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# Basic Algebra

### Mathematics - Algebra - Exponential Functions

It is estimated that the demand for a manufacturer's product is increasing exponentially at the rate of 2% per year. If the current demand is 5,000 units per year and if the price remains fixed at \$400 per unit, how much revenue will the manufacturer receive from the sale of the product over the next 2 years?

### Quick Algebra problem

One of the slowest fish is the blenny fish. The function y = 0.5x describes how many miles y the fish swims in x hours. Graph the function. Use the graph to estimate the number of miles the fish swims in 3.5 hours. Can you please help me with my son's algebra? They do not work from a book so there are no other examples f

### 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 - Errors Propagation

How well do we understand how errors propagate? Consider a problem whose correct answer is x =99.89. To get credit you have to submit an answer good to within 3.0% . (a) What is the largest answer that the system will accept -- give your answer to 0.5 % (b) What is the smallest answer that the system will accept -- give

### Functions and Graphs

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 10%, P = 1, and n = 1 and give the coordinates (t, A) for the points where t = 0, 1, 2, 3, 4. a) Show coordinates in this space b) Show graph here

### 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

### Quadratic Equation for Lowest Point of the Highway

Civil engineers are designing a section of a highway. They need to install a storm drain at the lowest point of a curve whose equation is y = .00003x^2 - .05x + 1000 where x is the number of feet above sea level. How many feet above sea level, the nearest foot, is the lowest point of the highway?

### Mathematics - Algebra - Open Top Box

A open box has a volume of 1000 cubic inches to be constructed from a 22 in by 30 in sheet of cardboard by cutting squares of equal size from each corner and folding up the sides. What size square should be cut from each corner?

### Mathematics - Algebra - Inequalities

An architect wants to design a rectangular room so that its length is 8 meters more than its width, and its perimeter is greater than 56 meters. If each dimension of the room must be a whole number of meters, what are the smallest possible dimension in meters of the room?

### Quadratic Equations: How Long Until an Object Hits the Ground

Question: A rock is thrown from the top of a building. The distance, in feet, between the rock and the ground t seconds after the rock is thrown is given by d = -16t^2 + 16t + 45. How long after the rock is thrown does it hit the ground?

### Algebra

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.)

### Mathematics - Algebra - Depreciation

A manufacturer buys \$20,000 worth of machinery that depreciates linearly so that its trade-in value after 10 years will be \$1,000. a) Express the value of the machinery as a function of its age and draw the graph. b) Compute the value of the machinery after 4 years. c) When does the machinery become worthless?

### 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

### Error in radius and volume

1. The top of a tower is a sphere with a diameter of 40ft. A layer of paint 0.08 inches thick is applied to the sphere. Approximate the volume of the paint that is used. 2. The radius of a sphere is measured with a percentage error within + or -0.04%. Estimate the percentage error in the calculated volume of the sphere.

### Fahrenheit and Celsius Temperature Conversions

Katie converts the outside temperature from degrees Fahrenheit to degrees celsius. She uses the formula below to convert the temperature. (F-32)5/9=C If the outside temperature is 50 degrees fahrenheit, what is the outside temperature in degree celsius?

### Ratios and Proportions-I am having a hard time with this Please help-this is in two parts.

Part 1: Describe a simple process for using rates and unit prices that might help someone who is having difficulty understanding these concepts. Include an example to explain the solution process.

### Algebra: A Decreasing Cube

Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by: V(s) =s^3 - 13s^2+ 54s -72. a) Find V(10). b) If the new width is s - 6 centimeters, then what are the new length and height? c) Find the volume when

### 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

### Algebra Application Word Problems : High-income Tax Bracket, Driving Time and Speed, Splitting up a Chocolate Bar and Systems of Equations

Chapter 1) 165. High-income bracket. The expression 97,653 + 0.35( x- 336,550) represents the amount for the 2006 federal income tax in dollars for a single taxpayer with x dollars of taxable income, where x is over \$336,550. a) Simplify the expression. b) Use the graph in the accompanying figure to estimate the amount of tax

### Issues Facing New Businesses - Bakery : Budgets, Costs, Profit and Revenue ...

Axia College Material Appendix C Starting a Business Starting your own business can be exciting and daunting at the same time. Businesses use math when managing finances, determining production levels, designing products and packaging, and monitoring labor. A bakery can be a highly profitable and rewarding business. Durin

After running various advertisements, you have received the statistics from each advertising outlet. A total of 800 ads were run. The following lists the breakdown of each: 380 ads were run over the radio. 240 adds were run in the newspaper. 300 adds appeared on the Internet. 185 ran both on radio and on the Internet.

### Algebra word problem

Customers of a phone company can choose between two service plans for long distance calls. The first plan has a \$21 one-time activation fee and charges 10 cents a minute. The second plan has no activation fee and charges 14 cents a minute. After how many minutes of long distance calls will the costs of the two plans be equal?

### 21 Algebra Problems : FOIL, Simplify, Word Problems and Quadratic Equations - (Please see the attached file for the fully formatted problems)

Please see the attached file for the fully formatted problems. 1) Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers. 2) Simplify by removing factors of 1. 3) Simplify. 7) Solve. 8) Divide and simplify. 9) Use the quadratic formula to solve the equ

### 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

### Polynomial to represent area

The owner of a daycare center plans to have a rectangular sandbox built in the outdoor play area. The width (in feet) of the sandbox is given by the polynomial 2x-5. If the length of the sandbox is designed to be 10 feet longer than the width, write a polynomial that represents the area of the sandbox.

### 13 Problems : Simplify, Solve for X, Complex Fractions and Lowest Common Multiple ... (Please see the attached file for fully formated problems)

Please see the attached file for fully formated Problems #44--Reduce each rational expression to lowest terms. Assume that the variables represent only numbers for which the denominators are nonzero. #64--Reduce each expression to lowest terms. Assume that all variables represent nonzero real numbers and use only positive

### 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.

### Write an equation

The Sugar Sweet Company is going to transport its sugar to market. It will cost 6500. to rent trucks, and it will cost an additional 250. for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S ,

### Mileage

In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 70 . The first car has consumed 30 gallons during that week, and the second has consumed gallons,35 for a total of 2250 miles driven by the two cars combined. What was the average gas mileage obtained by each