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Basic Algebra

Word problemsPolynomials Retail companies need to keep close track of their operations in order to maintain profitability. Often, the sales data of each individual product is analyzed separately, which can be used to help set pricing and other sales strategies. Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. 1. In this problem, we will analyze the profit found for sales of decorative tiles. A demand equation (sometimes called a demand curve) shows how much money people would pay for a product depending on how much of that product is available on the open market. Often, the demand equation is found empirically (through experiment, or market research). a. Suppose that a market research company finds that at a price of p = $40, they would sell x = 62 tiles each month. If they lower the price to p = $34, then more people would purchase the tile, and they can expect to sell x = 72 tiles in a month's time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. (Hint: Write an equation using two points in the form (x,p)). A company's revenue is the amount of money that comes in from sales, before business costs are subtracted. For a single product, you can find the revenue by multiplying the quantity of the product sold, x, by the demand equation, p. b. Substitute the result you found from part a into the equation R = xp to find the revenue equation. Provide your answer in simplified form. The costs of doing business for a company can be found by adding fixed costs, such as rent, insurance, and wages, and variable costs, which are the costs to purchase the product you are selling. The portion of the company's fixed costs allotted to this product is $400, and the supplier's cost for a set of tile is $2 each. Let x represent the number of tile sets. c. If b represents a fixed cost, what value would represent b? d. Find the cost equation for the tile. Write your answer in the form C = mx + b. The profit made from the sale of tiles is found by subtracting the costs from the revenue. e. Find the Profit Equation by substituting your equations for R and C in the equation . Simplify the equation. f. What is the profit made from selling 20 tile sets per month? g. What is the profit made from selling 25 tile sets each month? h. What is the profit made from selling no tile sets each month? Interpret your answer. i. Use trial and error to find the quantity of tile sets per month that yields the highest profit. j. How much profit would you earn from the number you found in part i? k. What price would you sell the tile sets at to realize this profit (hint, use the demand equation from part a)? 2. The break even values for a profit model are the values for which you earn $0 in profit. Use the equation you created in question one to solve P = 0, and find your break even values. 3. In 2002, let's pretend that Home Depot's sales amounted to $68,200,000,000. In 2006, let's pretend its sales were $92,800,000,000. a. Write Home Depot's 2002 sales and 2006 sales in scientific notation. You can find the percent of growth in Home Depot's sales from 2002 to 2006, follow these steps: ? Find the increase in sales from 2002 to 2006. ? Find what percent that increase is of the 2002 sales. b. What was the percent growth in Home Depot's sales from 2002 to 2006? Do all your work by using scientific notation. 4. A customer wants to make a teepee in his backyard for his children. He plans to use lengths of PVC plumbing pipe for the supports on the teepee, and he wants the teepee to be 24 feet across and 16 feet tall (see figure). How long should the pieces of PVC plumbing pipe be? (please see attachment)

Algebaic word problems (please see attachment)

Algebra word problems

Marginal revenue. A defense attorney charges her client $4000 plus $120 per hour. The formula R =120n + 4000 gives her revenue in dollars for n hours of work. What is her revenue for 100 hours of work? What is her revenue for 101 hours of work? By how much did the one extra hour of work increase the revenue? (The increase i

Complete each ordered pair so that it satisfies the given equation. 1---- y = 2x + 5: (8, ), (-1, ), ( ,-1) Use the given equations to find the missing coordinates in the following tables. 2------ y= -x+4 X Y -2 0 2 0 -2 3-------------Graph each equation. Plot at least five points for each equation. x - 2y = 6 4--------------find the slope of each line. 5--------------- 6---------------Graph the line with the given point and slope. The line through (-2, 5) with slope -1 7--------------- Draw l1 through (-4, 0) and (0, 6). What is the slope of any line parallel to l1? Draw l2 through the origin and parallel to l1. 8-----------------Write an equation for each line. Use slope-intercept form if possible. 9------------ 10-------------Find the slope and y-intercept for each line that has a slope and y-intercept. X+2y=3 11----------- Y+4x=8 12----------determine whether the lines are parallel, perpendicular, or neither. Y=x+7 Y=-x+2 13------------Write each equation in slope-intercept form. Y+3=-3(x-6) 14------------Find the equation of the line that goes through the given point and has the given slope. (-1, -5), -8 15-------¬Find the equation of each line. Write each answer in slope intercept form. The line is parallel to -3x + 2y = 9 and contains the point (-2, 1). 16------------Find the equation of each line in the form y = mx + b if possible. The line through (3, 2) with undefined slope 17----------------Write a formula that expresses the relationship described by each statement. Use k for the constant in each case. m varies directly as p. 18------------ Write a formula that expresses the relationship described by each statement. Use k for the constant in each case. u varies inversely as n. 19-----------------Find the variation constant, and write a formula that expresses the indicated variation. c varies inversely as d, and c = 5 when d = 2. 20-------------------- Solve each variation problem n varies directly as q, and n = 39 when q = 3. Find n when q = 8.

Complete each ordered pair so that it satisfies the given equation. 1---- y = 2x + 5: (8, ), (-1, ), ( ,-1) Use the given equations to find the missing coordinates in the following tables. 2------ y= -x+4 X Y -2 0 2 0 -2 3-------------Graph each equation. Plot at least five points for each equation.

laws of vector algebra

Draw appropiate figures to give geometric proofs for the following laws of vector algebra: (a+b)+c = a +(b+c) lambda(a+b) = lambda(a) + lambda (b) : lambda is any scalar a(b+c) = ab + ac .................................................................... a,b,c do not need to be coplanar. Full solution please

Time Card & Net Pay Calculation

Practice Questions Complete the following time card. Janice earns time and a half overtime when she works more than eight hours on a weekday or on Saturday. She earns double time on Sundays and holidays. Calculate Janice's net pay if she earns $9.75 per hour, is married, and claims one withholding allowance. Challenge Proble

Average Annual Return Equation

Venture capital. Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000(1 + r)2 = 27,000.

linear equation mathematical models

A butcher charges $2.80 for 2.5 pounds of hamburger. How do I write a mathematical model (linear equation) that allows the calculation of the cost of the hamburger based on buying any number of pounds?

Solving Quadratic Equations and Substitutions

1. An interesting method for solving quadratic equations came from India. The steps are: (a) Move the constant term to the right side of the equation (b) Multiply each term in the equation by four times the coefficient of the x2 term (c) Square the coefficient of the original x term and add it to both sides of the equation (d)

Demand for pools. Tropical pools sells an above ground model for p dollars each. The monthly revenue for this model is given by the formula R(p) = -0.08P^2+300P Revenue is the product of the price p and the demand (quantity sold) a) Factor out the price on the right- hand side of the formula b) Write a formula D(p) for the monthly demand c) Find D(3000)

Demand for pools. Tropical pools sells an above ground model for p dollars each. The monthly revenue for this model is given by the formula R(p) = -0.08P^2+300P Revenue is the product of the price p and the demand (quantity sold) a) Factor out the price on the right- hand side of the formula b) Write a f

"Squares everywhere" Determine the Perimeter

The figure has been divided into nine squares, the smallest one, darkly shaded, has sides of length one and the lightly shaded squares has side of length x. Determine x and also determine the perimeter of the large figure. See Attached

Solve by Quadratic Formula

See the attached file. Solve each equation using the quadratic formula. 1. x^2 + 5x + 2 = 0 2. 3x^2 = 6x - 1 Show your work step by step. Compute the discriminant. Then determine the number and type of solutions for the given equation. 1. 4x^2 - 2x + 3 = 0 2. 3x^2 + 4x - 2 = 0.

Equations and inequalities

Show your work step by step. Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Write and factor the trinomial. 1. x^2 + 16x 2. x^2 + 5x 3. x^2 + 4 x 5 Show your work step by step. Solve each equation by completing the sq

Factor out the common factor

Factor out the common factor. (5x - 2)2 + (5x - 2) Completely factor the expression. x4 - 3x3 + x2 - 3x Write the rational expression in simplest form. 4x2y xy - y Write the rational expression in simplest form. 9x2 + 9x 8x + 8 Write the rational expression in simplest form. x2 - 9 3 - x

Factoring by grouping

What is factoring by grouping ? When factoring a trinomial by grouping , why is it necessary to write the trinomial in four terms ?

Difference of Two Squares formula Discussion Question.

Some people say that the Difference of Two Squares formula helps them to multiply large numbers without a calculator. How would you use this formula to multiply 201 by 199? Find at least one more pair of numbers that can be multiplied this way.

An interest word problem using the polynomial.

P dollars is invested at an annual interest rate R for one year. If the interest is compounded semi-annually, then the polynomial P (1+ r/2)^2 represents the value of the investment after one year. Re write this expression without parentheses. Evaluate the polynomial if P = $200 & R = 10%

Solving for Unknowns

(1) A forensic scientist uses the expression 72.6 + 2.5T to estimate the height in centimeters of a female with a tibia of length T centimeters. If a female skeleton has a tibia of length 32.4 cm, then what was the height of the person? Find the length of your tibia in centimeters, and use the expression from this exerc

Several algebra problems

2. 3. 4. Find the coordinates of the x-intercept. 2x + y = -6 (-6, 0) (0, -3) (0, -6) (-3, 0) 5. 6. Janet invested $26,000, part at 6% and part at 3%. If the total interest at the end of the year is $1,080, how much did she invest at 6%? $11,000 $10,0

Mathematics - Algebra - Transforming Graphs

I understand that when you transform y = f(x) to y = f(ax) it is a stretch in the x direction of scale factor 1/a, but I can't find any reasoning as to why the scale factor is 1/a and not just a. Can you explain?

Mathematics - Algebra - Word Problem

You are a high school math teacher and are introducing matrices to the classroom next week. It is very important to you to make a connection between the real world and this topic, so you decide to research in which applications matrices are used. To your surprise, you find several very useful applications, such as decoding and e

An expression for expenditures and receipts

How do I create an expression for expenditures and for receipts on this problem? How many chips must be sold to produce a profit? To make x thousand computer chips requires fixed expenditures of $352 plus $42 per thousand chips. Receipts from the sale of x thousand chips amount to $130 per thousand.

Customer Purchasing Items Inventory

I have a customer that is purchasing purchasing a item packed 6,0000 per case @ 19.00 per case. they are buying 281,000 cases per year. I would like to sell them our new items that is packed 10,800 per case. 1. How many cases would be new items reduce their inventory by 2. If I sold the new item for $32.00, how

Algebra - Equations and Matrices

See Attached Exercise 5.5 25. Supply and Demand The supply function for a product is given by p=q²+2q+122 and the demand function for this product is p=650-30q, where p is the price in dollars and q is the number of hundreds of units. Find the price that gives market equilibrium and the equilibrium quantity. 29. Break-Ev

Mathematics in Investing Rate

Hi can some help me with the below questions? 1. What does 200% mean? If you have a job making $5 an hour and you receiva a 200% raise how much will you be making after the 200% raise? 2.Is is better to invest your money where it will earn interest at a rate of 7% per year or to invest it where it will be multiplied by 2/3

Cumulative Equation Problems

Ch. 10 Cumulative Problems 1) solve (X - 4)2 = 3 2) solve 5 (X - 2)2 = 3 3) solve - 9 (X - 3)2 = - 7 4) solve by completing the square 2 X2 - 8 X - 9 = 0 5) solve by completing the square 4 X2 + 2 X - 3 = 0 6) solve by using the quadratic formula 4 X2 - 3 X + 3 = 0 7) solve by using the quadratic formula 5

Functions & Graphs Your mission is to find real-world data for company sales, a stock price, biological growth, or some sociological trend ... A printer has a contract to print 100,000 invitations for a political candidate. He can run the invitations by using any...

Functions & Graphs Group Activity #3 Modeling Your mission is to find real-world data for company sales, a stock price, biological growth, or some sociological trend over a period of years that fits an exponential, logistic, or logarithmic function. To do this, you can look at a statistical graph called a histogram which d