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Basic Algebra

Absolute Values

I know that the two bars | | around the expression 2-x and x-2 stand for 'absolute value'. But how does using | | differ from using simple brackets such as: ( ) or [ ] ?

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

What is the total number of cars in the lot?

In a car lot 9 out of every 16 cars are used cars. Of the used cars, 2 out of every 3 are less than five years old. If the number of used cars less than five years old is 24, what is the total number of cars in the lot?

What is the daily production of vests in the medium size?

A certain company makes a total of 96 ski vests each day in sizes small, medium, and large. If the number of vests made daily in the small and large sizes combined is equal to the number of vests made daily in the medium size, what is the daily production of vests in the medium size?

Distance

A certain map is drawn so that a distance of 0.5 inch on the map represents 12.5 miles of actual distance. If the distance between two towns is 4.5 inches on the map, what is the actual distance, in miles, between the two towns?

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 +

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

Polynomial Ring

Polynomial Ring. See attached file for full problem description.

Short Algebra Fraction

Short Algebra Fraction. See attached file for full problem description. Please explain to me in a step by step detail as if were explaining to a child how to get the answer to this fraction.

Polynomial Ring

Polynomial Ring. See attached file for full problem description.

Exponential Function

Let f (x) = e^x/x^2 . Find all critical points of f (x) and classify them as maximums or minimums. State the intervals where f (x) is increasing and decreasing. Please show graph or work (pref. derivative).

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

Factoring

Please see the attached file for the fully formatted problems.

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

Simplifying Expressions

Simplify the expression: assume all variables represent positive numbers (81x^4 y) ^1/4 / (16xy^3) ^3/4

Riesz Representation Theorem and Hoelder's Inequality

On Problems 4 and 5 with 1<p< infinity and q the index dual to p, it will be helpful to remember from the proof of Young's inequality that, for y and z positive numbers, y^p = z^q if and only if y=z^(q-1) if and only if z=y^(p-1) and, under these equivalent conditions, zy = y^p =z^q. See attached file for full problem d