Saddler Height

(1) Angela needs 20 quarts of 50% antifreeze solution in her radiator. She plans to obtain this by mixing some pure antifreeze with an appropriate amounts of a 40% antifreeze solution. How many quarts of each should she use? (2) The saddle height on a bicycle should be 109% of the ride's inside leg measurement L. What is the

### 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.