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# Basic Algebra

### Should We Purchase That New Copier?

Campus Print Shop is thinking of purchasing a new, modern copier that automatically collates pages. The machine would cost \$22,000 cash. A service contract on the machine, considered a must because of its complexity, would be an additional \$200 per month. The machine is expected to last eight years and have a resale value of \$4,

### Writing Equations from Word Problems

The edges of a triangular homesite have lengths of 2x - 1, x, and x + 2. Write an expression for the perimeter of the property.

### Factoring: Binomials, Trinomials and Polynomials

Please see the attached file for the fully formatted problems. Find the greatest common factor for each of the following sets of terms. Factor each of the following polynomials (see attachment).

### Writing Equations from Word Problems

The floor plan of a house is rectangular. The house's length is 2x-10 and its width is x+3. Write an expression for the area of the house

### Given the pay structures for two different babysitters, determine the number of hours of babysitting at which the two babysitters charge the same amount of money.

A parent is deciding which babysitter to use in the neighborhood. Babysitter A charges \$20 per hour and a base rate of \$60 per day. Babysitter B charges a base rate of \$50 per day and \$25 per hour. For how many hours of babysitting do the two babysitters charge the same amount?

### Create a set of data that can be modeled as a polynomial function.

Details: Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as (V1/V2), raised to the third power, (V1/V2)3. Rational functions are also usefu

### In the real world, where might these so-called imaginary numbers be used?

1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). Questio

### Find the mass and radius of three of the nine planets in our solar system.

A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of tim

### Algebra Word Problems

The owner of a hobby store bought a case of 9-volt batteries for \$26.00. He marked the price up such that his profit was \$1.74 per battery. After selling 13 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

### How long will it take the object to hit the ground?

The height h in feet of an object after t seconds is given by the function: h = -16t^2 +60t + 9. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.

### X^2+12x+32=0

Explain in detail.

### Operations and Inequalities

1. What is the inherent meaning and justification of cross multiplication as it applies to solving an equality? 2. Is | x -2 | the same as | 2 - x |? Please explain your answer. 3. How do you express the following mathematically? a. y is at least 3 b. y is more than 3 c. y is at most 3 d. y is

### Various Algebra Questions

Various Algebra Questions. See attached file for full problem description. 1. Simplify: . Show work. 2. Simplify: Show work. Give the exact answer (including a radical). 3. (a) Is the graph of a circle a graph of a function? (Yes or no) (b) Find the center and the radius

### Is it possible to write consecutive rational numbers?

Is it possible to write consecutive rational numbers? Please explain why or why not.

### Question about Solve an algebraic equation

Details: Your company is considering various locations for expansion. It is your job to check out the various areas and the friendliness for business. One of the factors of interest is the average temperature. As you start your drive, the first electronic sign you see states that the temperature is 22.0 °C. You are not very

### Graphing a system of inequalities considering a small home-based company

A small home-based company produces both hand-painted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation

### Algebra Word Problem - How Many Children Attended the Play?

Adult tickets for a play cost \$4 and child tickets cost \$1. If there were 23 people at a performance and the theater collected \$80 from ticket sales, how many children attended the play?

### Simulation: Example Question

We wonder if our planning can provide the level of service customers will get with one oven and one prep table. The following information should allow you to simulate operations and determine an average service time from taking the order to serving the pizza et al. Do 50 iterations. Item Time Required Probability Ordering

### Evaluation and simplification of an expression

--What is the difference between evaluation and simplification of an expression? --3,4,5 are consecutive whole numbers. -13, -12, -11 are consecutive integers. Is it possible to write consecutive rational numbers? If yes, give an example. If not, explain why not. --How does a term differ from a factor?

### Ratio

Car x used k gallons of gas while traveling p miles, and car Y used s gallons of gas while travleing r miles. What was the ratio of the number of miles per gallon for car X to the number of miles per gallon for car Y?

### Algebra Problems

Find all real or imaginary solutions to each equation: 3v^2 + 4v - 1 = 0 Solve the equation 2y^2 - 3y - 6 = 0 (x-10)(x-2) = -20 Determine whether the parabola opens up or down: y = -1/2x^2 + 3 Find the vertex and intercepts for each parabola: g(x) = x^2 + x - 6 Find all real solutions to each equation: x^2 + x +

### Measuring and Comparing Earthquakes

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 your region of the world. Give the measurement of the earthquake. Explain what this measurement means.

### Algebra Word Problem - Crossing a bridge with a flashlight.

The band U-2 has concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side . It is night there is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, m

### Simplifying Expressions

Simplifying Expressions. See attached file for full problem description. Simplify the following expression as much as possible Rewrite the following in simplified radical form Simplify Write in simplified radical form by rationalizing the denominator Solve for Solve for w Write

### Factor each of the given polynomials (and/or do what is otherwise indicated).

1. Find the value of "c" such that the expression "(x^2) + 6x + c" is a perfect square. 2. Find the value of "a" such that the expression "(z^2) + 12z + a" is a perfect square. 3. Factor the expression 3*(u^4)*(y^4) - 48*(u^4) completely. 4. Factor the expression 36*(t^3) - 48*(t^2) - 20t completely. 5. Factor the ex

### Greatest Common Factor

Find the greatest common factor 1. 16x^2z, 40xz^2, 72z^3 Factor each polynomial 2. 9a^2 - 64b^2 3. x^3 + ax + 3a + 3x^2 4. 18z + 45 + z^2 5. x^2 - 5xs - 24s^2 6. A triangular sail has a area of x^2 + 5x + 6 square meters and a height of x + 3 meters. find the length of the sail's base.

### Logarithms : Power Rule

Fill in the blank to make a true statement. To solve 4^x =27, we can take the logarithm of each side of the equation to get log (4^x) = log (27). The power rule for logarithms would then provide a way of moving the variable x from it's position as an _________ to the position of a coefficient. Is the blank, negative value, ba

### Relation Between Relatively Prime Integers

Modern Algebra Ring Theory (XXXVI) Polynomials over the Rational Field Euclidean Ring Irreducible Polynomial If m and n are relatively prime integers and ( x - m/n ) divides ( a_o + a_1x + ... + a_r x^r ) where the a's are integers, prove that m divide

### Prime Polynomials

Give an example of a polynomial of a degree 2 that satisfies the following two conditions: (1) the coefficient of x^2 is 1 and (2) the polynomial cannot be factored. Explain why the polynomial cannot be factored. Give an example of a polynomial with degree 2 that can be factored as the product of two polynomials of degree 1 e

### The C-V-P Equation

The company sells lawnmowers for \$895 each. The variable cost per lawnmower is \$520. The company's monthly fixed costs are \$84,500. Using the C-V-P equation, compute the amount of profit the company will have for a month in which the company sells 375 lawnmowers.