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Basic Algebra

Quadratic formulas to solve quadratic equations

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

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?

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.

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

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

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

Answer study guide

(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.

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: 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


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

Uncountable Basis

It can be shown that R (the set of all real numbers) is an infinite-dimensional vector space over Q (field of rationals). Is it true that any basis (by basis I mean algebraic basis or Hamel basis) of R over Q has to be uncountable ?

Z-Modules and Modules Associated with Representations

1)I understand what a standard R-module (ring-module) is, but I have heard talk of modules associated with representations. Could someone please give me some idea of what these are? 2) I am trying to find all modules over Z-the Integers; so far, I have only come up with additive groups. How can I find all others?

What is the advantage of using exponents rather than radicals?

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. What is an example of an equation easier to solve as a rational exponent rather than as a radical sign.

Finding the Discriminant in a Quadratic Equation

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. What I need to do is figure out how to create three unique equations where the discriminant is positive, zero, or negative. For each case, please explain what t

Exponential and Logarithmic Functions and Examples

1. Give an example of an exponential function. Convert this exponential function to a logarithmic function, then plot the graph of both functions. 2. Given the following values 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, x, and y, form: A linear equation in one variable A linear equation in two variables A quadratic equation A polynom

Exponential and Logarithmic Function Graphs

Referring to the graph below (which is attached), identify the graph that represents the corresponding function. I need to justify my answer. y = 2^x y = log2x (where the 2 is lower case below log, not above)then; x Also, I need to plot the graphs of the following functions and show them. f(x)=6^x f(x)=3^x - 2 f(x)