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# Basic Algebra

### Graph the Functions and Show the Points of Intersection

For the equation, perform the following: a) Solve for all values of x that satisfies the equation. b) Graph the functions y = x and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs. (Please see the attached file for fully formatted problems).

Please see attached file. Name: 1)Solve algebraically. Trial and error is not an appropriate method of solution. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type as cuberoot(x) and show raising to the nth power as ^n, l

### Simplifying an Equation

Perform each operation and simplify: 6a^2-7a-3/a^2-1 divided by 4a^2-12a+9/a^2-1*2a^2-a-3/3a^2-2a-1

### Algebra Word Problems: Who Wins the Race

Florence and Larry race on a windy day: 100 yards with the wind, they instantly turn around, and race 100 yards back against the wind. Larry is unaffected by the wind, but Florence only goes 90% as fast running against the wind as when running with no wind. Running with the wind improves Florence's no-wind speed by 10%. On a day

### Challenged the tortoise again on bicycle races

Years after the famous foot race, the hare challenged the tortoise again on bicycles. The hare was able to pedal at a rate of 15 mph. while the tortoise could pedal only 12 mph. Knowing he was slower, the tortoise makes up a lame excuse for being given a 27 mi. head start in the 165 mi. race. 1. WHo won the tortoise and hard

### Perfect Square Trinomials

Please answer these questions: 1. Is the following trinomial a perfect square? xsquared - 2x + 1. 2. Is the following trinomial a perfect square? xsquared + 2x -1. 3. Find the constant term that should be added to make the following expression a perfect squared trinomial x squared + 3x. 4. Solve by completing the squa

### Effective Rate for Interest: Bank Loan

Carey Company is borrowing \$200,000 for one year at 12 percent from Second Intrastate Bank. The bank requires a 20 percent compensating balance. What is the effective rate for interest? What would the effective rate be if Carey were required to make 12 equal monthly payments to retire the loan? (Amount borrowed - Compensating ba

### Mathematics - Algebra: Word Problem

An efficiency study conducted for the Cassiopeia cabbage Company showed that the number of cases of cabbage packed by the average worker t hours after starting work at 8a.m. is given by -t^3+4t^2+12t, 0 or greater than t or greater than 4. (0<T At what time during the morning shift is the average worker at peak efficiency?

### A property management company manages 200 apartments renting for ...

A property management company manages 200 apartments renting for \$800.00 each with all the apartments rented. For each \$10.00 pre month increase in rent there will be 2 vacancies with no possibility of filling them. what rent per apartment will maximize the total monthly revenue?

### Determining Distance: Motorcycle Break Down Example

A motorcycle breaks down and the rider has to walk the rest of the way to work. The motorcycle was being driven at 45 mph and the rider walks at a speed of 6 mph. The distance from home to work is 25 miles and the total time for the trip was 2 hours. How far did the motorcycle go before it broke down?

### Determining Distance: Running and Walking Example

A man running at an average rate of 6 miles per hour runs 1/6 of the way to the railroad station in 15 minutes and walks the rest of the way. How many hours would it take him to walk the entire distance at an average rate of 4 miles per hour? a. 2/3 b. 1 c. 5/3 d. 9/4

### Power of a Quotient Rule, Polynomials, FOIL Method, Displacement and Speed of Vehicles

In drag racing, both vehicles begin at a dead stop, and then accelerate through 1/4 mi. Let us say, for the sake of discussion, that our two vehicles are not quite matched in power. That is, vehicle A can accelerate from 0 mph to 60 mph in 5 secs. Whereas the vehicle B can accelerate from 0 mph to 60 mph in 4 secs. DQ 1:

### Writing Equations From a Phrase or Sentence

Write a mathematical phrase or sentence for your classmates to translate. Ten more than six times some number.

### A couple of I think quick questions . . .

Hi! I'm using old tests to study for an abstract algebra exam and of course the old exams do not come with solutions. This means that I need help. I tend to struggle with proofs because I forget some steps or I am not as rigorous as I should be. Thus I need to see actual complete rigorous proofs so that I can make sure that I re

### Graphs, Quadratic Equations, Vertex, Discriminants, Maximum Height and Word Problems ... (Please see the attached file for the fully formatted problems)

Please see the attached file for the fully formatted problems. MTH133 Unit 2 - Individual Project - A Name: 1) Solve the following by factoring ... 2) If , find a) f(2) b) f(-1) Show your work here: 3) Solve 6x2 + 3x - 18 = 0 using the quadratic formula. Read the information in the assignment list t

### Solving Equations and Inequalities using Substitution Method

Please see attachment. I've been working on this for the last few days. Some of the problems I understand and some I do not. 1. Perform the indicated operation: 2 (see the attached file). 3 5 2. Use order of operations to simplify: 25 - 3(22 + 1) = 3. Simplify: 5(2a - 3b) + 3(4

### Rounding off

Can you tell if my answer is right I rounded off to the nearest ten thousands. 900,000 is this correct? I get so confused when it comes to rounding off numbers.

### What is the difference between an equation and an expression? Include an example of each. Can you solve for a variable in an expression?

What is the difference between an equation and an expression? Include an example of each. Can you solve for a variable in an expression? Explain. Can you solve for a variable in an equation? Explain. Write a mathematical phrase or sentence for your classmates to translate.

### Algebra: equations and inequalities

1. Evaluate: 7 -|(-3)(2) - 2| 2. Simplify: 7x - (4 - 2x) 3. Ross jogs at a rate of one mile every 0.25 hours. At what rate is he jogging in miles per hour? 4. Solve for x: 5(2x-3) =x+3 5. Solve for x: (1/2) x - 1/3 = (1/4) x+ 1/6 6. Solve for x: 2x- 3 = ax 7. Solve: |3x-9|=3 8. Solve the in

### Relation on the set of ordered pairs of positive integers

Let S be the set of ordered pairs of positive integers, let z = (5,8), and define R so that (x1, x2) R (y1, y2) means that x1 + y2 = y1 + x2. Show that the given relation R is an equivalence relation on the set S. Then describe the equivalence class containing the given element z of S, and determine the number of distinct eq

The volume of a box is the product of its length, width, and height. Find a function f that models the volume of a box if the width of the box is 9 feet and its height is 3 feet more than its length. Find the volume of the box if the length is 21 feet.

### Mathematics - Algebra - Slope

The table shows how many inches are in varying numbers of centimeters. cent in 3 1.17 4 1.56 5 1.95 8 3.12 10 3.9 Use cent for x and in for y and graph the points. What is the slope of the graph? what is the meaning of the slope?

### Algebra: Breakeven Point for Theta Corporation

The revenue of Theta Corporation is given as R=15x, where x is the number of units produced (in thousands). If the cost is how many units will have to be produced before the company breaks even?

### Application Word Problems : Fractions, Ratio and Proportion, Perimeter of Triangle and Rearranging Formulas

96. World grain demand. Freeport McMoRan projects that in 2010 world grain supply will be 1.8 trillion metric tons and the supply will be only _3/4 _of world grain demand. What will world grain demand be in 2010? 94. Fahrenheit temperature. Water boils at 212°F. a) Use the accompanying graph to determine the Celsius tempe

### Functions and Graphs of Unit Price

Suppliers of transistor radios will market 10,000 units when the unit price is \$20 and 62,500 units when the unit price is \$35. Determine the supply function if it is known to have the form P = a¡Ìx+b (a ¡Ý0, b ¡Ý 0) Where x is the quantity supplied and p is the unit price in dollars. Sketch the graph of the supply

### Functions

Refer to the following scenario to answer questions #1 through #5.Tanya waits tables for customers in her mothers restaurant. She earns an average \$4.00 in tips for each table, and will make about 8 trips to the table for each meal. She make a chart to show her work and tips for 8 to 12 tables. Use the chart to analyze the data

### Mathematics - Algebra - Functions.

Rapid Transit - After x weeks, the number of people using a new rapid transit system was approximately N(x) = 6x^3 + 500x + 8000 a) At what rate was the use of the system changing with respect to time after 8 weeks? b) By how much did the use of the system change during the eighth week?