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Basic Algebra

Polynomials

Imagine your younger relative, of middle school age, was taking an algebra course and asked for your help, how would you teach the multiplication of polynomials to him/her?

Solving algebra word questions

1. What quantity of a 60% acid solution must be mixed with a 30% solution to produce 300 mL of a 50% solution? 2. A pot contains 6L of brine at a concentration of 120g/L. How much of the water should be boiled off to increase the concentration to 200 g/L? 3. A merchant blends tea that sells for $3.00 a pound with tea tha

Continuous compounding

Suppose $1000000.00 will be recieved after 25 years. Find the value 5 years from now (t=5), V(5), assuming continuous compounding at the rate r(t) = 0.05 + t/1000 if t<=10 and 0.06 t >10. I know the answer is 304982.77, but can not get it to work out. Please show all of your work.

Solve and graph the inequality

Solve and graph the inequality -8 < x + 3 < 6 What is the solution set? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The solution set is ________

Domain of an odd root radical function

How would you explain to a seventh grader the difference between the domains of an odd root radical function and an even root radical function? How would you change your explanation for someone who had taken high school algebra?

Law of Radicals

What law of radicals allows you to treat radical expressions as exponential expressions? How would you explain this to someone else and how would you explain adding like radicals? Include an example with your explanation. Use the following notation for square root: sqrt(3).

Algebra: Equation of a Line

Please explain in details the steps to solve the problem below: Find the equation in standard form of the straight line that passes through the point midway between (-7, -12) and (-5, 2) and has a slope of 3.

Solving Absolute Value Inequalities (AVI) Step-by-Step

What is the best method for solving absolute value inequalities? The first most important part about solving absolute value inequalities is to understand that there are two types of inequalities. These are |ax+b|<c and |ax+b|>c. These inequalities have totally different solutions. This is because of the difference between the t

Adding rational expressions

What are the similarities and differences between the procedures needed to solve each of the following problems? Show your work and include a verbal breakdown of each step. 2/x + 5/6 and 2/x + 5/6 =2

Creating and Factoring Trinomials

Choose three integers a, b, and c? Feel free to choose negative numbers. Use a, b, and c to create a trinomial ax2 + bx + c. Can you factor this trinomial? How would you create a trinomial that will factor?

Mathematical Formulas

What does the following mean? Y = 3 V Xi = 2 So the equation reads Y equals 3 and the upside V is supposed to be an upside down A, Xsquare equals two. I don't understand how to write the sentence to convey what is going on with the equation... I hope someone can help soon.

Given Ordered Triple

Determine if the given ordered triplet below is a solution of the following system. x + 3y = -12 9x - 5y = -12 8y-7z = -45 (-3,-3,3) Is the ordered triple a solution to the system? Yes No

Algebraic Calculations

This problem its difficult for me: Provide a numerical answer to each of the following questions and also show the calculations you used to find the answers. 1.How many different ways can 30 runners place in an Olympic qualifying marathon? 2.If only the eight fastest runners advance to the Olympics; how many different ways

Compound Inequalities with Signs and Directions

See the attachment. Choose the correct description of the graph of the compound inequality x - 1 ? 7 or 2x ? 22. (I "believe it is d, since the greater/less than or equal sign calls for a closed circle. Also, considering the directions of the arrows i.e. x ? 8 and x ? 11). a. A number line with an open circle on 8, shading

Inequalities Compound Equivalents

Need help working the following: 1. Which of the following is not an equivalent form of the compound inequality: x + 10 > 20 and x + 10 ? 26 a. 20 < x + 10 ? 26 b. 10 < x and x ? 16 c. A number line with a closed circle on 16, shading to the right, and an open circle on 10, shading to the left. d. A number line with a

Proof of Wallis's Formula from Euler's Product Formula

The attached document has the Euler Product Formula we are required to use for the proof on the second page. The value of Gamma(1/2) is sqrt(pi). I have seen a proof of this using Euler's product formula for Sine and pi/2, but I'm not sure how to proceed. A detailed solution would be appreciated.

Social Inequality in the West and Open Societies

In regards to the Western context, is there a point at which the level of inequality becomes so great that it is detrimental for individuals trying to improve their situation and to the future of the society as a whole?

Interval Notation

1. The sets and are defined as follows. Write and using interval notation. If the set is empty, write . 2. Graph the system below and write its solution. Note that you can also answer "No solution" or "Infinitely many solutions." 3. Solve the compound inequality. or Write the solution in

Writing the Equation in a Slope-Intercept Form

Please provide help solving the following problems: 1.For the given equation, list the intercepts and test for symmetry. Y=x^3-512 2. Find the slope-intercept equation of the line with the following properties: Perpendicular to the line X=8 ; containing the point (-6,0).

Algebraic Calculations

Sketch : f(x) = -2x^3 + 26x - 24, including the full algebraic calculations of the following. a) x & y-intercepts (Do NOT use guess & check for all x-intercepts) b) relative maxima and minima c) points of inflection Calculus may be used.

Find the radius of a cylindrical container

A packaging design team has determined that a cost-efficient way of manufacturing cylindrical containers for their products is to have the volume, V, in cubic centimeters, modeled by: V(x) = 9pix^3 + 51pix^2 + 88pix + 48pi. The height, h, in centimeters, of each cylinder is a linear function given by h(x) = x + 3. Divide the

Conversion between cubic yard and cubic feet

An Airconditioning systemcan circulate 280 cubic feet of air per minute. How many cubic yards of air can it circulate per minute? The air conditioning system can circulate about_____? Cubic yards per minute. The answer must be an integer or a decimal point.

Quadratic Equations for Ticket Sales

Ticket Sales: Living in or near a metropolitan area has some advantages. Entertainment opportunities are almost endless in a major city. Events occur almost every night, from sporting events to the symphony. Tickets to these events are not available long and can often be modeled by quadratic equations. Application Practic

Algebra Word Problem: Three Candy Corn Jars

In my favorite shopping mall downtown there is a specialty shop that's bound to please anybody's sweet tooth. It's a candy store called Candylandia. In this store you can find just about any kind of candy your tastebuds would savor. One favorite and traditional candy is the candy corn. Candylandia sells candy corn in three d

Age and Retirement Savings Income

1. How old are you? At what age do you hope to retire? These questions are really about answering: How many years do you have until your retire? 2. Assume you are about to set up a new retirement savings account at a 4% annual interest rate (APR). Based on how you want to live in retirement, and any other sources of retirement

Graph and Solve the System of Inequality

See the attached file. CheckPoint 11) Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $190, plus 40% of the rest. Under plan B, Giselle would pay the first $220, but only 30% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $220 in

Galois Extension

** Please see the attachment for a full problem description ** Suppose that K/F is a Galois extension, the Norm of alpha is an element of K is N_K/F := (please see the attached file) and trace is Tr_K/F(alpha) = (please see the attached file). Suppose also (please see the attached file) that Gal(K/F) is cyclic and K, F are fi