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Basic Algebra

Rounding to the nearest 1/2 inch

When measuring a line with a ruler. When the question asks you to round to the nearest 1/2 inch, how do you determine if it is the nearest whole number or the nearest 1/2 number? Is the answer always a whole number?

Properties of addition and multiplication puzzle

Follow the steps to see if the puzzle works. § Start with 60 and divide by 2. § Add your telephone number. § Subtract 25. § Multiply by 3. § Subtract 15. § Multiply by 2 § Divide by 6. The remaining digits should be your telephone number. Why does this work? What properties of addition & multiplication

The Division Theorem

Let p and a be positive integers and suppose that p|a2. a) Show that p|(ra + sp)2 for all integers r; s. b) Use part a), the definition of prime integer, and Theorem 15.1.1 to construct a proof by induction that p|a. [Hint: If a (< or =) p consider p = qa + r, where 0 (< or =) r < a. If p < a consider a = qp + r, where 0 (<

Inequalities Using Interval Notation and Set-Builder Notation

4(3w+4)greater than or equal to 4(2w+12), it says to put answers in interval notation, that goes along with this one: 4-(3/2x-3)>1/2(x+5) I am not sure how to sove either one of these, they are somewhat the same except the second question asks for the answer in set builder notation.

Solving and Graphing Inequalities

2X+4Y is greater than or equal to 8? The question is choose the ordered pair, which is the solution of the inequality.

Graphing a System of Inequalities : Find Coordinates and Vertices

Given the system of inequalities. Find the coordinates of the vertices. 6y-x is less than or equal to 8 -y+3x is less than or equal to 6 x is less than or equal to 0

Equations for Absolute Values

The absolute value of 1/2n+2 is equal to the absolute value of 3/4n-2. How do I solve when there are fractions involved?

Change of Variables Investigated

Show that the change of variables.... Reduces 21.1 to the simpler and more familiar form from Ch. 18 Greenberg text, change of variables Please see the attached file for the fully formatted problems.

Do people use algebra in their jobs or their lives?

1. Very rarely do people use algebra in their jobs or their lives. At most, people use arithmetic. If this is the case then why do you suppose it is that we study algebra in the first place?

Method found in the proof below to find a primitive elements

Use the method found in the proof below to find a primitive element for the extension Q(i, 5^(1/4)) over Q. *Recall that the extension field F of K is called a simple extension if there exists an element In this case, u is called a primitive element. **Theorem: Let F be a finite extension of the field K. If F is separabl

Galois Theory: Algebraic Extension of a Perfect Field

Show that any algebraic extension of a perfect field is perfect (using the below hint only). Hint: Let K be a perfect field and F an algebraic extension of K. If F is not perfect, then there is a polynomial f(x) an element of F[x] that has an irreducible factor p(x) with a repeated root u. Here u is algebraic over K; let g(x)

Galois Group Example Problem

Show the Galois group of (x^2-2)(x^2+2) over Q (rationals) is isomorphic to Z_2xZ_2 (Direct product group of integers modulo 2). For your choice of your mapping theta, that is operation preserving, 1 to 1, and onto please show that is well defined.

Domain of the inverse of a logarithmic equation

Let f(x) = 3 - 7e^(x+5). The domain of f^-1(x) is: _______

Solving logarithms with different bases

7 log6 9(log2 80 - log2 5) Please see the attached file for the fully formatted problem.

An interesting problem on monotonicity

Find the number of solutions of the equation x+y=xe^y+ye^x

How many different types of this shirt are made?

A particular brand of shirt comes in 12 colors, has a male version and a female version, and comes in three sizes for each sex. How many different types of this shirt are made?

Solve each equation and check for extraneous solution.

Solve each equation and check for extraneous solution. # 41. ----------------- / 2x^2 - 1 = x # 42. ------------------------ / 2x^2 - 3x - 10 = x Solve the equation # 85 ----------------------- / x^2 + 5x = 6 # 91 ----------------------- /

Group Theory - Abelian Group: Show that if every element of the group G is its own inverse, then G is abelian.

Modern Algebra Group Theory (XX) Relation between Cyclic Group and Abelian Group Show that if every element of the group G is its own inverse, then

Write the following as rational numbers:

2. Write the following as rational numbers: a) 0.731; (31 barred) b) 12.8697 (8697 barred) Please see the attached file for the fully formatted problems.

Algebra: Solve 10 equations

Page 313 Solve each equation. # 8 ( a + 6 )( a + 5 ) = 0 # 9 ( 2x + 5 )9 3x - 4 ) = 0 # 12. t^2 + 6t - 27 = 0 # 48 - 2x^2 - 2x + 24 = 0 # 49 11 Z^2 + ---z = -6 2 # 52 3x (2x + 1 ) = 18 Page 364 Solve each equation. Watch for ext

Algebraic Numbers and Fields

Let be fields, and algebraic over F. show that if and only if for some . ---

If the group G has four elements, show it must be abelian.

Modern Algebra Group Theory (XVI) Abelian Group If the group G has four elements, show it must be abelian.

Splitting Fields : Let F be an extension field of K of degree 2, then F is the splitting field over K for some polynomial.

Let F be an extension field of K of degree 2, then F is the splitting field over K for some polynomial.

Integers, Cube Found

There are four integers between 100 and 1000 that equal to there cube added together 153......1+125+27=153 370......27+343+0=370 407......64+0+343=407 What is the fourth?

Systems of Logarithm Equations

I do not fully understand how to complete a system of equations that includes logarithms. This was the sample problem given.

Area of a region bounded by an equation

Find the region bounded by the graph of the equation. Estimate the area to confirm answer. Show a slice. Calculate the area of the region. y = square root of x-10 and y=0 between x=0 and x=9 y = square root of x and y= x-4 and x = 0

Matlab Hermite Interpolation

(See attached file for full problem description with equations) --- I need some guidance on a Matlab programming project. The project concerns Hermite polynomial interpolation. We are given values and and their derivatives and at and respectively, and we look for coefficients such that if

Mathematical Reasoning - Phil and Phyllis are Siblings.

Phil and Phyllis are siblings. Phyllis has twice as many brothers as she has sisters. Phil has the same number of brothers as sisters. How many girls and how many boys are in the family?

Rational expressions

(See attached file for full problem description with equations) --- Pg.283 Factor the GCF in each expression 59. 60. Pg. 306 Factor each polynomial completely, if polynomial is prime, say so 35. 40. Pg 338 Perform indicated operation 22.