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Basic Algebra

Real-Life Models of Logarithmic Functions.

Many different kinds of data can be modeled or measured easily using exponential and logarithmic functions. For example, consider ideal gases: Pressure versus volume give a curved plot, but a log graph of pressure versus volume provides a linear plot that is easier to interpret. Log plots are also used in the study of the rates

Factoring

8) 9x^3 - x 9) 16x^2 - 40x + 25 10) 2y^3 - 16 11) x^4 + 125x 12) 9x^5 - 18x^4 13) z^4 - 16 14) x^3 - 27 15) Solve: 25x^2 - 64 = 0

Factoring

1) 12x^3 + 16x^2 - 400x 2) x^3 + 3x^2 + 2x + 6 3) x^2 - 3x + 2 4) 3x^2 + 6x - 24 5) 4x^2 + 4x -15 6) 8x^2 + 8x - 6 7) 12y^3 + 28y^2 + 8y

Exponential and Logarithmic Functions

Please see the attached file for the fully formatted problems. 1. Convert the following equations into logarithmic form: a. 9 = 4x b. 3 = 6y c. 5 = 7y d. X = 9y 2. Convert the following equations into exponential form: a. X = log3 6 b. -5 = log3 y c. X = log4 y d. 1000 = log5 Z

Simplifying and Factoring Expressions

1. Simplify. 2. Write in descending-exponent form, and give the degree. x5 + 9x7 - 1 3. Find the value of the polynomial 6x - 1 when x = 3 and when x = -3. 4. Simplify. Write your answer with only positive exponents. m2m-10 5. Subtract 2x - 3x2 + 5x3 from 5x3 + 4x - x2. 6. Multiply. 3x

Write each fraction in simplest form.

Please complete the following 15 equations and make sure to show ALL WORK! Thanks in advance! Please complete the following and make sure to show ALL WORK! Section 5.1 Write each fraction in simplest form. 18. 24. 36. 50. Geometry. The volume of the box is represented by . Find the polynomial that represents the ar

Factoring

1) Factor 16x^2 - 25 2) Factor 15x^6 - 9x^5 + 12x^4 + 9x^3 3) Factor 8x^3 + 64 4) Factor x^2y^2 + 11x^2y + 24x^2 5) Factor 3x^2 - 18x - 48

Factoring Polynomials

Factoring the Difference or Sum of Two Cubes A. Factor each polynomial completely, given that the binomial following it is a factor of the polynomial. B. Factor each polynomial completely. C. Factor each polynomial completely, if prime say so. D. Factor each polynomial completely, if prime say so. E. Decreasing cube. Eac

Simplifying Expressions

Please give detailed explanation. Please see attached file for full problem description. Simplify. cos ( /2 - x) (csc x - sin x)

Simplify trig expression

Please give detailed explanation. Please see attached file for full problem description. Simplify sin2x( 1 + cot2 x) A). sin2x - tan2x B).

Factoring Polynomials

57 Factor each polynomial. If the polynomial is prime, say so. 67 Factor each polynomial. 105 Factor each polynomial completely. If prime say so. 109 Use factoring to solve problem. Area of a sail. A triangular sail has an area of sq. meters and a height of x + 3 meters. Find the lengt

Factoring Polynomials

11) 6x³+4x²-10x 12) 15x^5-2x^4-x³ 13) 49y^4-25 14) x^14 - y^4 15) x²+4 16) 72-2y² 17) x²+16xy+64y² 18) 25x³-10x^2+x

Factoring and Common Factors

Please see the attached file for the fully formatted problems. Factoring and Common Factors 39. 67. 93. The area of a painting. A rectangular painting with a width of x centimeters has an area of square centimeters. Find a binomial that represents the length. Area = 95. Amount of inve

Simplifying Expressions

How do you: 1) Simplify (13x^4 - 3x^3 + 2x^2) - (4x^5 - 6x^4 + 5x^3 + 2x^2 - 4x^0) 2) Simplify 5x^3(4x^2 - 11x) 3) Simplify (3y - 2)(4y^2 + 3y -5) 4) Simplify (3x - 5)(2x +1) 5) Simplify (x^2 + 4)(x^2 - 5) 6) Evaluate 2x^3y - 5xy^2 +5xy + 3y - 4 for x = -2 & y = +3 7)

Simplifying Expressions

1) Simplify (7x^3y^2 + 4x^2y^2 - 5xy^2) - (2x^3y^2 - 3x^2y^2 + 3xy^2) 2) Simplify (6^-2x^3y^-4)2 divided by 2^-4x^3y^-4 3) Simplify (4u -5v)^2 4) Simplify 2 X 10^7 divided by 5 X 10^-2 and how do you write in Scientific notation? 5) Evaluate: a) SR (8/81) b) -(25

Calculating Exponents

Solve the problem. Express the answer in scientific notation to two decimals unless requested otherwise. ( Please show work.) 1. If the speed of lights is 3.00x 10 to the power of 8 m/sec, how long does it take light to travel 2.29x 10 to the power of 11 m, the distance from the sun to Mars? Round to one decimal place. 2.

Algebra Word Problems

If twice the sum of a number plus three is decreased by - 2, the result is 10. Find the number.