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Basic Algebra

Other zeros

(See attached file for full problem description) If P(x) = x^3 + x^2 - 5x + 3, and if x = 1 is a zero of P, find the other two zeros.

Cyclic Multiplicative Group : Field of Order 2^7

1. Prove that the multiplicative group of a field of order 2^7 is cyclic. Note: This problem can be solved in a few lines. Do not construct the field of order 2^7 to solve the problem. 2. Prove that the only subfield of a field of order is a field of order 2.

Linear, quadratic, rational, or exponential functions

a) Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? b) Which one of the basic functions (linear, quadratic, rational or exponential) is related to the arithmetic sequence? c) Which one of the basic functions (linear, quadratic, rational or exponential) is rel

Factoring

(See attached file for full problem description) Factor completely over the integers - y^3 - 1000 z^6

Answer study guide

(See attached file for full problem description) --- 1. Which property of the real numbers is illustrated by the following statement? 9 ? (7 + 11) = 9 ? 7 + 9 ? 11 A) Commutative property of multiplication B) Associative property of addition C) Associative property of multiplication D) Distributive property 2.

Fixed Rate and Logarithm Change of Base Formula

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P(1+r)^nt, let r= n 10%, P=1 and n=1 and give the coordinates(t,A) for the points wher

Logarithmic functions explained in this solution

The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by A is the amount of returned. P is the principal amount initially deposited. r is the annual interest rate (expressed as a decimal). n is the compound period. t is the number

Voting

After their star pitcher moved to another town, the eight remaining members of the company baseball team needed to select a new pitcher. They used approval voting on the four prospects, and the results are listed below. An "X" indicates an approval vote. Which pitcher is chosen if just one is to be selected? (see attached

The possibilities of voting

(See attached files for full problem description) --- 1. Four members are running for president of the Local Math Club - Alicia (a), Brice (b), Charlie (c), and Destiny (d). The voter profile is summarized in the table. Use the Hare method to determine the winner. Number of voters Ranking 17 c > d > a > b 11

Study guide

(See attached file for full problem description) STUDY GUIDE 1. Solve. x2 + 5 = 21 A) B) C) ±4 D) 2. Solve. 9x2 = 14 A) B) C) D) 3. Solve. 5(x - 2)2 = 3 A) B) C) D) 4. Is the following trinomial a perfect squa

Bol-ful and Ful-bol Numbers; Unit Conversions

7. An integer is a ful-bol number if it is divisible evenly by the square of an integer that is greater than on. For example, 343 is a ful-bol number because it is divisible by 49 which is the square of 7. A bol-ful number is a ful-bol number which, when the digits are reversed, it is still a ful-bol number. Note: 343 is a

Please explain in detail

1. A swimming pool is twice as long as it is wide. It took 1,224 square feet of material to covar a 6-foot wide deck around the pool. How wide is the pool? 2. The height reached by a ball thrown vertically upward is directly proportional to the square of tis intial velocity. If a ball reaches a height of 46m when it i

College Algebra

1. Which of the following numbers are examples of integers? -7, -9/3, -1.0, -3/8, 0, 2.2, 5, 6.66666 2. Multiply and simplify your answer as much as possible: (4f - 3)(7f + 1) [to express (f)(f) use f^2] 3. If n is a negative number, what is the absolute value of n? 4. Factor: 25p^2 -

Uncountable Basis

It can be shown that R (the set of all real numbers) is an infinite-dimensional vector space over Q (field of rationals). Is it true that any basis (by basis I mean algebraic basis or Hamel basis) of R over Q has to be uncountable ?

Z-Modules and Modules Associated with Representations

1)I understand what a standard R-module (ring-module) is, but I have heard talk of modules associated with representations. Could someone please give me some idea of what these are? 2) I am trying to find all modules over Z-the Integers; so far, I have only come up with additive groups. How can I find all others?

What is the advantage of using exponents rather than radicals?

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. What is an example of an equation easier to solve as a rational exponent rather than as a radical sign.

Polynomial Functions : Positive Degree

The questions are asking for solving h(x) of positive degree. --- 1A) Let F be a field and let e(x), f(x), g(x) and h(x) be polynomials in F[x] with h(x) of positive degree. Prove that if e(x) = gcd(g(x),h(x)) and e(x) divides f(x), then there is a polynomial j(x)  F[x] such that g(x)j(x)  f(x) (mod h(x)).

Finding the Discriminant in a Quadratic Equation

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. What I need to do is figure out how to create three unique equations where the discriminant is positive, zero, or negative. For each case, please explain what t

Algebra and complex numbers

Can you please show me how to calculate the following with showing full workings? (See attached file for full problem description) --- 1, X = p/q (1 + 1n r) Evaluate r when x = 0.34, p = 1.08 and q = 1.84 X = p/q (1 + 1n r) = qx/p = 1 + 1n r 2, Z1 = 5-j4 Z2 = 4+j7 Z3 = -6-j7 Z4 = j2

Exponential and Logarithmic Function Graphs

Referring to the graph below (which is attached), identify the graph that represents the corresponding function. I need to justify my answer. y = 2^x y = log2x (where the 2 is lower case below log, not above)then; x Also, I need to plot the graphs of the following functions and show them. f(x)=6^x f(x)=3^x - 2 f(x)

Probabilities

In the game of odd man wins, three people toss coins. The game continues until someone has an outcome different from the other two. The individual with the different outcome wins. Let X equal the number of games needed before a decision is reached. Prove by induction that the density function of X is (see attached).

Literal Equations

I am having a hard time solving literal equations. I know the process is the same as you would solve any linear equation, but I still am having trouble grasping the whole concept. Is there any way of making this easier to learn?

Graphing

(See attached file for full problem description) --- 1. Graph the system x^2 + y^2&#8804;16 y&#8804;4-x^2 2. Graph the solution { y<1/4x Bracket covers both entries but I don't know how to make it bigger. y&#8805; -2x+3 3. Show the graph of the systems of inequalities? 16x^2+64y