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# Basic Algebra

### Few quest functions and math

Let K be a field. (All of this works just as well for a division ring.) Let V be an n-dimensional vector space over K and let A = EndK(V), the ring of n n matrices over K. The ring A is clearly Artinian since it has finite dimension over K. We need to see that the 2-sided ideals are either (0) or A. 1. Let W be a subs

### Algebraic Sets

II. The three different media outlets of radio, Internet, and newspaper are to be offered on weekends or weekdays, and then either between 7 a.m.-3 p.m., 3 p.m.-11 p.m. or 11 p.m.-7 a.m. How many different possibilities exist? List the possibilities and verify your listing with the multiplication principle for counting. III.

### Transportation, Transshipment, and Assignment Problems

Gravel has been ordered from Lo Tran by Ace Construction. The Lo Tran trucks carry 3 tons max per load. The costs per ton per truck to move gravel between sites is listed below. What are the optimum loads, routings, and costs of addressing this contract? Please see the attached file for the fully formatted problem.

### Algebra - Systems of Equations - Word Problems

The table below is based on surveys of double-income families and the percent of men and women in these families who said they had the greater responsibility for various areas of the housework. In the category of paying bills, a total of 98% of this responsibility was taken on by either women or men. (One can surmise that in 2%

### Find the Domain of Each Rational Expression

Find the domain of each rational expression. 28. x^2 - 3 over x + 9 Reduce each expression to lowest terms. 73. 3a - 2b over 2b - 3a Perform the indicated operation. 26. b^3 + b over 5 * 10 over b^2 + b 52. (6y2 - y - 2) / 2y + 1 over 3y - 2 Find the LCD for the given rational expressions, and convert each rational

### Proportions and word problems

83. Filling the tank. Chantal filled her empty gas tank in x minutes. a) Write a rational expression for the rate at which she filled her tank. b) Write a rational expression for the portion of the tank that is filled in 2 minutes. Solve the equation 59. 4/c-2 - ½-c + 25/c+6 Use a proportion to solve each problem. 47

### Equations and graphing

See attached For problems 1 - 7, simplify the following expressions.: Problems 8 - 11: Solve each equation. 12. Solve the inequality and express the solution in interval notation.: 2(x - 4) < 3x + 8 Problems 13 - 18, Solve each system by the algebraic method of your choice (either substitution or addi

### Algebra - Equations...

Please show all steps: v 1. - = 2 2. 16 = k 8 - 11 3. -15 + n =-9 4. v --- =8 5. -17x=-204 7

### Who should study algebra?

Should algebra be taught to everyone? Who should study algebra? The statements below serve as possible answers to these questions and are only 'food for thought.' I welcome your constructive ideas and comments on one or several of them. Whether you agree or do not agree, the study of algebra is good for the brain. The b

### Solving and Graphing Inequalities: Example Problem

Solve and graph the inequality : y < 2x - 3

### Introduction abstract algebra

Let M and N be two Normal subgroups of G. Prove that (1) MN=NM (2) MN is a normal subgroup of G (3) if M ^ N = {e} then MN/N and M are isomorphic ( ^ means "and") Thank you

### Logarithmic and exponential expressions

Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents. Find the pH of an acidic substance of your choice. Using this pH, show how to find the hydrogen ion concentration, [H+], of the substance using th

### Inequalities and functions solving by elimination and substitution

I'm studying and I need to check these answers against mine. Thank you for your help. Inequalities and functions... 1. 5 x + 4y=8 2. 75 + 6 9 3. Distribute: 8(w-3) = -24 4. Find the value of x: 8x - (5x+6)=3 5. Solve by elimination method: what is the solution? 5x + 6y = 2 10x + 12y = 4 6. Solve by substitution

### Simplifying and Combining Algebraic Terms

Please see the attached file for the fully formatted problems. 1. Simplify - 5 (7 - 2 ) - 3(4 - 7 ) - 13 - (-5 ) or in linear form [ - 5 (7 - 2 ) - 3(4 - 7 ) ] / [ - 13 - (-5 ) ] ___________________________________________________________________ 2. Simplify 7 - 2(14x - 2y) + 4( x -

A member of the Road Runner Club likes to exercise every day by walking and jogging at least 3 miles. She walks at a rate of 4 mph and jogs at a rate of 8 mph. With only half an hour to exercise, how much time can she spend walking and jogging and cover at least 3 miles? a) Give 3 possible solutions.

### Equations and graphing problems

1.The equation y= -1777x+25,153 can be used to predict the number y of gun deaths in The United States x years after 2000, that is, x=0 corresponds to 2000, x=2 corresponds to 2002, x=4 corresponds to 2004, And so on. Predict the number of gun death in 2004 and 2005. In what year will the number of gun death be 11,160? The

### Algebra problems - Graphing, Solving and Using equations

1.The equation y= -1777x+25,153 can be used to predict the number y of gun deaths in The United States x years after 2000, that is, x=0 corresponds to 2000, x=2 corresponds to 2002, x=4 corresponds to 2004, And so on. Predict the number of gun death in 2004 and 2005. In what year will the number of gun death be 11,160? Th

### Divisibility Proofs Minimal Polynomial

Hello, I need a detailed solution to the attached problem: Let A be a finite dimensional F-algebra, a is in A a unit of finite order m..... Hint for part (a): p | x^k - 1 <=> x^k = 1 in F[x]/p <=> m|k since m = ord(x) in F[x]/p

### Basic Algebra and Word Problems

Please see the attached file for the fully formatted problems. 1. 5/12+7/8= 2. ?7/6 3. -44-22= 4-(-10)= 4. 7*-3/2*-1/9 5. 6. 7. 8. 9. Solve for t 224=106-t 10. Solve for y 6=-3/2y 11. Distributive property 9(x+9) 12. 3s-12=45 13. Solve for w 4w-8=-12 14. Solve for y 2(y+6)-8y=-30 15. Solve f

### Applications of Exponential and Logarithmic Functions

Part1: Using the library,web resourses,and other materials, find the hydrogen ion concentration,[H+], of the substance using the formula. Discuss the meaning of pH and [H+], the pH scale and why your chosen substance is acidic. Use scientific notion or enough decimal places so that your answer has at least 3 place values. For e

### Writing Equations from Word Problems: Example

Write algebraic expressions for the following unknown integers. See Example 4. 1) Three consecutive even integers Translating Verbal Expressions into Algebraic Expressions 2) The rate, given that the distance is 200 feet and the time is x + 3 seconds 3) The perimeter of a rectangle, given that the length is x yards

### Inverses of Hyperbolic Functions

Find and prove a formula for the inverse hyperbolic tangent, arctanh(x) . The formula should involve a natural logarithm. Also, check the answer by substituting the definition of tanh x into your inverse formula and simplify. Show all work please.

### Cross-multiplication & inequalities

Please explain to me,What is the inherent meaning and justification of cross-multiplication as it applies to solving an inequality?

### Algebra - Fractions, Decimals and Areas

Please see the attached file for the fully formatted problems. Gasoline is about \$4 per gal. You use about gallons each day driving to and from work. How much should you budget for gas over the next month (about 20 workdays)? Find the least common multiple of 10, 15, and 25. A) 150 B) 3,750 C) 50 D) 30 Add.

### Evaluating Expressions with Absolute Values

Place each of the following sets in ascending order. 16. Evaluate. 32. 44. Add 40. 48. Evaluate each of the following expressions 58. Label each of the following statements as true or false. 66. 72. Business and finance. Jean deposited a check for \$625, wrote two for \$68.74 and \$29.95 and used

### Conducting Regression Analysis in Minitab

Background: I have data set for two litter sites "C" and site D. Around 90 litter bags filled at site C, mass of each bag were same initially, after time 0.246 years masses of 45 bags were noted and after .493 years masses of another 45 bags noted. Similar exercise done at another site"D". The negative exponential model of

### Abstract Algebra Problems: Algebraic Proof

** Please see the attached file for the complete problem description **

### Basic Algebra : Adding and Subtracting Real Numbers and Fractions

Please see the attached file for the fully formatted problems. 9.1 Place each of the following sets in ascending order. 16) = When a set of numbers is written from smallest to largest, the numbers are said to be in ascending order.

### Equations and expressions

See attached Add the polynomials Find the product Find the opposite of the polynomial Simplify Find the quotient and the remainder. Write without negative exponents Factor out the greatest common factor Factor completely Solve the given equation Reduce the given expression to lowest terms Solve the equation fo

### Algebra - System of Equations - Word Problems

Part 3: Maria's Mantillas. Maria plans to make two different kinds of mantillas (veils), some out of lace and some out of a sheer cotton fabric. She also plans to make two sizes of mantillas, one size for women and one size for young girls. She has 150 yards of the lace fabric and 200 yards of the cotton fabric. She will need 2