Share
Explore BrainMass

# Basic Algebra

### Algebra Word Problems : Time, Speed and Distance

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour longer than Smith's. How fast was each one traveling?

### Algebra : Estimation, Word Problems and Optimization

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35... 2. Make a conjecture about the relationship between the original number and the final number in the following process. Pick a number Multiply the number by 12 Add 12 to the product Divide the sum by 4 Subtract

### Radicals and Rational Exponent Notation

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

### Find a polynomial that represents the revenue for one week.

If a manufacturer charges x dollars each for soccer balls, then he can sell 3000 - 150x soccer balls per week. Find a polynomial that represents the revenue for one week. Find the weekly revenue if the price is \$8 for each soccer ball.

### What is the maximize the area of a rectangular patio?

I have 400 feet of lumber to frame a rectangular patio. I want to maximize the area of the patio. What should the dimensions of th patio be. Show how the maximum area of patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.

### Solve a Quadratic Equation: Explain what the value of the discriminant means to the graph of y = ax^2 + bx + c.

When using the quadratic formula to solve a quadratic equation ax^2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the

### Finding Consecutive Integers

Find three consecutive integers such that the sum of their squares is 77.

### Series and Functions

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, ratio

### The intensity level of an earthquake is based on the Richter scale.

The intensity level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weakest possible tremor. What is the formula for measuring earthquakes? Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in you

### Inequalities Word Problems: Example

1) Solve each equation for x. x-a=-x+a+4b 2) Building a ski ramp. Write an inequality in the variable x for the degrees measure of the smallest angle to triangle shown in the figure, given that the degree measure of the smallest angle is at most 30 degrees. See attached file for full problem description.

### Explain what the value of the discriminant means to the graph of y = ax^2 + bx + c

When using the quadratic formula to solve a quadratic equation y = ax^2 + bx + c, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminant is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

Solve the following: 1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for th

### EXPONENTIAL MODELING:

EXPONENTIAL MODELING: I want you to locate data that can be effectively modeled using an exponential function. Check the scatter plot to be sure that your data is appropriate for an exponential model! Please include the following components in your finished assignment: 1. A data table showing your original data, with a re

### Logarithmic Equations Word Problems : Radioactive Decay

The amount of radioactive element R in grams present t years from now is given by the formula R = 10.9e-0.003t. How much of R is present initially? How much is left after 35 years (to the nearest tenth of a gram)?

### Simplifying Expressions : Laws of Exponents

Ronnie invested P dollars in a 2 year CD with an annual rate of return of r. After the CD rolled over three times, its value was P( (1+r)^2)^3. Which law of exponents can be used to simplify the expression. Simplify it.

### Simplifying Expressions

Show all steps. Find each quotient: (14y + 8y^2 + y^3 + 12) / (6 + y)

### Finding a polynomial that represents the area

The length of a rectangular swimming pool is 2x - 1 meters, and the width is x + 2 meters. Write a polynomial that represents the area. Find the area if x is 5 meters.

### Simplifying Expressions

Perform the indicated operation - please show all steps: 46. (w^2 - 2w + 1) + (2w - 5 + w^2) 60. (t^2 - 6t + 7) - (5t^2 - 3t - 2)

### Sets and Functions : Set Difference

The difference between two sets A and B, denoted by A - B, is the set of all elements in A and not in B, thus A - B = A&#8745;B'. Show that A - (BUC) = (A - B)&#8745;(A - C).

### Sets and Functions : Set Difference

The difference between two sets A and B, denoted by A - B, is the set of all elements in A and not in B, thus A - B = A&#8745;B'. Show that (AUB) - C = (A - C)U(B - C).

### Sets and Functions : Set Difference

The difference between two sets A and B, denoted by A - B, is the set of all elements in A and not in B, thus A - B = A&#8745;B'. Show that A - (B - C) = (A - B)U(A&#8745;C).

### Algebra Questions: Please solve these equations related to arithmetic sequence and geometric sequence

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d)

### Algebra Problem Set: Inequalities, Absolute Value

66. Young's rule for determining the amount of a medicine dosage for a child is given by C = where a is the child's age and ad is the usual adult dosage, in milligrams. The dosage of a medication for a 5 year old child must stay between 50mg and 100 mg. Find the equivalent adult dosage. 52. 2|2x - 7| + 11 = 25

See attached file for full problem description. 1. After an accident, how do police determine the speed at which the car had been traveling? The formula r = 2 sqrt(5L) can be used to approximate the speed r, in miles per hour, of a car that has left a skid mark of length L, in feet. How far will a car skid at 65mph? at 100

### Algebra questions: solving equations, simplifying, graphing, etc.

Algebra Questions. See attached file for full problem description. 1. Solve 15x = 2x2 + 16 2. The width is 7 feet less than the length; the area is 18 square feet. Find the length and width. 3. Solve x2 + 4x - 12 < 0 4. Solve (x + 3)/(x - 4) < 0 5. Find f(-13) for f(x) = third root of (2x - 1) 6. Rewrite (third roo

### Applications of Lagarithms and Exponents : Measuring the Loudness of Sound

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear. Using the Library, web resources, and other course material, research how sound is measured. Include the following items in your posting: The formula for meas