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Basic Algebra

15 Algebra Problems : Find Equation for Line; Describe Graph and Slope

Please see the attached file for the fully formatted problems. Q1. Solve {see attachment} Q2. Solve 9 - 7+15/5 - (6-3)4 Q3. Solve {see attachment} Q4. Find the equation for the line with slope 3/5 and passing through the point (4, 2). Q5. Solve |2x-5| >= 14 Q6. A store issued coupons worth 20% off from any pu

10 Algebra Questions

1. The width of a rectangle is 8 feet less than the length. If the area is 20 square feet, find the length and the width. 2. Solve the equation: x(x - 4) = 12 3. A boat travels 30 miles upstream against the current in the same amount of time it takes to travel 42 miles downstream with the current. If the rate

Perfect square/cube/fifth power

INSTRUCTIONS TO OTA 1. typeset solutions 2. send solution as attachment 3. Use words to explain solutions. DO NOT RELY ONLY ON ALGEBRAIC MANIPULATIONS/ OR SYMBOLS. Find the smallest positive integer N such that N/2 is a perfect square, N/3 is a perfect cube and N/5 is a perfect fifth power.

Lowest Common Multiple (Prime Factorizations)

Let a and b be integers. A common multiple of a and b is an integer n for which a|n and b|n. We call an integer m the least common multiple of n provided (1) m is positive, (2) m is a common multiple of a and b, and (3) if n is any other positive common multiple of a and b, then n [greater than or equal to] m. The notation fo

Partial Induction Proof of Cauchy's Integral Formula

See attached file...it is a full induction proof of Cauchy Integral Formula, with the base case step missing. All I have to do is show that it holds for "n=1", using the rest of the proof as an example...however i am having trouble showing it.

Wireless Communication Problem Set

1. When the FCC conducted the original A and B block PCS auction, what were the companies that won the license for Cleveland Ohio? What is the MTA number for Cleveland? How many pops were covered by the license? 2. Who was the winner original high bidder(s) for the D-Block auction for Houston BTA? What was the BTA number? Wh

21 Algebra Problems : Factoring, GCF and Word Problems

SHOW ALL STEPS WITH SOLUTION. FACTOR OUT THE GCF IN EACH EXPRESSION. 1. 12X^4T + 30X^3T - 24X^2T^2 2. 15X^2Y^2 - 9XY^2 + 6X^2Y FACTOR EACH POLYNOMIAL 1. 3X^2 + 6X + 3 2. X^3 + X^2 - X - 1 3. 3A - 3B - XA + XB FACTOR OUT EACH POLYNOMIAL AND FACTOR OUT THE GCF 1. H^2 - 9HS + 9S^2 2

Finance : McDonalds Stock and Trend Lines

Please see the attached file for the fully formatted problems. 1. Pick your favorite financial site on the web 2. Go there and get the stock price for McDonalds for the first trading day in March and April of this year 3. Develop a trend line slope (change in dollars per month) 4. Check the stock price for the first trad

Lagrangian multiplier

Use Lagrangian multipliers to find the points on the ellipse with the equation x^2+xy+y^2=3 that are closest to and farthest from the origin

10 Algebra Problems : Simplifying and Binomials

Please see the attached file for the fully formatted problems. For questions 1 through 4, simplify the expressions. 1. 9 - (- 2) + (3 - 4) 2. - 2/3 - ½ 3. - 8 ÷ 4?3 4. - 8 ÷ (4?3) 5. Evaluate the expression - 6(x + 3) for x = 2 6. Look at this expression: 12x³y + 3x²y² + xy³. Is this a binomial? Of what

Growth rate

A bacteria culture starts with 760 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1520 bacteria. Express the population after t hours as a function of t.

Induction Proof: Strings of Digits

If n >= 1, the number of strings using the digits 0,1, and 2 with no two consecutive places holding the same digit, is 3x2^n-1. For example, there are 12 such strings of length three: 010, 012, 020, 021, 101, 102, 120, 121, 201, 202, 210, and 212. Prove this claim by induction on the length of the strings. Is the formula tr

A system of two springs in series and parallel.

Prove that when two springs are attached one at the end of the other, the coefficient of the final spring becomes 1 / (1/k1 + 1/k2 ) where k1 and k2 are the coefficient of the two individual springs. Then consider two systems of springs, one in which a mass m is attached two the end of two springs which a

Algebraic Identities into Geometrical representations

Draw and describe how each of the following algebraic identities could be represented geometrically: a) (a-b)^2 = a^2 - 2ab + b^2 b) a(b+c)=ab + ac c) (a+b)(c+d)=ac+bc+ad+bd Please use illustrations of each with an explanation of the illustration so I can understand the process used to complete this type of problem. THA

College Algebra

Hello, Can you please show me how to do this problem and how it would look graphed? Thanks x +3y = 6

Are the equations independent, dependent, or inconsistent?

1. Perimeter of a rectangle. the length of a rectangular swimming pool is 15 feet longer than the width. if the perimeter is 82 feet, then what are the length i width. 2.Household income. Alkena and Hsu together earn $84,326 per year. if Alkena earns $12,468 more per year than Hsu, then how much does each of them earn per y

Prove that there is no bijection between any set A and its power set P(A) of A.

There is no bijection between any set A and its power set P(A) of A. For finite sets, proof is trivial since |A| = n and |P(A)| = 2^n. For finite sets, this is done by contradiction. Suppose there is a bijection $ between a set A and its power set P(A). Consider the set B={x|x is a member A where x is not a member $(x)}For e

Prove same cardinality

Prove that Rsquared has the same cardinality of R (hint: think of shuffling two string of digits) See attachment for full question

Integer problems

Suppose that integers 1,2,3,4,5,6,7,8,9,10 are arranged randomly along a circle. 1) show that For each circular arrangement, there exists at least three adjacent numbers whose sum is greater than 17 2) take n + 1 integers from {1,2,3,....., 2n}. Show there exist two integers, one divides the other completely.

Several problems in basic algebra

Please include answer and steps to solve problem and explain if needed. 1) What is 10^-1 + 10^0 + 10^1? 2) 16 is 20% of.... 3) If f(x) = x^2 + 1, then 2f(x) = ? 4) If f(x) = x^2 + 1, then f(2x) = ? 5) If f(x) = x^2 + 1, then f(y) = ? 6) If 2x + y = 3, and x - y =3, what is x? 7) If 2x + y = 3, and x

Analytic Functions for Zeros

Please see the attachment Using the Pythagorean theorem (see attached) and knowing the sinz and cosz are analytic functions. What can we say about (see attached) Show that cos(A+B)=cosAcosB-sinAsinB using exponential expressions for sin and cos What are the zeros of

Various Algebra problems and equations

See Attached for details and questions Problem 8 Find the LCD and perform the following operation: Problem 9 For the following parabola find (you are not required to plot this solution): (1) maximum value (2) the vertex (3) the x -intercepts (4) y-intercept (5) the domain (6) the range Problem 10 Solve the t

Various Algebra Questions

Simplify the following expression (avoid negative exponents in the final answer): See Lecture 1 and Lecture 5 for an optional procedure *see attached for equations* Simplify the following expression (avoid negative exponents in the final answer): See Lecture 1 and Lecture 5 for an optional procedure. *see attached for equa

Question about Uniform motion

The fundamental formula for such problems is where d represents the distance covered when moving at a speed s during a length of time t. This formula can be solved for s or t (if d is in miles and t is in hours, then s has the units of miles/hour) Smith bicycled 45 miles going east from Durango, and Jones bicycled 7

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,......

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