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# Basic Algebra

### Are the two zeros of this equation integers, rational numbers, or irrational numbers?

DQ 6: How would you express the zeros of the equation x2 - 2 = 0 ? Are the two zeros of this equation integers, rational numbers, or irrational numbers? DQ 7: Note the cubic equation x3 - 6x2 + 11x - 6 = 0. I will claim that x = 1 constitutes a root of that equation ( replace x by 1 in the equation to verify ).

### Burnside's Formula

There are 70 = C(8,4) ways to color the edges of an octagon, with four black and four white. The group D8 operates on this set of 70, and the orbits represent equivalent colorings. Count the number of equivalence classes. D8 is the dihedral group associated with an octagon. Please refer to the attachment for more details.

### Constructing a field with p^2 elements

How can we construct a field having p^2 elements, p being an odd prime. Please explain in detail. (Hint: Think about polynomial rings.)

### Females who Live with Non-relatives

The table below shows where people over 65 in the US live. A total of 23% of elderly men live either alone or with relatives. The sum of double the percent of men who live alone and triple the percent who live with relatives exceeds the percent of US women over 65 who live with their spouse by 13%. What percent of elderly men

### Revenue per available seat mile (RevPASM)

Alaska Airlines had passenger revenues of \$2.644 billion with a total of 24.22 billion available seat miles. Their reported load factor (average capacity usage) was 77.3% and RevPASM was 10.9 cents. With all other factors remaining constant, what would you project for RevPASM if Alaska Airlines could successfully increase the

### Continuous functions

1.Show that a polynomial function is continuous at every point of R. 2. Show that a rational function (a quotient of two polynomial functions) at every point where it is defined.

### Ordered Pair Solution and Graphing

Chalkboard Activity Please pick 5 questions from the list below. Solve those 5 problems, showing your work, and submit them to your Individual Forum. ________________________________________ Problem Set 1 (choose one) 1. Decide if the ordered pair (-3,5) is a solution to 9x + 7y = 8 and 8x-9y = -69 2. Decide if the

### Algebra: Word Problem

Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pounds of sugar. a. Set up the inequalities representing the baker's possible cho

### Math: Linear Inequalities

1.What is the situation when two linear inequalities have no solution? 2.What are the conditions when the solution of a system of linear inequalities will be in the first quadrant? 3.Why is it true that at x-intercept, the value of y is 0, and at y-intercept, the value of x is 0?

### Two Rational Expressions

#1) Subtract these two rational expressions: 2/(3x-1) - 1/(x+1) #2) Solve for x (find the values of x) in the following equation: 2/(3x-1) - 1/(x+1) = 0 Hint: Use the answer of problem #1 (simplified expression).

### Abstract Algebra: Odd Prime

** Please see the attached file for the complete problem description ** Need help with attached problems Let p an odd prime, show that either p == 1 mod 4 or p == 3 mod 4. Show that no prime of the form 4n + 3 can be written as a2 + b2 for some integers a and b. Show that 17 is not prime in J[i], by finding a factorizati

In using the factoring method of solving quadratic equations, we put it in the form: (x+a)(x+b) = 0, where a and b are two constants (think of them as two `numbers'). If the right-hand side of this equation is not zero (let us say, another constant "c"), do you think it can be solved? If so, how? If not, why not?

### Hello (Week 2)

Please help with my review class. This is supposed to be elementary Algebra, but I am having a hard time understanding it. Please help me to understand better and if are able to help please explain so that I can understand it. Thank you.

### Ordering numbers with negative exponents

Order the expressions by choosing Less than, greater than or equal to = 8^-2 is ? to (1/8)^-1 (1/8)^-1 is ? to (1/8)^-2 (1/8)^-1 is ? to 8^-1 is ? choose less than, greater than or equal to

### Algebraic word problem

Suppose that there are two types of tickets to a show: advance and same-day. The combined cost of one advance ticket and one same-day ticket is \$75. For one performance, 20 advance tickets and 30 same-day tickets were sold. The total amount paid for the tickets was \$1,900. What was the price of each kind of ticket?

### Applying Exponential Growth & Decay Rates

1. Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds? At what round the tournament canâ??t be played? Chart the decay rate. 2. In one locality, the H1N1 flu (aka swine flu) sp

### possible dimensions of the design

Lina has 24 square ceramic tiles, each with 1 inch sides she wants to arrange them in a rectangular design on a tabletop. What are the possible dimensions of the design? There were half as many blue jays as chickadees at a bird feeder. There were fifteen more chikadees than finches. If there were 18 blue jays how many of chic

### Land trust has received a \$130,000 donation to save flying squirrels.

A land trust has received a \$130,000 donation to save flying squirrels. They have identified five different areas to target as ecological reserves for flying squirrels. Three of the projects are in Oregon and two are in Washington. Each of the Oregon reserves would require a \$70,000 investment and would each provide habitat f

### Use the quadratic formula to determine roots

(a) Use the quadratic formula to determine the roots of the equation x^2 - 2x = 2. Estimate the roots to the nearest tenth. (b) Determine the vertex and use the information obtained in part (a) to sketch the graph of y = x2 - 2x - 2.

### Solving for x variables

Chalkboard Activity Please pick 5 questions from the list below. Solve those 5 problems, showing your work, and submit them to your Individual Forum. ________________________________________ Problem Set 1 (choose one) Solve for x or y - 1. 2x+10= -5+x 2. 13-3+9x=10x 3. 2(10-2x)= -3

### Algebra: Word Problem of a Hang Gliding Service

The profit function for the Recklus Hang gliding Service is P(x) = -0.4x^2 + fx - m, where f represents the set up fee for a customer's daily excursion and m represents the monthly hanger rental. Also, P represents the monthly profit in dollars of the small business where x is the number of flight excursions facilitated in that

Assuming that all variables represent positive real numbers rewrite the following in simplified radical form square root of 20w^12 Can you also tell me how to write questions in this forum when using radicals and square roots and to the power of?

### Simplify product rule

If we use the product rule to simplify (-1)^(1/2) * (-1)^(1/2), we get: a) (-1)^(1/2) * (-1)^(1/2) = (-1)^1 = -1 If we use the power of a product rule, we get b) (-1)^(1/2) * (-1)^(1/2) = (-1. -1)^(1/2) = 1^(1/2) = 1. Which of these computations is incorrect? Please explain.

### Mathematics Problems

1. On a trip to the supermarket you buy an economy pack of Soft-4-U toilet tissue. At home you read this information on the side of the pack: 12 rolls 2 ply tissue Average 225 sheets per roll Sheet size 125 mm x 110 mm This sets you thinking about the size of the toilet rolls before you unpack them. (a) Assumin

Comparing wind chills. Use the formula from Exercise 107 to determine who will feel colder: a person in Minneapolis at 10°F with a 15-mph wind or a person in Chicago at 20°F with a 25-mph wind. (this is the formula from exercise 107) W=91.4 -(10.5+6.7(radical symbol)v-0.45v)(457-5t)/110 In the above formula I have wri

### Modern algebra (ring)

Let R={a+b(sqrt(2)) | a, bâ?? Z}. (a): Show that R is a ring. (b): Let M = {a+b(sqrt(2)) â?? R | 5|a and 5|b}. Show that M is a maximal ideal of R.

### medicine proportional to a patient's body weight

A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 102 pounds requires 153 milligrams of medicine. What is the weight of a patient who requires 151.5 milligrams of medicine? Please show the process of solving it.

### Robotic system capable of traversing the maze

We need to program a robot that will make the robot autonomous in a restrained environment, like a simple maze. For example, if the robot is to enter on the left side it must find its way to the right side without ever touching the walls. The robot has a sonar sensor to allow it to see. The program that allows it to traverse

### Expressions and LCD

Which expression is the LCD for (3x-1) over (22 times 3 times x(x+2)) and (2x+7) over (2 times 32 times x(x+2)^2) a) 2 * 3 * x(x+ 2) b) 36x(x + 2) c) 36x2(x + 2)^2 d) 23 * 33x3(x + 2)^2

### Application for Amber

The amazing Amber. Amber has been amazing her friends with a math trick. Amber has a friend select a three-digit number and reverse the digits. The friend then finds the difference of the two numbers and reads the first two digits of the difference (from left to right). Amber can always tell the last digit of the difference. E