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# Basic Algebra

### Sigma-Algebra, Measures, Properties of Measures

Let m be a sigma-algebra, M_1 and M_2 are measures on m. a). Is M = M_1 + M_2 a measure? b). Is M = M_1 - M_2 a measure? c). Is M = M_1M_2 a measure? Either prove or disprove by providing a counter example.

### Solving 3 Quadratic Equations : Optimum Methods

I had a 50 problem assignment, and have 3 questions that I either want to check my answers with a tutor, or had no idea how to figure them out. I have attached a Microsoft Word document, and would prefer getting that sent back to me with the work and answers shown so that I can understand it. Thank You! --- (See atta

### Write the Equation of a Line Given : Two Points; Slope and a Point or A Point and a Perpendicular Line

WRITING AN EQUATION FOR THE LINE CONTAINING THE INDICATED POINTS: 1. (0,0) AND (3, 30) 2. (-4, -4) AND (-3, -3) 3. (-6, -6) AND (-3, 1) 4. (4, -8) AND (3, -6) 5. ( -1/2, 7) AND -4, 1/2) 6.(-9, 1) AND (-1/2, 1) Those are the types of problems I am having trouble in writing equations containing indicated points. How do

### Greatest common divisor

Suppose that n is an integer >1 and a,b are positive integers. Prove... --- (See attached file for full problem description)

### Algebra: Least Common Multiple

Let n ≥ 2 and k be any positive integers. Prove that (n - 1) | (nk - 1). (We can use induction.) (Please show each step of your solution. Thank you.) --- (See attached file for full problem description)

### Reflect on the learning of radical expressions and their applications, and then consider how you might apply a radical expressions to your daily life.

Reflect on the learning of radical expressions and their applications, and then consider how you might apply a radical expressions to your daily life. Explain this application, and elaborate on what the equation might be. Does the study of these types of equations help anyone understand the application better?

### Area of a rectangle

A rectangle is twice as long as it is wide. If it has an area of 24.5 inches, what are its dimensions? English Language Mathematical Language the width and length of the rectangle ? The length is twice the width

### Fractions: The Least Common Denominator (LCD)

For the following expressions, complete this task: Find the LCD for the given rational expressions, converting each rational expression into an equivalent rational expression with the LCD as the denominator. Expressions: 4b/75a, 6/105ab 1/3x^2, 3/2x^5 3/8a^3b^9, 5/6a^2c

### Removing Symbols and Grouping Like Terms

1. Simplify: Remove the symbols of grouping and combine like terms. 5[3(4x - 2) - 3(6 - x)] + 7 2. Subtract (18x2 - 5x + 4) from (3x2 - 3x - 8) 3. Simplify: (27a3 b6 )2/3 4. Simplify: (102x+1)(104x) 5. Simplify and express your answer with positive exponents only. #6 & 7: Perform the indicated o

6 2/3 (8x ) 5 9 3 sq root. 24X y 3 sq root. 1 ___ 2 2X Solve for X 10X-2(5-X) = 7X-2(3+x)

### Algebra Help

I need step by step instructions on simplifying this finance equation. For example: How the sq rt was removed Multiply this term by this term How it is plugged into quadratic to find answer? I'm a returning student and I haven't studied algebra in 15 years. I've had this problem solved previously, but I'm still un

### See Attached Files for Details

Please See Attached Files for Details.

### Present value of Perpetuity

FIVE YEARS AGO, AN ALUMNUS OF A SMALL UNIVERSITY DONATED \$50,000 TO ESTABLISH A PERMANENT ENDOWMENT FOR SCHOLARSHIPS. THE FIRST SCHOLARSHIPS WERE AWARDED 5 YEARS AFTER THE MONEY WAS DONATED. IF THE AMOUNT AWARDED EACH YEAR (IE:, THE INTEREST) IS \$5OOO, THE RATE OF RETURN EARNED ON THE FUND IS CLOSEST TO? A. 7.5% PER YEAR B.

### Perform Computations in Scientific Notation

(See attached file for full problem description with equations) --- 1. Perform the following computation. Write the answer in scientific notation. 2. Perform the indicated operation. Solve for x. Reduce your answer to lowest terms. 3. Perform the indicated operation. 4. Solve this equation. Solve for x. 5. S

### Irreducible Representations of a Quaterion Subgroup

Let G be the subgroup of quaternions of 8 elements, that contains ±1, ±i, ±j, ±k with relations i^2=j^2=k^2= +/-1, ij=k, jk=i, ki=j, ij=+/-ji, ik=+/-ki, jk=+/-kj. Classify irreducible representations of G over C.

### Instantaneous Current, Voltage and Power

The instantaneous current and voltage in an electric circuit are given by i = Icos50 pi t v = Vcos(50 pi t + pi/6) Determine an expression for the instantaneous power in the circuit, p = iv, as the sum of two cosines. If I is 3 mA and V is 5 V, calculate the maximum value of p, giving your answer in watts correct to three si

1 + 3+1=0 x2 x

### Solving Equations (4 Problems)

Solve equation. Watch for extraneous solutions #30 6 + 7 =y-1 y-2 y-8 y-8 Solve equation and check for extraneous solutions # 35 square root oft 2t+4= square root of t-1 Solve each equation #88 square root 9x2= x+6 Solve each equation by using the quadratic formula. 3z2-8z+2=0 ---

### Solve Algebraic Equations for a Given Variable

Please help to find the solution set in real numbers of an equation such as: 2(3x-6x+1) = 3(1-2x)-1.

### Rearranging subject of formula

Make U the subject of the formula I=24e^-0.3U

### Rational expressions and their real-life applications

Based on the eduation and learning curve of rational expressions and their applications, consider how someone might apply rational expressions in their daily life. Explain this application, and discuss what the equation might be. Did the study of these types of equations help to understand the application better?

### Radical Expressions: Limitations of Square Roots

Discuss any difficulties you might have with grasping the concepts used in radical expressions. How would you explain square roots, cube roots, nth roots, and radicals to a student who is having difficulty understanding these concepts? What are some limitations of square root?

### Log n!, Summation and Theta Relation

Prove that log n! and sum from i=2 to n log i have a theta relation to n log n.

### Factoring a Cubic Equation

Question: Each of the three dimensions of a cube with a volume of x^3 cubic centimeters is increased by a whole number of centimeters. If the new volume is x^3 + 10x^2 + 31x + 30 cubic centimeters and the new height is x + 2 centimeters, then what are the new length and width?

### System of Differential Equations : Solve Using matrix Algebra

Using the matrix algebra technique find a general solution to x'=3x-4y, y'=4x-7y

### Mass of Planets, Gravitational Accelerations, Pendulum, Real-World Applications of Imaginary Numbers and Accuracy of Formulas

A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of tim

### Plotting the Curve on a Standard Graph

Approximately, where would the curve, log Y = log 2X plotted on standard graph paper intercept the Y-axis?

### Quantitative Methods : Integer Variables - Restrictions and Flexibility

Why does the use of integer variables create additional restrictions but provide additional flexibility?

### Expanding a Logarithm

How do I expand the logarithm log (subscript y) (13x/2)?