### 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.

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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.

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:

#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

Simplify. (m^6)^9 Simplify. (y^6/z^6)^9 See attached file for full problem description.

1. Give an example of a single polynomial with degree 3, whose value is 4 when the variable is equal to 1. 2. Give an example of a single polynomial with degree 3, whose value is 29 when the variable is equal to 2. 3. Find a polynomial with degree 3 whose values are 4 and 29 when the variable is equal to 1 and 2, respectiv

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

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

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??

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

*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

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

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

Find the Taylor polynomial of order 3 for f(x) = sin x, centered at Xο = pi/2 (Xο ο is a subscript)

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).

The equation 6x^4 - 25x^3 + 32x^2 + 3x - 10 has two real roots of -1/2 and 2/3. By algebraic division and solving a quadratic equation, find the other two roots. See attached file for full problem description.

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)

Two nonnegative numbers multiply to 10. How small can their sum be?

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.

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)

6 less than 8 times a whole number is 2 more 4 times that number.

3(x-2)-6x=15 simplify as much as possible -7(x+7)= -5x-9+5(-8x-6)=

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.

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.

See attached file for full problem description.

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: (

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 _______

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.)

Sin q/cos q+ cos q/ sin q= sin(a+b) cos b -cos (a+b) sin b

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

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.