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Basic Algebra

Determining Indices

1. x^-1/4 = 125x^1/2. Answer given 1/625. 2. 8x^-2 = 343x^-1/2. Answer given 4/49. 3. 2x^1/3 = 81/8x^-1. Answer given 27/8.

Factoring Polynomials

1. Which one is a prime number of 330. a. 11*3*5*2 b. 33*5*2 c. 11*3*10 d. 3*5*2 2. Find the GCF of the set of monomials of: 528, 624 a. 48 b. 50 c. 528 d. 624 3. Factor out the negative of the greatest common factor of: -4b + 20 4. Factor the polynomial: 81a^8b^4c^8 - 4d^10 5. Factor the polynomial:

Algebraic expressions of the production function

#2) Following are different algebraic expressions of the production function. Decide whether each one has constant, increasing, or decreasing returns to scale. a. Q = 75L0.25 K0.75 b. Q = 75A0.15 B0.40 C0.45 c. Q = 75L0.60 K0.70 d. Q = 100+50L+50K e. Q = 50L+50K+50LK f. Q = 50L2 + 50K2 g. Based on the answers for the

College algebra, asymptotes

Find the oblique asymptote, if any, of the rational function, and prove algebraically. See attached file for full problem description.

Algebra

Solve each proportion: 34) b = -3 3 4 40) c + 3 = c + 2 c - 1 c - 3 Solve each equation: 8) y - 1 = 3 X + 3 4 18) 1 = E__ R + r

Cross Exchange Rate

A currency trader observes that in the spot exchange market, 1 U.S. dollar can be exchanged for 9 Mexican pesos or for 111.23 Japanese yen. What is the cross-exchange rate between the yen and the peso; that is, how many yen would you receive for every peso exchanged??

Quadratic Equations (21 Problems)

1. Solve. 5(x - 2)2 = 3 A) B) C) D) 2. Is the following trinomial a perfect square? x2 - 2x + 1 A) Yes B) No 3. Find the constant term that should be added to make the following expression a perfect-square trinomial. x2 + 8x 4. Solve by completing the square. x2 + 4x + 3

Algebra: Various Radical Equations

*All work must be done on attached template using Equation Editor. Please follow all directions exactly.* Part 1 Explain how you solved one math problem from the CheckPoint assignment in 4 complete sentences (copy the original problem that you solve) to explain in a way that another student would be able to follow your direc

Solving Equations

Combine like terms: -3x2 + 8x - 7x2 + 9 + 2x - x2 + 11 Solve for x: 5x - 12 = 4x + 5 Solve for x: -3(4x + 3) - 2 = 7 - 2x + 3 Solve for x: (x + 3)/4 - 3/2 = (x + 4)/8 Translate to an algebra statement; do not solve: Twice the difference of seven times a number and four yields the same result as the same number i

Solving Quadratic Equations

Please see the attached file for the fully formatted problems. 1. Decide all values of b in the following equations that will give one or more real number solutions. Solve the following three quadratic equations, using what you consider to be the optimum method for each problem (factoring, square root method, etc.). Why

Geometric Sequence : Population Growth

Example of geometric sequence: population growth A population that starts at 100 and doubles in growth every eight years: The expression would give the population t years after the growth starts. I would like the information about this geometric series example (regarding the 8 years with an initial value of 100).

Quadratic Taylor Polynomial

Suppose that p(x) = 3 - 4x + x² is the quadratic Taylor polynomial approximation based at Xο (ο is a subscript for x) = 1 to a function g. Indicate whether each of the following statements must be true, cannot be true, or might be true. Justify the answers a) g(1) = 0 b) g'(1) = -4 c) g"(1) = 2 d)

Simplifying Radical Expressions

Use the properties for radicals to simplify the following expression. Assume that all variables represent positive real numbers (see attachment for equation). See attached file for full problem description.

Algebra problems: radical expression and quadratic equation

See attached file for full problem description. 1. Use property 2 to simply the following radical expression. sqrt(10/49) 2. Use the properties for radicals to simply the following expressions. Assume that all variables represent positive real numbers. sqrt(5/3), sqrt(12x^3/5) 3. simply by combining like terms: sqrt(63)

Ratio Numbers

If the ratio of a to b is equal to the ratio of b to a, what can you say about the two numbers a and b? Are they the same or different? Justify your answer by either giving a convincing argument or by giving some examples with detailed explanation.

Domain for a Function

1. State the largest possible domain for the definition of the function. f(x,y) = cube-root(y^2-x) 2.The plane 2y+4z = 5 meets the cone z^2 = 4(x^2+y^2) in a curve. Use the method of Lagrange multipliers to find the point on this curve nearest to the origin.

Simplifying and Solving Equations

1. Find the product: 6a-4(a5 + 3x2) 2. Find the product: {(-3x3)2}2(-4x4)3 3. Find the GCF (Greatest Common Factor) for the following group of polynomials: A) 7yx3, 21x3y B) (x - y), (x4 - y4), (x2 - y2) 4. Perform the indicated operation and write the result as a polynomial in the standard form: (

Basic Algebra

28 Algebra Problems Please see the attached file for the fully formatted problems. 1. Write in simplest form. 6x^7 ____ 24x^3 2. Write in simplest form. 5r^3st^2 _______

Graphing, Parabolas and Quadratic Equations

Please see the attached file for the fully formatted problems. Sample #1 Sample #2 Sample #3 Find the roots of the quadratic equation: . (If there is more than one root, separate them with commas.) Sample # 4 Solve the equation for . (If there is more than one solution, separate them with commas.)

Area of a window

A window is in the shape of a square of side s, witha semicircle of diameter s above it. Please help me unable to figure out how to write a function that express the total area of the window as a function of s

Rearranging Equations

Let ER, CR and vol be three variables. I am seeking to find an expression for ER from the following equation: See attached file for full problem description.