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# Basic Algebra

### 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

### Factoring Out the Greatest Common factor

Given the following equation (see attachment), please factor our the greatest common factor.

### Solve Equations Variables

F= mv^2 for r - r 1= 1+1 for r - r r1 r2 V=4r2 h for h - 3 Can you please help and give a detail explanation on to solve these equations with a step by step process, please ,, Thank You,, Rudy

### Logarithmic Equations for Price Demands

5 log10 (x-2)=11 & 8^-2^-x=431 p=5000(1-4/4+e-0.002x) Find the demand for a price of (a) p=600 and (b) p=400

### Mathematical Induction Proof

A.) Use the Principle of Mathematical Induction to prove that n3 > n2 + 3 for all n &#8805; 2. b.) Use mathematical induction to prove that every amount of postage of six cents or more can be formed using 3-cent and 4-cent stamps.

### Samples and population

(1). Voting,,,If 220 out of 500 voters surveyed said that they would vote for the incumbent, then how many votes could the incumbent expect out of the 400,000 voters in the state? (2). Miles and Hours,,, If Alonzo travels 230 miles in 3 hours, then how many miles does he travel in 7-hours? (3). Bear Population,,,To

### Motion Problem

If Sergio drove 300 miles (m) at (x+10) miles per hour(m/hr), the how many hours did he drive? Use the formula for "t" given above.

### Sales Revenue Polynomials

A department store sells 20 portable stereos per week at \$80 each. The manager believes that for each decrease of \$5 in the price, 6 more stereos will be sold. Show the price P by means of a polynomial. Show the quantity Q by means of a polynomial.

### Division of Polynomials

(2u^3 - 13u^2 - 8u + 7)/(u-7)

### Negative Exponents and Scientific Notation

Please use scientific notation to reduce the following fraction ((3.5x10^-8)(4.4x10^-4))/(2.43x10^45)

See Attached

### Division Of Polynomials

Simplify: [(4*h^5*k)-(6*h^2*k^2)]/(-2*h^2*k)

### Multiplication of Binominals

Multiplication of Binomials: - Use FOIL - Use distributive property *Please see attachment for expression

### Simplify / Reduce the Expression (Radicals)

Simplify the following expression: (see attachment) Hint: The first step is to make the radical a perfect cube (so that exponent equals index) so as to eliminate the radical from the denominator. Note: A radical expression of index n is in simplified form if it has: ? no perfect nth powers as factors of the radicand ?

### Law of Exponents (CD; Annual Rate of Return)

Ronnie invested P dollars in a 2-year CD with an annual rate of return of r. After the CD rolled over two times, its value was P((1+r)2)3. Which law of exponents can be used to simplify the expression? Simplify the expression.

### Evaluate: Travel Time

Question: After leaving moose jaw, Hanson drove 200 kilometers at x km/hr and then decreased his speed by 20 km/hr and drove 240 additional kilometers. Make a table by writing a rational expression for his total traveling time. Evaluate the expression for x=100.