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Basic Algebra

Algebra Operations with Polynomials

1. For each polynomial listed below, determine i the degree of the polynomial ii the coefficient of the leading term iii the constant term a. P(x) = x + 1 b. Q(x) = 3x + 2 c. R(x) = x2 + 2x + 1 d. W(x) = 4x2 + x + 3 e. Z(x) = 3x3 + 2x2 + x

Challenged the tortoise again on bicycle races

Years after the famous foot race, the hare challenged the tortoise again on bicycles. The hare was able to pedal at a rate of 15 mph. while the tortoise could pedal only 12 mph. Knowing he was slower, the tortoise makes up a lame excuse for being given a 27 mi. head start in the 165 mi. race. 1. WHo won the tortoise and hard

A property management company manages 200 apartments renting for ...

A property management company manages 200 apartments renting for $800.00 each with all the apartments rented. For each $10.00 pre month increase in rent there will be 2 vacancies with no possibility of filling them. what rent per apartment will maximize the total monthly revenue?

A couple of I think quick questions . . .

Hi! I'm using old tests to study for an abstract algebra exam and of course the old exams do not come with solutions. This means that I need help. I tend to struggle with proofs because I forget some steps or I am not as rigorous as I should be. Thus I need to see actual complete rigorous proofs so that I can make sure that I re

Solving Equations and Inequalities using Substitution Method

Please see attachment. I've been working on this for the last few days. Some of the problems I understand and some I do not. 1. Perform the indicated operation: 2 (see the attached file). 3 5 2. Use order of operations to simplify: 25 - 3(22 + 1) = 3. Simplify: 5(2a - 3b) + 3(4

Algebra: equations and inequalities

1. Evaluate: 7 -|(-3)(2) - 2| 2. Simplify: 7x - (4 - 2x) 3. Ross jogs at a rate of one mile every 0.25 hours. At what rate is he jogging in miles per hour? 4. Solve for x: 5(2x-3) =x+3 5. Solve for x: (1/2) x - 1/3 = (1/4) x+ 1/6 6. Solve for x: 2x- 3 = ax 7. Solve: |3x-9|=3 8. Solve the in

Relation on the set of ordered pairs of positive integers

Let S be the set of ordered pairs of positive integers, let z = (5,8), and define R so that (x1, x2) R (y1, y2) means that x1 + y2 = y1 + x2. Show that the given relation R is an equivalence relation on the set S. Then describe the equivalence class containing the given element z of S, and determine the number of distinct eq


Refer to the following scenario to answer questions #1 through #5.Tanya waits tables for customers in her mothers restaurant. She earns an average $4.00 in tips for each table, and will make about 8 trips to the table for each meal. She make a chart to show her work and tips for 8 to 12 tables. Use the chart to analyze the data

Quadratic and radical equations and expressions

Please see the attachment for examples that I need solved. These will serve as reference to what I currently am working on. Thank you. Find the root Use the product rule to simplify. All variables represent nonnegative real numbers. Use the rules of exponents to simplify each expression. Write each radical expression in s

Distributive property and negative monomial

Give an example of using the distributive property for a negative monomial times a trinomial with different signs on the terms[for example:-3x(2xy+3y-2x)] and show each step of the distribution. Why do you think many students make sign errors on this type of problem? What would be your advice to a student who has trouble with si

Substitituion Method

Solve each system by substitution. Determine whether the equations are independent, dependent, or inconsistent. 36.y =-3x+19 y = 2x-1 38. y = -4x-7 y =3x 42. y = x+4 3y-5x = 6 56. 2x- y = 6 2x - y = 3 Solve each system by the substitution method. 70. x + 3y =2 -x + y =1 Solv

Mathematics - Algebra - Elasticity and Revenue

Elasticity and Revenue Suppose that q = 500 - 2p units of a certain commodity are demanded when p dollars per unit are charged, for 0<=p<=250. a) Determine where the demand is elastic, inelastic, and of unit elasticity with respect to price. b) Use the results of part (a) to determine the intervals of increase and

Break-even Analysis

During the summer, a group of students builds kayaks in a converted garage. The rental for the garage is $1,500 for the summer, and the materials needed to build a kayak cost $125. The kayaks can be sold for $275 apiece. a) How many kayaks must the students sell to break even? b) How many kayaks must the students sell to


A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. The rancher wants the enclosed area to be 350 meters. What dimensions should the rancher use to obtain this area. Note: I was given 4x + 3y=100 as a formula below the picture of the two adjacent rectangles. (Please see the attachment.)

Linear and quadratic trend lines

From 1997 through 2004, the value of US exports to Mexico was as shown below. Data are in billions of dollars. Year: 1997 1998 1999 2000 Exports: $71.4 $78.8 $86.9 $111.3 Year: 2001 2002 2003 2004 Exports: $101.3 $97.5 $97.4 $110.8 a. Fit a linear trend e

Exponential and logarithm problems

Hello, I am having trouble with these 6 questions, can someone please help. The problems are attached. 1-In the formula A = Iekt , A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a

20 Algebra Problems : Solve for X, Simplify and Radical Expressions

2) Solve. Use a comma to separate answers as needed. Type N if there is no solution. 4) Rewrite with a rational exponent. 5) If the sides of a square are lengthened by 8cm, the area becomes 256 cm . Find the length of a side of the original square. 6) Express using a positive exponent. 7) Subtract the polynomia

Graphing : Ordered Pairs, Slopes, Intercepts and Line Equations

Complete each ordered pair so that it satisfies the given equation. 7. y _ 3x _ 9: (0, ), ( , 24), (2, ) 17. y = -2x+5 X Y -2 0 2 -3 -7 Graph each equation. Plot at least five points for each equation. Use graph paper. 70. x- 2y - 6 71. x - 3y - 6 Find the slope of each side 7. 9.

Questions ... (Please See attachment)

I am having some issues with these questions. I am just not getting it. Please help. All questions that are circled. (Please see attachment) The graphs of the following systems are given in (a) through (d). Match each system with ... Solve each system by the substitution mehtod. Determine whether ... Solve each system

Factoring Polynomials

I need some help with these problems. Please see attachment. Please show all work to each equation Factor out the GCF in each expression 1) 15x^2y^2 - 9xy^2 + 6x^2y 2) a(a + 1) -3(a + 1) Factor each polynomial completely 3) x^3y + 2x^2y^2 + xy^3 Use grouping to factor each polynomial completely 4) x^3

Simplfy Quadratic Equations

See the attached file. 1. Multiply Simplify your answer 2. Simplify your answer. Type a fraction or an integer. Type N if the root is not a real number. 3. Subtract. Simplify by collecting like radical terms if possible. Simplify your answer. Type an exact answer, using radicals as needed. 4. Multiply and si