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# Basic Algebra

### Factor the following expression completely

1. Factor the following expression completely 36x3 - 16x 2. Andrew factored the expression 28x^3-6x^2-10x as 2x(14x^3-3x^2-5x). But when Melissa applied the distributive law and multiplied out 2x(14x^3-3x^2-5x), she got 28x^4-6x^3-10x^2 ; thus, Andrew's solution does not appear to check. Why is that? Please help Andrew to

### Perimeter Algebra and Quadratic Equations

1.) A gardener wants to create a triangular garden in the shape of a right triangle with shortest side length x - 2y ft. and the middle length side x + 4y ft. What is an algebraic expression for the area of the garden? Be sure to multiply this out and express in simplest correct mathematical form, including units. 2.) Find th

### Determining if variables are directly proportional

For each of the relationships described below, determine if the variables are directly proportional. Write a sentence or two for each to justify your answers. a.) Total number of words a typist can type and the number of minutes spent typing if he or she types 72 words per minute. b.) The temperature of an asphalt road at

### Mathematics and the Medieval Era

What are some key people and developments in regards to mathematics during the Medieval era?

### Finding the Price of the Call Option by the Black-Scholes

Parameters Strike price = \$120; Expiration time = 1 year; Annual interest rate = 0.05; Stock volatility = 0.35. For the initial stock price, S0 = 100.45 Requirements 1. Find the price of the call option by the Black-Scholes formula rounded to the nearest cent.

### Algebra Problems Term Coefficient

1. List the terms, coefficients, and degree of the following polynomial: -4x3 + 6x2 - 5x + 1/3 2. Write all of the following statement(s) that apply to the following polynomial: -8x + 2x2 - 3 It is a binomial. It can be evaluated at x = 1/3 It has a coefficient of 8. It is quadratic.

### Example Algebra Problems

1. Short Answer. Add the following: (-2.5x2 + 9x - 7.9) + (3.3x2 - 1.9x + 1.9) 2. Essay question: show all work. Find the difference: (-7x2 + 5x - 9) - (2x2 + 7x + 5) 3. Find the product: -9x(4x2 - 2x + 1)

### Equation for Electricity Bill in One Month

A household electricity bill for one month in which 2,494 kWh (kilowatt per hour) were used includes, among other charges, a distribution charge. The bill reads: Current Charges Charges for - UTILITIES Residential Rate: RS for Jun 9 - Jul 12 Distribution Charge: Customer Charge

### Math Problems

1. Sketch a graph of the following equations a. b. y = |x| + 2 c. 2. Find the equation (in the form ) of a line through points (1, 7) and (-3,2) 3. The relationship between air temperature T (in ?F) and altitude h (in feet above seal level) is approximately linear up to an altitude of 20,000 feet. If th

### Algebra Solutions: Solve using the Addition Principle

1. Solve using the addition principle. m - 3 = 5 A) 2 B) -2 C) 8 D) -8 2. Solve using the addition principle. s + 5 = 8 A) -3 B) 13 C) 3 D) -13 3. Solve using the addition principle. x - = 0 A) - 9 B) 9 C) D) - 4. Solve using the addition principle. 8 = z + 3 A) -11 B) 11 C) 5 D) -5

### Proving or Disproving Claims

Please see the attached file for the complete problem description. Note: a) and b) are independent; for each of them it should be separately decided if that combination is an ideal and for the first point of the question all ideals are in Z[sqrt(-5)].

### Simplifying an Algebraic Expression Involving Indices

Raise the quantity in parentheses to the indicated exponent, and simplify the resulting expression. Express answers with positive exponents. 1. ( x^-2 y^-1 / 2x^0 y^3 )^3 2. ( 24y^-1 / 72x^-3 y^4)^2

### Finding the Number of Motor Vehicle Deaths

The number of motor vehicles deaths increased by 13.75 times from 1912 to 2003. There were 39,525 more deaths in 2003 than in 1912. Find the number of motor vehicle deaths in each of the two years. Note that the number of motor vehicles on the road increased from 1 million to 230 million between 1912 and 2003.

### Algebra Problems Simplification

Simplify the following expression. square root of negative 8 square root of negative 24 Simplify the following expression; express in terms of i. square root of negative 48 Simplify the following quotient of complex numbers into the form a + bi. negative 8 minus 8i over 1 plus 2i

### Annual profit functions

Annual profit in thousands of dollars is given by the function, P(x) =5000 -(1000/(x -1)), where x is the number of items sold in thousands, x > 1. I need to find out how to come up with this solution? Find the profit for 5 different values of x. P(x) = 5000 - (1000/(x-1) P(2) = 5000 - (1000/1) = 4000 P(3) = 5000 - (1000/2)

### Proof about integers and rationals

let x,y,z,w be rational numbers a) Let epsilon>0. If x is epsilon-close to y, then y is epsilon-close to x. b) Let epsilon, gamma >0. If x is epsilon-close to y, and y is gamma-close to z, then x and z are (epsilon + gamma)-close. c) Let epsilon>0. If y and z are both epsilon close to x, and w is between y and z (i.e..

### Find x value in quartic equation

To solve the quartic equation, one of the approaches is to seek squares on both sides. For example, to find x, in ax^4+bx^2+cx=d. One way is to convert the equation to the following format: (square root of a x^2+e)^2=(gx+h)^2. However, when a, e, g and b becomes irrational number, it is difficult to apply this strategy. Here, I

### Asymptotic Behaviors of Various Functions

1) Determine the order of the following expressions as ??0: ?(?(1-?) ), (4?)^2 ?, 1000?^(1?2), ln?(1+?), (1-cos??)/(1+cos?? ), ?^(3?2)/(1+sin?? ), ?^(3?2)/(1-cos?? ), sech ^(-1) ?, exp?(tan?? ), ln[1+(ln?(1+2?))/(1-2?)], ln[1+(1+2?)/(?(1-2?))], ?_0^? exp?(-s^2)ds. 2) Arrange the following in descending order for ??0.

### Word problem

A girl is celebrating her seventh birthday. Each guest is served one large slice of chocolate cake, a hamburger, French fries, and some oranges. Identify the food groups mentioned above. If one slice of chocolate cake contains 35g of carbohydrate, 15g of fat and 5g of protein, calculate the kilocalories that each slice

### Step-by-Step Solutions: Systems of Equations

Solve the system of equation x + 3y= 32 -3x +2y =8 Solve the system of equation x +y =6 x-y= -7

### Scale factor after dilation

find the scale factor after a dilation centered at the origin if H(4*square root of 2, -3 square root of 5), P (-2 * square root of 2, 2 * square root of 5) and H(square root of 128, - square root of 180) P(- square root of 32, square root of 80)

### Congruent Modulo m

Please submit solution as a PDF or MS Word file. Prove proposition 4. Proposition 4: If m?2 is a fixed integer and a,b,c?Z then: (1) a?a mod m (2) If a?b mod m then b?a mod m (3) If a?b mod m and b?c mod m, then a?c mod m Much thanks!

### How to calculate net income

Company reports the following operating results for the month of August: Sales \$350,000 (units 5,000); variable costs \$210,000; and fixed costs \$90,000. Management is considering the following independent courses of action to increase net income. 1. Increase selling price by 10% with no change in total variable costs. 2. R

### Quadratics, Definitions of Functions, Relationships Between Exponents & Logarithms, Inverse Functions.

Write a word problem involving a quadratic function. How would you explain the steps in finding the solution to someone? Is the compound interest formula (such as would be used to calculate a car loan) an example of a function? If yes, of what type of function is it an example? Why might you identify it with that type of func

### find sides of right triagle when you know hypoteneuse

see attached file. Find a, b and h. know hypotenuese is square root of 3 plus square rrot of 12

### Two Proofs for a Modern Algebra Class

Please help me learn how to write these two proofs correctly for my Modern Algebra class. Please submit all work as either a PDF or MS Word file. ** Please see the attached file for the complete problem description **

### Samples of Basic Algebra

1. If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4 marbles can be drawn? 2. Seven workers decide to send a delegation of 2 to their supervisor to discuss their grievances. a. How many different delegations are possible? b. If it is decided that a certain employe

### Concept Checks for Binomial Coefficients

1. Determine the binomial coefficient for the fifth term in the expansion of (x+y)^9 Write the binomial expansion for each expression: 1. (a-b)^7 Write the indicated term of each binomial expansion: 1. Twelfth term of (2x+y^2)^16

### Slopes, Lines and Graphs

An airplane climbs from sea level to a cruising altitude of 31,500 feet at a rate of 6300 ft/min. After cruising for 20 minutes, the airplane begins its descent at a rate of 3500 ft/min. If we were to sketch a graph of the airplane's flight pattern, which measurement would the x-axis represent? Which measurement would the y-axis

### Properties of Logarithms and Simplification of Expressions

Use the properties of logarithms to rewrite each expression. Simplify the result if possible. 1. log2 ((2*square root 3)/5) Given log10 (2) = 0.3010 and log10 (3) = 0.4771, find each logarithm without using a calculator. 2. log10 (20/27)