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# Basic Algebra

### Two different forms of solutions of Linear Diophantine Equation ax + by = c

If (xo,yo) is a solution of the Linear Diophantine equation ax + by = c , then the set of solutions of the equation consists of all integer pairs (x,y), where either x = xo + tb/d and y = yo - ta/d ( t = ........,-2,-1,0,1,2,........) or , x = xo - tb/d and y = yo + ta/d ( t = .........,-2,-1,0,1,2,......

### Integer Multiples Explained

Express and explain -15.6x10^-20 as an integer multiple of 2.3x10^-20

### Solving a Basic Algebra Word Problem

Sally received a bill for a total of 8 hours labor on the repair of her bulldozer. She paid \$50 to the master mechanic and \$90 to his apprentice. If the master mechanic gets \$10 more per hour than his apprentice does, write the following: ?Expression for wages in \$/hr by the master mechanic ?Expression for wages in \$/hr

### Algebra Word Problem

A taste test with 200 randomly selected people found that only three of them said that they would buy a box of new Sweet Wheats cereal. How many boxes could the manufacturer expect to sell in a country of 280 million people? Question also in attachment

### Algebra equation (extraneous solutions)

Solve the equation below (watch for extraneous solutions). See attached for equation

### Sum

What is the sum of 1,605+1,219+1,153

### Diverse algebra questions

Could I please get step-by-step solutions to these problems to help me understand? I have attached a pdf file and a word file, they have the same questions. Thank you very much (rewrite using only positive exponents, calculate equations, simplify, Pythagorean Theorem,Graph the inequality,Rationalize the denominator, Solve by

### Solving for a Variable Equation

See Attached for equation

### Solving Algebraic Equations

Solve for R See Attached for equation

### Equations with rational expressions

Equations with rational expressions See Attached for Equation

### Factoring Quadratic Equations Solving for x

Solve for X See Attached for equation -2x^2 - 2x + 24 = 0 Pg. 313 # 48 Solve for x Section 6.6/Quadratic equations by factoring Reference: Examples 4 and 5 Check The original equation

Solve for T See Attached for equation

### Solve by completing the square

Solve by completing the square See attached for equation

### Solving equations with radicals and exponents

Solving equations with radicals and exponents. (square root 2x^2 - 3x - 10) = x

### Sales Revenue Linear Equations

Sale managers normally want to increase revenue R by selling more. For example, a manager may know by experience that revenue R will increase or decrease according to the following mathematical linear model for a a sales price P and quantity sold Q of a certain commodity: P=Po +-px [This represents a linear equation with posi

### Algebra Word Problem

Smith bicycled 45 miles going east from Durango, and Jones bicycled 70 miles. Jones averaged 5 miles per hour more than Smith, and his trip took one-half hour (1/2 hr) longer tan Smith's. ? Write an expression for Jones' speed in terms of Smith's speed ? Write an expression for Smith's speed ? Write an expression for the

### Polynomial Equations Functions

See attached equations

### Rational expression...

Find the LCD for the expressions below and convert each rational expression into an equivalent rational expression with the LCD as the denominator. -3/ (2 p2 + 7p -15) p/ (2 p2 - 11p +12) 2/ (p2 + p -20) (See expression in Attachment)

### Word problems: Variable expressions

If Carrie walked 40 miles in x hours, then how fast did she walk? If 9 pounds of pears cost x dollars, then what is the price per pound? If Ramon can mow the lawn in x-3 hours, then how much of the lawn does he mow per hour? (Question also in attachment).

### Volume of a cube

A cubic shipping container had a volume of a3 cubic meters. The height was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container now is a3+2a2-3a cubic meters. By how many meters were the height and width changed. Note: Appendix A gives the formula for

### See Attachment

Problem 1 Use grouping to factor the following polynomial completely. x^3 + ax + 3a + 3x^2 Note: Factoring means to express a polynomial or a number as a product of its factors (in the case of polynomials, the factors are prime polynomials).

### Shared Work Entire Driveway

After a heavy snowfall, Brian can shovel the entire driveway in 30 minutes. If his younger brother Allen helps, the job takes only 20 minutes. If we let x represent the time for Allen to clear the entire driveway by himself, write an expression for the following: ? Rate of work (job/minute=1 driveway/minute) by Brian ? Rate of

### Polynomial Denominators - Reduce to Lowest Terms

Reduce each answer to lowest terms (See Attached for question)

### Reduce to Lowest Terms; LCD

Perform the indicated operation. Reduce each answer to lowest terms (see attachment)

### 10 Beginner Algebra Questions

1. Solve by factoring: 2x^2 + 5x = 3 3. Solve by using the square root property: 3x^2 = 16 6. Solve by completing the square: 2x^2 - 3x - 4 = 0 7. Solve using the quadratic equation: 2x^2 - 3x - 4 = 0 (See attachment for all questions)

### Finding Lowest Common Denominator (LCD) for Rational Expression

Find the LCD for the given rational expression, and convert the rational expression into an equivalent rational expression with the LCD as the denominator. *(Please see attachment for expression)

### Factoring Polynomials and Primes

Factor the polynomial below, if prime say so. Section 6.5 Reference: Examples 3 and 4 Factor each polynomial completely. If a polynomial is prime say so. Note: See page 303 "Factoring a Difference or Sum of Two Cubes" to factor (m3+n3). This is a good example of factoring by long division and leads to the formula below

### Factoring Polynomials Completely

See Attached Section 6.4 Reference: Examples 4 and 5 Factor each polynomial completely

Factor 9w-w^3