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# Basic Algebra

### Simplifying Expressions

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

### Difference of Two Squares and the Square of a Binomial

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

### Algebra - Government Voting Example

A bill is sent to the President of the United States when it has passed both houses of Congress. A majority vote in both the House of Representatives (435 members) and the Senate (100 members) is needed for the bill to passed on the President. The majority vote is a majority of the members presents, as long as more than one-half

### Inequalities

How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation and put an inequality sign in its place, is there ever a time when the same value will be a solution to both the equation and inequality?

### 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??

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

### Simple C Code

What are the values of sum1 and sum2? Let the function fun be defined as int fun(int *k) { *k += 4; return 3 * (*k) - 1; } Suppose fun is used in a program as follows void main() { int I = 10, j = 10, sum1, sum2; sum1 = (I / 2) + fun(&i); sum2 - fun(&j) + (j / 2); } What are the values of sum1 and

*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

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

### Inequalities Word Problem

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

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: (

### Logarithms : Earthquakes and the Richter Scale

The intensity level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weakest possible tremor. What is the formula for measuring earthquakes? Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in you

### 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 _______

### Logarithmic Functions

Logarithms: a) Using a calculator, find log 1000 where log means log to the base of 10. b) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to t

### Various Algebra Problems

*ALL WORK MUST BE DONE ON ATTACHED TEMPLATE* Part 2: Section 5.1 pp. 427-429 Exercises 18,24,36,50 5.2 pp. 434-436 18,34,48 5.3 pp. 441-442 16,24,36,44 5.4 pp. 454-455 54,58,62,74 Part 1: Explain how you solved one ma

### 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

### Exponential Functions : Population Growth

Human populations can be modeled using an exponential growth function. Use the Library for research or other resources to find the following: current world population current U.S. population current growth rate of the world population current growth rate of the U.S. population Starting in the current year, determine th

### FOIL, Inequalities with Absolute Values and Factoring

Please see the attached file for the fully formatted problems. 9. Simplify using FOIL Solve the inequalities 3. |x - 4| < 5 A -1 > x > 5 B -5 < x< 5 D x > 9 E -1 < x < 9 F -4 > x > 4 4. |x - 2| > = 3 B -1 > x > 5 C x > 3 D x < -1 or x > 5 E x < 2 or x > 3

### Basic Algebra

30 Problems Please see the attached file for the fully formatted problems.

### Exponential and Logarithmic Functions : Effect of Doubling

With the exponential function e^x and logarithmic function log x how do I graphically show the effect if x is doubled? I need to also calculated the values for e^x and e^(2x) and plotted the values of e^x and e^(2x) then I need to also calculated the values for log x and log 2x and plotted the values of log x and log 2x .

### Finding the Surface Area of a Cube

Surface area of a cube. The formula A = 6V^-2/3(-2/3 power) gives the surface area of a cube in the volume V. What is the volume of a cube with a surface area 12 square feet? In addition please include the steps to solve for V if at all possible.

### Factoring

Please solve the attached 10 algebra practice problems attached.

### Selling Stocks and Retaining Portfolio Ratio

You own 1000 shares of Robotica Galactica (RG) at \$39.00 per share. You also own 500 shares of Algebraic Flavors and Fragrance International (AFFI) at \$100 per share. You would like to liquidate a part of your holdings to generate about \$40,000 in cash for an emergency use. How would you sell your stock so that in your portfolio

### Solve the attached 6 practice problems

Pg. 317 Factor out the GCF in the equation: #66. 15x^2 y^2 - 9xy^2 + 6x^2 y Pg. 324. Use grouping to factor the polynomial completely: # 78. x^3 + ax + 3a + 3x^2 Pg. 332. Area of a sail. A triangular sail has an area of x^2 + 5x +6 square meters and a height of x + 3 meters. Find the length of the sail's base. Area

### Modeling data with polynomial functions and rational functions

(1) Create a set of data that can be modeled as a polynomial function. Please provide a reference to the data. Plot the data using Microsoft Excel including the equation for the fit. Discuss how closely the data seem to match to the best fit line. (2) Do the same for data that can be modeled using a rational function. Includ