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Basic Algebra

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.

Quadratic Equations

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

Solve for coefficient.

When (x-2)^17 is expanded, what is the coefficient of x^12? Be careful, don't forget about the -2.


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

Radical Ideals

See attached file for full problem description. Here A^n is affine n-space over a fixed algebraically closed field i.e. is the set of all n-tuples of elements of that algebraically closed field question asks to show that "ideal of an algebraic variety is radical"

Situation Puzzle

This is a situation puzzle tile that I'm working on. The numbers 0-9 are allowed to be used once only. (Do not count the numbers that were given in the problem.) The dashes represent one number. Candy bars costing _____ _____ cents each were on sale with a price of _____ for _____ _____ cents. This was a savings of 4 _____

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

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)

Checker Tiles

I'm working ahead of my daughter. They are working on checker tiles and out of the 20 packets I'm down to the last 3 that are giving me problems. They are situation tiles and it has been sorta like using algebra to figure them out. I want to help her out and know that she is getting them correct but I'm unable to answer them

Trigonometric Equations

Use factoring, the quadratic formula, or identities to solve the following equations: 25 sin x cos x-5 sin x +20 cos x = 4 cos^2 x + 5 cos x=1 cos 2x + sin x =1

Sets and Functions

Topology Sets and Functions (IV) The Algebra of Sets If { Ai } and { Bj } are two classes of sets such that { Ai } is subset of { Bj }, show that Ui Ai is subset Uj Bj and ∩j Bj is subset of


Prove log10(cot x) = -log10(tan x)

Situation Tiles

I'm trying to help my daughter working a packet of situation tiles. Out of 15 packets, I'm down to 3 where I'm struggling to figure out the problems. They are situation tiles and it has been sorta like using algebra to figure them out. I want to help her out and know that she is getting them correct but I'm unable to answer t

Lagrange Multipliers

Using Lagrange multipliers, find the maximum and minimum values of f(x,y) = x^2*y subject to the x^2 + y^2 = 1 constraint.

Perfect One-Factorization

Construct a perfect one-factorization of K_2n for infinitely many values of n. Prove the factorizations are perfect!

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

Radical expressions

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


1) Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=-2x(squared) + 8X - 1 2) An equation of a quadratic function is given -- f(x)= -2X(squared - 12X + 3 - Determine without graphing, whether the function has a minimum value or a maximum value. - Find the minimum or max

quadratic equation and inequality

1) What is the meaning and purpose of the axis of a quadratic function? 2) Solve the inequalities. State the solution set using interval notation for: (x - 4) / (x + 3) < 0 and then for: (x - 4) / (x + 3) > 0 What do you get when uniting the two sets of solutions? 3) The surface area A, of a cylinder with heigh

Solving equations

Find all real and imaginary solutions Find exact and approximate solutions: Find two positive real numbers that differ by 4 and have a product of 4. See attached file for full problem description.

Algebra questions: quadratic equations, word problems

See attached file for full problem description. 4. a) Solve 36x2 + 49 = 0 b) Find the x-intercept of f(x) = 36x2 + 49 6. Solve 3x2 - 7 = 0 16. Solve (t - 2)2 = 25 56. Use the hang-time function V(T) = 48T2, relating vertical leap to hang time. Tracy McGrady, of the Houston Rockets, has a vertical leap of 40