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# Basic Algebra

### Radical and rational exponent notation

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

### How do you find the solution to a quadratic equation by factoring, completing the square and using the quadratic formula?

1) Using the quadratic equation x2 - 3x + 2 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the lin

### Various Algebra Problems

Algebra Problems. See attached file for full problem description.

When using the quadratic formula to solve a quadratic equation ax2 + bx + c = 0, the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. (When the discriminate is negative, then we have the square root of a negative number. This is called an imaginary number, sqrt(-1) = i. ) Explain what the value

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

### How many milliliters of each solution should be used?

A 5% solution of a drug is to be mixed with some 15% solution and some 10% solution to get 20 ml of 8% solution. The amount of the 5% solution used must be 2 ml more than the sum of the other two solutions. How many milliliters of each solution should be used?

### Quadratic Equations and Maximum and Minimum Values

Note that x^y computes any number to any power (integer, fraction, decimal). 1)Using the quadratic equation x2 - 3x + 2 = 0, perform the following tasks: a)Solve by factoring. b)Solve by completing the square. c)Solve by using the quadratic formula. 2)For the function y = x2 - 6x + 8, perform the followi

### Algebra multiple choice questions

(See attached file for full problem description with PROPER EQUATIONS AND SYMBOLS) --- The average of the numbers 5, 9, 10, 13, and a equals 11. Find the value of a. a. 16 b. 17 c. 18 d. 20 A shirt is on sale for \$34.40, which is 20% off the original price. Find the original price of the shirt. a. \$36.40 b. \$41.28

### Algebra multiple choice questions

(See attached file for full problem description for PROPER EQUATIONS AND SYMBOLS) --- If f(x) = x(x + 3)(x ¨C 1), use interval notation to give all values of x where f(x) > 0. a. (¨C3, 1) b . (¨C3, 0) ¡È (1, ¡Þ) c . (1, 3) d . (0, 1) ¡È (3, ¡Þ) If f(x) = x(x ¨C 1)(x ¨C 4)2, use interval notation to give

### Answer to Mathematics Question: Algebra Word Problems

A designer attempts to arrange the characters of his artwork in the form of a square grid with equal numbers of rows and columns, but finds that 24 characters are left out. When he tries to add one more row and column, he finds that he has 25 too few characters. Find the number of characters used by the designer.

### Please explain in detail the steps to complete these 2 problems

16. 3logx + 2log y - log z 17. 6 log a - 3 log b - log c + 2 log d

### Properties of Logarithmic Functions

Find log7 12 (to four decimal places) See attached file for full problem description.

### Contemporary Mathematics

Any help that you could give me on these problems would be greatly appreciated. I am completely lost and the book doesn't seem to help me much. (See attached file for full problem description with diagrams) --- Instructions: ? Identify the document by typing your full name and section number next to the yellow text.

### solving quadratic equations and inequality

Solve 13) Approximately 1% of US students were studying abroad in 1994. Based on data from the Institute of International Education, the number of US students in study-abroad programs from 1994-1997 can be modeled using the equation y = 7248x + 76207, where x =0 corresponds to year 1994. Using this model, what would you expec

### Find x to 4 decimal places

Find x to 4 decimal places: 1n x - 41n 3 = 1n (5/x)

### Alcohol Solution Productions

1. A passenger train leaves the train depot 2 hours after a freight train leaves the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours. 2. Solve 3. How many liters of a 70% alcohol solution must

### Relational Algebra Expressions

Cannot use SQL - must show expression Tables in a relational database: Hotel (hotelNo, hotelName, city) Room (roomNo, hotelNo, type, price) Booking (hotelNo, guestNo, dateFrom, dateTo, roomNo) Guest (guestNo, guestName, guestAddress) A) Need to generate the relational algebra expression for the fo

### Applications of Quadratic Equations - Word Problems

1. Solve using the quadratic formula: x^2 = 2x - 10 a) Show what you use for a, b, and c. b) Show your two answers 2. Brent is flying a kite on 50 feet of string. The kite's vertical distance from Brent is 10 ft more than its horizontal distance from Brent. Find its horizontal and vertical distances from Brent. Sh

### Parabolas and Quadratic Equations: Minimizing Costs

Callaway Golf Company has determined that the daily cost C of manufacturing x Big-Bertha-type gold clubs may be expressed by the quadratic equation C(x) = 5 x 2 - 620 x + 20,000, a) How many clubs should be manufactured to minimize the cost? b) At this level of production, what is the cost per club? c) What are the fi

### College Level Algebra

1) How do I use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? b) I don't have a clue how to solve this one. Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Another difficult problem. Using the formula for the

### Linear, quadratic, rational, or exponential functions

a) Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? b) Which one of the basic functions (linear, quadratic, rational or exponential) is related to the arithmetic sequence? c) Which one of the basic functions (linear, quadratic, rational or exponential) is rel

(See attached file for full problem description) --- 1. Which property of the real numbers is illustrated by the following statement? 9 ? (7 + 11) = 9 ? 7 + 9 ? 11 A) Commutative property of multiplication B) Associative property of addition C) Associative property of multiplication D) Distributive property 2.

### Polynomial, Rational, Exponential, and Logarithmic Functions

1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Please Place Answer Here:

### Logarithms : Change of Base Formula

Most calculators have 2 different logs on them: log which is based 10, and in which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers availabe to the computer, 0 and 1. When a computer scientist needs a logarithm, he/she needs a log to base 2

### Fixed Rate and Logarithm Change of Base Formula

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P(1+r)^nt, let r= n 10%, P=1 and n=1 and give the coordinates(t,A) for the points wher

### Logarithms

Logarithms: a) Using a calculator, find log 10000 where log means log to the base of 10. b) Most calculators have 2 different logs on them: log, which is based 10, and ln, which is based e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available t

### Logarithmic functions explained in this solution

The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by A is the amount of returned. P is the principal amount initially deposited. r is the annual interest rate (expressed as a decimal). n is the compound period. t is the number

### Voting

After their star pitcher moved to another town, the eight remaining members of the company baseball team needed to select a new pitcher. They used approval voting on the four prospects, and the results are listed below. An "X" indicates an approval vote. Which pitcher is chosen if just one is to be selected? (see attached

### The possibilities of voting

(See attached files for full problem description) --- 1. Four members are running for president of the Local Math Club - Alicia (a), Brice (b), Charlie (c), and Destiny (d). The voter profile is summarized in the table. Use the Hare method to determine the winner. Number of voters Ranking 17 c > d > a > b 11