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Basic Algebra

Strong Induction: Example Problem

Use strong induction to show that when a convex polygon P with consecutive vertices VI, V2, ... , Vn is triangulated into n - 2 triangles, the n - 2 triangles can be numbered 1, 2, ... , n - 2 so that Vi is a vertex of triangle i for i = 1,2, ... , n - 2.

Solve: Rational Exponents and Radicals

What is a rational exponent? How are rational exponents related to radicals? Give an example of how an expression with a rational exponent can be rewritten as a radical expression. Explain how the process of combining radicals through addition and subtraction is similar to combining polynomials. What makes two radicals like radi

Graph the parabola using the quadratic formula

(2-(-2)^)^ - 5 x 4 -(4w + u) - 4 (6u + 4w) The surface area of a right prism is given by , where is the area of the base, is the perimeter of the base, and is the height of the prism. Solve for . Solve for . Simplify your answer as much as possible. . Write

Radical Signs for Expressions

Solve and check the following equation; Explain/demonstrate how you derived your answer. Note: the radical sign extends over the expression 3x + 2. â??3x+2 - 2â??x = 0 Answer the following questions; Define a radical. What happens to a solution if the radicand is negative? Why do simplified radicals pro

Wind Chill

W = 91.4- (10.5 + 6.7v-0.45v)(457 - 5t), where W and t are in degrees Fahrenheit and v is in miles per hour (mph). a) Find W to the nearest whole degree when t =25°F and v =20 mph. b) Use the accompanying graph to estimate W when t =25°F and v =30 mph. Comparing wind chills. Use the formula from above to determine wh

Parabolic Equation

Your bridge design has two towers, each with height ( h) of 300 ft above the road. Two suspension cables connect the two towers. The equation modeling the shape of these cables is parabolic. The total distance (d) between the two towers must be 3500 feet. The lowest point (l) of the cable above the road must meet 8 feet. Find t

Mathematical Induction Statement

Let p(n) be the statement that 1^3 + 2^3 + ... + n^3 = (n*(n + 1)/2)^2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step.

Compute the firm's profit, Derive an expression for marginal

Ï?=-10-48Q+15Q^2-Q^3 a. Compute the firm's profit for the following levels of output: Q=2,8, and 14. b. Derive an expression for marginal profit. Compute marginal profit at Q=2,8, and 14. Confirm that profit is maximized at Q=8. (Why is profit not mazimized at Q=2?)

Algebra: Quadratic Equations

A. Why do you factor a quadratic equation before you solve? B. Why are there usually two solutions in quadratic equations? Under what conditions will a quadratic equation have only one solution? No solutions? C. How can you tell before solving the equation how many solutions to expect?

Rational expression, Rational equation, Polynomial

A. Choose an example of a rational expression, and present a step by step solution. B. Under what situation would one or more solutions of a rational equation be unacceptable? C. Define a polynomial and a rational expression. What makes a rational expression unique? Provide two original examples of a rational expression an

Exhibiting Rational Expressions

(1) Explain how multiplying and dividing rational expressions is similar to multiplication and division of fractions. Give an example of each and compare the process. (2) When simplifying the rational expression (x+8)/(x+2), explain why it is improper to cancel out the x's. State a general rule for canceling factors in a rati

Determine the degree of the polynomial

For each of the following polynomials, (a) list the degree of each term; (b) determine the leading term and the leading coefficient; and (c) determine the degree of the polynomial. (1) A 10-ft wide round water trampoline is floating in a pool measuring x ft by x ft. Find a polynomial for the remaining surface area of the pool

GCF of Monomials and Expressions

Please show all work for all problems listed. Thank you This will help me with future problems like these. Find the GCF of the monomials. 16x2z, 40xz2, 72z3 Factor the GCF of expression. 15x2y2 - 9xy2 + 6x2y a(a + 1) - 3(a + 1) Factor each polynomial completely. x3y + 2x2y2 + xy3 Use grouping to factor e

Converting word problem to algebraic expression

1.) Write the following as an algebraic expression using x as the variable : the sum of a number and -8 2.) Write the following as an algebraic expression using x as the variable: Five more than the product of 7 and a number. 3.) Solve -3 ( -19+4 )/-5

Factoring Equations

1. Factor 2. Factor. 3. Factor completely: . 4. Factor . 5. Factor. 6. Factor completely: . 7. Factor the quadratic expression . 8. Factor. 9. Factor completely: . 10. Factor completely: . 11. Factor the quadratic expression . 12. Factor. 13


1. Simplify the following expression, and rewrite it in an equivalent form with positive exponents (12x^7y^9)/(36xy^7 2. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. (-3x^6y)^3 3. Simply the following expression, and rewrite it in an equivalent form with positive e

Binomials, Zero-Product property, and quadratic equations

How can you tell if a binomial is a difference of two perfect squares? Explain the process of factoring a difference of two perfect squares. Give an example. Explain the zero-product property. Give a simple example of its use. How is this property used to solve a quadratic equation? Give an example.

Method for Factorization of an Algebraic Expression

Hello, please help with: A. I would like you to look at the variables, and find the GCF of the variables, place those letters next to the GCF of the coefficients outside of your parenthesis. Complete the last step of the problem, and display the factored form of the expression, and provide a check, to prove your answer is

The Amount Of An Investment

The amount of an investment of P dollars for t years at simple interest rate of r is given by A=P + Prt. a. Rewrite this formula by factoring out the greatest common factor on the right-hand side. b. Find A if $8300 is invested for 3 years at a simple interest rate of 15%.

Three Basic Algebra Problems

Section 4.1 Question #62 - Simplify. Assume that no denominator is 0 and that 00 is not considered (x25)6 Section 4.2 Question number 12 - Express using positive exponents. Then, if possible, simplify a −3 b

Math Problems Quotients

Help with the following problems. Please work the problem out. Thank you 1. Simplify -5y^4(y^5)^2 15y^7(y^2)^3 2. Parenthesis is around the whole problem. (3^3)^2 3 3. Simplify w^-4 w^6 4. Simplify * Parenthesis is around the whole problem* (2s^-1t^3)^-3 6s^2t^-4 5. Write in standard notation. 9.3 x 10

Algebra complex zeros

1) Factor the polynomial completely. P(x) = x^2 + 9 P(x) = Find all its zeros. State the multiplicity of each zero. (If an answer does not exist, enter DNE.) real zero x=______ with multiplicity______ complex zero x=_______(positive imaginary part) with multiplicity ____ co

Factor Out - Algebra Complex Zeros

1) A polynomial P is given. P(x) = x^4 + 49x^2 (a) Find all zeros of P, real and complex. (Enter your answers as a comma-separated list. If a root has multiplicity greater than one, only enter the root once.) x = (b) Factor P completely. P(x) = 2) A polynomial P is given. P(x) = x^3 â?' 10x^2 + 50x (a) Find all zer

Finding rational zeros and factoring polynomials

1) Find all rational zeros of the polynomial. (Enter your answers as a comma-separated list. If a zero has multiplicity greater than one, only enter the root once.) P(x) = x^3 â?' 6x^2 + 11x â?' 6 x= Write the polynomial in factored form. P(x) = 2) Find all rational zeros of the polynomial. (Enter your answers as a c

Algebra Assignment

1. From the graph below, state the coordinates of the point at which the two lines intersect (Note to my BrainMass pal, if you are not able to read the numbers, they are ) Down: 7, 6, 5, 4, 3, 2, 1, 0 Across the numbers are - 6 -4 -2 -1 0 2, 4, 6, 2. Solve using the substitution metho

Topoogical equivalence of an open interval and the real line

Prove that the open interval (-pi/2,pi/2) considered as a subspace of the real number system, topologically equivalent to the real number system. Prove that any two open intervals, considered as subspaces of the real number system, are topologically equivalent. Prove that any open interval, considered as a subspace of the r

Laws of Exponents

Post a 200- 300 word response to the following: Explain the rules of exponents and provide one example of each: Multiplying Monomials: Product of Powers Power of Power Power of a Product Dividing Monomials: Quotient of Powers Power of a Quotient Please help.

Algebraic Properties of Functions

1 and 2 can have multiple answers 1) Which of the given functions is a one-to-one function? Select all that apply g(x)=2sqrt(x+5) g(x)=5x^2-2 h(x)=x^4+5 f(x)=Abs(x) f(x)=-5x+2 2) Which of the given functions is a one-to-one function? Select all that apply g(x)=3sqrt(x) f(x)=-2x+3 g(x)=2x^2-3x f(x)=1/x h(

Need help on this problem

Show the total cost expression and calculate the EOQ for an item with holding cost rate 18%, unit cost $8.00, annual demand of 40000, and ordering cost of $48.