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Basic Algebra

Polar equations of conics

(6 problems) Q:1 write a polar equation of a conic with the focus at the origin and the given data. 1.Parabola, directrix x=4 2.Hyperbola, eccentricity 2, directrix y = -2 3.Ellipse, eccentricity 0.8, vertex (1, ∏/2) Q:2 (a)find the eccentricity,(b)identify the conic,(c)give an equation of the directrix, and (d)sket

Algebra : Graphs, Interest and Basic Statistics

Please show me how you do this I am so unsure of the processes and want to make sure I know what I am doing. 1. Mr. Knight owned of a family business. He sold of the business to his sister. What portion of the business does he still own? 2. Rocco scored 81, 89, 68, 92, and 77 on his mathematics quizzes. Round each s

Radical Equations and Squaring Both Sides

In solving an equation involving radicals, it is sometimes necessary to square each side of the equation. But doing this can introduce extraneous roots, which do not satisfy the original equation. After squaring both sides, when you then take the square root of both sides again, you do not get back the original equation exactl

Applications of Systems of Equations : Buying a Home

Buying a Home For most people, buying a house is a great investment that can offer security in an uncertain world, but buying a house is also a commitment. Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. 1. Suppose you are in the market for a

Writing Equation Word Problems: Factoring

Solve each problem by factoring. 1. Area of a painting. A rectangular painting with a width of x centimeters has an area of x^2 + 50x square centimeters. Find a binomial that represents the length. 2. Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by A =

Order of Arithmetic Operations

Evaluate the following expression exactly: 9876543210 --------------------------------------------------------------- 98765432112 - 9876543210 * 9876543212

Ratio and Proportion

By setting up and solving a proportion involving x for the car that you have chosen. State the type of car, the mileage, and show both the set up of the proportion and the steps to solve.

Factoring Polynomials (28 problems)

Find the greatest common factor for each group of monomials. 1.) 16x^2z, 40xz^2, 72z^3 Factor out the GCF in each expression. 2.) 15x^2y^2 - 9xy^2 + 6x^2y Factor out the GCF in each expression. 3.) a (a+1) -3 (a+1) Factor each polynomial. 4.) 9a^2 - 64b^2 Factor e

Soving Equations with Inequality

See the attached file. Solve using the addition and Multiplication principle; 1. 9x-6<-33 2. A car rents for $50 per day plus 20 cents per mile; You are on a daily budget of $88. What mileage will allow you to stay within your budget? The solution is {m l m < ? } 3. The formula R = - 0.075t + 3.85 can be used to pr

Algebra: Logarithms and Systems of Equations

See the attached file. 1. Express in simplest form: = = 2. Solve each system for x and y: 2x-y=29 5x+3y= -17 x-2y= -2 3x-5y= -6 3. Find each value: Log Log = 4. Solve for x: Log Log 5. Solve for X round off to 4 decimal place: 5 =7 6. Evaluate: E

Synthetic Division, Rational Zero Theorem, Domain and Asymptotes

Please help me with the attached problems by explaining how to solve them. Use synthetic division to divide the polynomial 4x3 + 10x2 - 11 by x + 3, and state the quotient polynomial and the remainder. [Be careful - notice that there is no x term.]. Show work. Consider the polynomial f(x) = 5x3 - 9x2 - 17x - 3. (a) By u

Shape of a Polynomial Graph

If you have an arbitrary polynomial P(x) of the nth degree in x, and you graph the equation y = P(x), describe the overall shape of this graph. What happens when x gets large in the positive and negative directions, and how many peaks and valleys does the graph have? How many times does the graph cross the x-axis? (To simplif

logarithm and exponential function

Just want to check answers. 1. Write the expression as the logarithm of a single number or expression with a coefficient of 1. Assume all variables represent positive numbers. log 30 - log 6 A) log 11 B) log 5 C) log 24 D) log 2. Find the value of the expression. log10 10 A) 1 B) -1 C) 0 D) 10

Factoring and Graphing Equations

Please help me solve the problems in the attached practice work. 1) Solve the following by factoring: a) 5t^2 - 10t = 0 b) x^2 - 3x - 10 = 0 2) If f(x) = 3x^2 + 5x - 2, find: a) f(-2) b) f(4) 3) Solve 3x^2 + 19x - 14 = 0 using the quadratic formula. Read the information in the assignment list to learn more ab

Managerial Accounting : Fixed and Variable Costs

Costs can be classified into two categories, fixed and variable costs. These costs behave differently based on the level of sales volumes. Suppose we are running a restaurant and have identified certain costs along with the number of annual units sold of 1000. Item: Raw Materials (cost for hamburgers) Total Annual Cost: 650

Important information about rational and radical expressions

See attached Week4: Class work: Radicals and Rational Exponents 1. Square root of a rational perfect square. Be sure to write your answer in lowest terms and simplify. 2. Square root simplification. Rewrite the following in simplified radical form. 3. Simplifying a radical expression: Problem type 1. Assume th

Argue that m x m is Not Equal to m + m

Here is what I have can you add anything to help this out? You want to show that if m is a natural number (0, 1, 2, 3, ...), then m x m is not equal to m + m. You can do this simply by showing that it is not in at least one case (because if it's not true for at least one natural number, then it's not true for natural numbers

Important information about rational equation

1. When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression? Please show an example 2.Please show an example of a rational equation and present a step-by-step solution.

Equations, Simplifying, and Least Common Denominator

See attached document. Section 6.1 #18 Which numbers cannot be used in place of the variable in the rational expression? (2y+1)/(y2-y-6) #102 Simplify (-2x-8)/(x2+2x-8) Section 6.2 #24 Simplify (3/a2+a)(2a+2/6) #76 Simplify ((w2-1/(w-1)2)/((w-1)/(w2+2w+1)) Section 6.3 #20 Build the rational expression into an e

Normal subgroup generated by X

(i.e.: A = the intersection {N a normal subgroup of G: X subset of N} A=bigcap {Nlefttriangle G:Xsubseteq N}-this is the tex for what was written on the study guide.) Let Y = {gxg^-1|x is X, g in G}. Show that A=<Y> I need a rigorous proof with explanations so that I can study and understand please. I have an exam

Algebra Word Problem

The mathematical problem for the class is : You have been assigned to ship 480 eggs to children for Easter. How many trucks would have to be loaded if you could pack 12 eggs in each carton and fit 20 cartons on each truck?

Polynomial Study Guide

See attached document Section 5.1 # 40 Find the greatest common factor for the group of monomials 16x2z, 49xz2, 72z3 #72 Factor out the GCF in each expression. a(a+1) - 3(a+1) Section 5.2 #16 Factor the polynomial. 9a2 - 64b2 #80 Use grouping to factor the polynomial completely. x3 + ax + 3a + 3x2 Section 5.3 #

Algebraic expressions

Problem : If the diameter of a circle is 1.3 x 10^-12 meters, then what is its radius? Problem : The perimeter of a rectangular backyard is 6x+6 yards. If the width is x yards, find a binomial that represents the length.

Mathematical expression similar to a fragment of a sentence

Below are examples expressions for a variable. I need to explain my problem and answer just like the examples below, please give me a few problems to explain just like the samples below thanks... A mathematical expression is similar to a phrase or fragment of a sentence. An expression has no subject and no verb or relatio

Algebraic Expressions and Variable Solution

Equation is a statement asserting the equality of two expressions; they are constructed from algebraic expressions. They are separated into left and right sides and joined by an equal sign. Expression is a group of letters that are used for numbers. Equation 820 + Y - 820 = 1820 - 820 Expression A x 12

Factoring and Trinomials

What is factoring by group? When do you factor a trinominal and why is it necessary to write the trinominal in four terms? Please show examples.

Basic Algebra: Determing Cost Function

1. A telephone company charges a fee of $29.99 per month for basic local service. A fee of $4.95 per month is added for customers wanting up to 500 minutes of long distance at $0.04 minute. a. Write a cost function to determine the amount a customer with the local and long distance plans would be charged that is based on the

Combine algebraic sets to yield other sets.

II. The three different media outlets of radio, Internet, and newspaper are to be offered on weekends or weekdays, and then either between 7 a.m.-3 p.m., 3 p.m.-11 p.m. or 11 p.m.-7 a.m. How many different possibilities exist? List the possibilities and verify your listing with the multiplication principle for counting. III.

Few quest functions and math

Let K be a field. (All of this works just as well for a division ring.) Let V be an n-dimensional vector space over K and let A = EndK(V), the ring of n n matrices over K. The ring A is clearly Artinian since it has finite dimension over K. We need to see that the 2-sided ideals are either (0) or A. 1. Let W be a subs