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# Basic Algebra

### College Algebra : Solving Equations (9 Problems)

Please help with the following attached questions: 8, 14, 16, 20, 42, 44, 46, 52 and 58 (See attached file for full problem description)

### College Algebra

Please help with the following attached questions: 16, 20, 30, 32, 42, 50, 56 and 64. (See attached file for full problem description)

### Simplifying and Expanding Polynomial Expressions (8 Problems)

Please help with the following attached questions: 12, 14, 18, 32, 42, 50, 56 and 64. (See attached file for full problem description)

### College Algebra : Absolute Values Expressions and Equations (9 Problems)

Please help with the following attached questions: 2, 14, 16, 24, 22, 30, 36, 50 (See attached file for full problem description)

### College Algebra

Please answer the following attached questions: 14, 16, 20, 34, 42, 52, 66, 72 (See attached file for full problem description)

### Addition and Multiplication Tables in Algebra Coding Theory

How do I figure out the addition and multiplication tables for: Z mod 2 [x] / (x^2) ?

### Logarithm Problems : Change of Base, Graphing and Solving for X

Find the exact values: 1) log (base 10) 1000 2) ln e^-100 3) log (base 5) (1/25) 4) log (base10) (0.1) 5) log (base 12) 3 + log (base 12) 48 6) 2^(log(base 2) 3 + log(base 2) 5) 7) e^(ln 15) 8) e^(3ln2) 9) log(base 8)320 - log(base8)5 -------------------------------------------------------------------------------

### Quadratic Equation Applications

1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic formula. 2) For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the line of s

### Problem Set

(See attached file for full problem description) --- ? Identify the document by typing your full name and section number next to the yellow text. ? Rename the file by adding your last name to current file name (e.g., "u1ip_lastname.doc"). ? Type your answers next to the yellow text. ? To show your work, you will need t

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. How can I create three unique equations where the discriminant is positive, zero, or negative, and for each case, explain what this value means to the graph of

### Basic equations with logarithms

Basic equations with logarithms. See attached file for full problem description.

### Putting a function in a form y=

Y = x^2 - 4x - 5 = x^2 - 2*2*x - 5 = ( x^2 - 2*2*x +2^2 ) - 2^2 - 5 = (x-2)^2 - 2^2 - 5 = (x-2)^2 - 4 - 5 = (x-2)^2 -9 y = (x-2)^2 -9 How do I put this in the form y=a(x-H)^2+K, how do I graph this function, and why is it not necessary to plot points to graph when using y=a(x-h)^2+K?

### Algebra word problem

If John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be? How do I set up this equation?

Using the Quadratic equation: x2 - 4x - 5 = 0. How do I solve this by factoring? by completing the square? & solve by Quadratic formula?

### Algebra : Lowest Terms, Solve for X and Word Problems (10 Problems)

Please see the attached file for the fully formatted problems.

### For a subgroup H of G define a left coset of H in G as the set of all elements of the form ah, h in H. Show that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.

Modern Algebra Group Theory (XXVII) Subgroups of a Group Cosets of Su

### For a subgroup H of G define a left coset of H in G as the set of all elements of the form ah, h in H. Show that there is a 1-1 correspondence between the set of left cosets of H in G and the set of right cosets of H in G.

Modern Algebra Group Theory (XXVII) Subgroups of a Group Cosets of S

### Systems of Inequalities and Finding the Minimum Value : 4x + 3y > 72 and 6x + 10y < 174

The minimum value of z = 5x + 15y, subject to 4x + 3y > 72 6x + 10y < 174 x > 0, y > 0 occurs at: A. (0, 17.4) B. (9, 12) C. (18, 0) D. (29,0)

### Problem 12

Select the point which is in the feasible region of the system of inequalities: 4x + y < 8 2x + 5y < 18 x > 0, y > 0 A. (2,4) B. (-1,2) C. (1,3) D. (4,1)

### Tautologies, The Laws of Logic, The Basic Logical Laws, Absorption Laws (II) : Prove that p disjunction (p conjunction q) <=> p is a tautology

Modern Algebra Logic (XXII) Tautologies The Laws of Logic

### Tautologies, The Laws of Logic, The Basic Logical Laws, Distributive Laws (III) : Prove that p conjunction (q conjunction r) <=> (p conjunction q) conjunction (p conjunction r) is a tautology.

Modern Algebra Logic (XIX) Tautologies The Laws of Logic

### Tautologies, The Basic Logical Laws, Distributive Laws : Prove that p disjunction (q conjunction r) <=> (p disjunction q) conjunction (p disjunction r) is a tautology.

Modern Algebra Logic (XV) Tautologies The Laws of Logic

### Logic, Tautologies, The Basic Logical Laws, The Laws of Addition

Modern Algebra Logic (X) Tautologies The Laws of Logic The Basic Logical Laws The Laws of Addition (I) To prove that p => pVq is a tautology. The fully formatted problem is in the attached file.

### Logarithms, Exponents, Logarithmic Form and Exponential Form (12 Problems)

1. Convert the following equations into logarithmic form: a. 9 = 4^x b. 3 = 6^y c. 5 = 7^y d. X = 9^y 2. Convert the following equations into exponential form: a. X = log36 b. -5 = log3Y c. X= log4Y d. 1000 = log5Z 3. Simplify the following expressions: a. X5 * X7 b. Z10/Z11

The product of two consecutive even numbers is 1088. Find the numbers.

### Solve Quadratic Equations

17. Solve the equation 3 x^2 + 5x = -2 for x. 18. Solve the equations x^2 + 5x + 2 = 0 for x.

### Inverse, Logarithms, Exponents and Solve for X

Find inverse f(x)= 1/X-1 Convert to an expression involving exponent Loga 4=3 Laws of exponents. 5^3 /5^(3-1) Solve x^3 -6x^2 +8x=0 Find x, y intercepts 2x^2-4x+1

### Solve for X when X is a Power (Exponent) 4^x-2^x=0 4^x=8^x

4^(1-2x) =2^(1-2x) 4^x-2^x=0 4^x=8^x

### Follow the example and use the least upper bound property of the real numbers to prove that any positive real number has a cube root.

Given an example of squared roots: Let x be a real number such that x > 0. Then there is a positive real number y such that y2 = y?y = x Let S = {s &#1108; R: s>0 and s2<x} The S is not empty since x/2 &#1108; S, if x<2 and 1 &#1108; S otherwise. S is also bounded above since, x+1 is an upper bound for S. Let y be the l

### Denumerable and Induction

1. Show that if A and > are denumerable disjoint sets then A u > is denumerable 2. Show that every set of cardinalty c contains a denumerable subset 3. Show by induction that 6 divides n^3 - n for all n in N