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# Basic Algebra

The most common business application involving exponents is the calculation of compound interest. Let's introduce some nomenclature. PV = present value ; the money you pay into the plan today. t = the duration of an investment program, in years. FV = future value ; that is, the money you expect to have after n years.

This SLP provides some insight into the use of quadratic formulas in business and natural science. 1.A company's costs, in millions of dollars, are given by the equation, C = x2 - 3x - 27, where x is the number of items sold, in thousands. What are the costs when 1,000 items are sold? 1,500 items? 2.A company's costs, in

Show all of your work in a Word document and submit by the end of the module. 1-4: Solve by factoring: 1. 4x2 - 25 = 0 2. x2 - 12x + 36 = 0 3. x2 + 14x + 45 = 0 4. 6x2 - x - 15 = 0 5-7: Solve by completing the square. 5. x2 - 4x + 3 = 0 6. x2 + 5x - 1 = 0 7. 2x2 + 7x - 15 = 0 8-10: Solve by using the quadratic formula:

### Simplifying indicated operations

Show all your work in a Word document and submit by the end of the Module. Perform the indicated operations and simplify. (A radical in simplest terms contains no perfect squares; do not use decimals.) 1. 2 √12+ √27 2. 4 √3+ 6√75 3. 2 √y+ √(8z) 4. (√3)( √15) 5. (√8)( √12) 6. (3√y)( -2√y) 7

### Sequences and Series of Functions

1. Write the following in expanded for then find the sum a) ^7(Sigma sign) k=0 (k=1)(k+2) b) ^7(Sigma sign) k=4 3k Note: The sigma sign does not show up when pasted here. The 7 is on top of the sigma sign and the k= 0 or k=2, respectively, lies below the sigma sign. 2. Express the following series using sigma notation: a

### Linear equations, management decisions, production scheduling, and financing

1. Solve the system of linear equations, using the Gauss-Jordan elimination method. a) 2x + 3y = 2 x + 3y = -2 x - y = 3 b) 3x - 2y = 5 -x + 3y = -4 2x - 4y = 6 c) x - 2y = 2 7x - 14y = 14 3x - 6y = 6 2. Management Decisions. The Management of Hartman Rent-A-Car has allocated \$1,008,000

### Racial Inequalities: An Analysis

See the attachments. - White households have on average 22 times the wealth of average Black households and 18 times the wealth of average Latino households - On average, more money is spent on White children than Black and other non-White children in public schools - Public schools are nearly as segregated today as the

### Reflection of a line across the line y = x

(a) Write the equation of a line that intersects the negative x-axis and the positive y-axis at points not equidistant from the origin (0, 0). (b) Draw the line. (c) Draw the line that is the reflection of your line across the line y=x. (d) Find the equation of the line drawn in Part (c). Do not convert fractions, if a

### Solving equations algebraically

Solve the following equations algebraically. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may ty sqrt 3 (x) as cuberoot (x) and shraising to the nth power as ^n, like x ^3 is typed x^3. a) t sqrt (2/3) =4 b)5 sqrt (x + 1 )= 3 c)

### Algebra: Celebrity Body Mass Index

The United States is becoming more health conscious, and as a result, the problem of obesity has gotten more attention. The Body Mass Index (BMI), relates a person's height and weight, and is often used to determine if someone is overweight. The table below tells the weight status for a given BMI. BMI Weight Status Below 18.5

### Let A and B be arbitrary n x n matrices whose entries are real numbers. (a) Use basic matrix laws only to expand (A + B)^2. Explain all steps. (b) Is (A - B)(A + B) = A^2 - B^2 ? Explain as you did in part (a).

1. Given the matrices A, B and C, compute: (a) AC + BC (It is much faster if you use the distributive law for matrices first.) (b) 2A - 3A (c) Perform the Boolean Product operation on the following zero-one matrices. Please refer to the attachment for the complete question. 2. We know that matrix algebra behaves si

### Algebra: Weighted Average

Just to be clear, please do the math for me, I do not wish to know how to find out my grade, they show me online and I still can't get it right. Based on the information provided please tell me what my grade is. DF = 35% Assignments = 35% MT = 15% F = 15%, Grades%: DF1= 100 As1= 0 DF2= 100 As2= 100 DF3= 0 A

### Exponential and Logarithmic Functions - Compound Interest

Examples of Exponential and Logarithmic Functions. Excercises to follow. Explanation: Start by writing the beginning amount into cell C1 (pink). The program automatically copies that number to cell B5 (pink), which is the beginning amount for the first period. Type the multiplier into cell C3 (blue). The program automa

### Solving by Elimination and Dependent and Inconsistant Systems

1. Solving a system by elimination. Solve each system of equations: a. 2x - y + 3z = 14 b. X + y = 2z = -5 c. 3x + y - z = 2 d. x - 3y + 2z = -11 e. 2x + 4y + 3z = -15 f. 3x - 5y - 4z = 5 2. Dependent and Inconsitent systems. Solve each system: a. 4x - 2y - 2z = 5 b. 2x - y - z = 7 c. -4x + 2y + 2z = 6 3. Paranoia

### Force diagrams, vectors and equations of motion

A parachutist and her parachute have a combined mass of 80 kg. She steps out from an aircraft travelling horizontally at 90m s−1 at a height of 300m above the ground, and falls for 5 seconds before instantaneously opening her parachute. In the free fall phase of the motion, take the origin of coordinates to be a point on the g

### Monthly interest and balance on credit cards

It's time to go shopping! You grab your Best Purchase credit card, which has an annual interest rate of 18%. The unpaid balance on your card for the current billing cycle is \$285.76. On your shopping trip, you purchase four items: a Blu-ray player, two 4-GB flash drives, and a 19-inch flat-screen television. You purchase all the

### Introductory Algebra

1. Simplify by factoring. Assume that all variables under radicals represent nonnegative numbers. √(36x^6) Answer or note that the square root is not a real number. Show all work. 2. Use the quotient rule to simplify. Provide answer using exponential notation. Show all work. -12a^5b^6c^12 / 3a^2b^3c^9 3. The amo

### Graphing Exponential Functions and Evaluating Logs

Question One: Let f(x) = 4^x, g(x) = (1/3)^x+1 and h(x) = -2^x f(-1) Question Two: Evaluate each log: #24 log8(64) ... note that the 8 is subscript Question Three: Simplify: 3^log^(5.5).

### Simultaneous Equations: Word Problems

For Halloween, Mr. Olowitz bought 8 bags of candy bars and 4 bags of lollipops for a total cost of \$51.56. Later that day he realized he didn't have enough candy and went back to the same store and bought 3 more bags of candy bars and 3 more bags of lollipops for a total cost of \$23.82. While in the store on his second trip, Mr.

### Approximating real zero, free falling object and profit

Question #1 Given f(x)=6x^4-7x^3-23x^2+14x+3, graph using a graphing tool. Use the graph to approximate each real zero as a decimal, accurate to the nearest tenth. Question #2 For a body falling freely from rest (neglecting air resistance), the distance the body falls varies directly as the square of the time. If an objec

### Algebraic Synthetic Division

See the attached file. In problems 1 through 4, write out the polynomial that has the listed factors: Example: (x), (x-1) ANS: x2-x 1. (x-2), (x+3) 2. x, (x-2), (x-1) 3. (x-2i), (x+2i) 4. x, (x-1), (x+1), (x-2) In problems 5 through 8, write the polynominal having the listed roots: 5. i 6. 2, 1,

### Simplifying exponential equations

32. Zero exponent. Simplify each expression. 5y^2z(y^-3z^-1) 38. Changing the sign of an exponent. Write each expression without negative exponents and simplify. 5^-2xy^-3 3x^-2 52. The quotient rule for exponents. Simplify each expression. 2r^-3t^-1 10r^5t^2∙t^-3 64. Use the rules of exponents to simplify eac

### measure theory: show is countable

Let {x_alpha}_[(alpha)(E)(gamma)] be an indexed collection of non-negative real numbers. The sum of this collection is defined to be the supremum of the set of all sums over finite subsets of gamma. This is The sum of_[(alpha)(E)(gamma)]x_(alpha) = sup{(the sum of)_(alpha)(E)(S)x_(alpha): S is finite subset of gamma} Prove t

### Miscellaneous algebra questions

1. Rationalize the denominator. √13 - √14 / √13 + √14 2. The maximum weight that a rectangular beam can support varies jointly as its width and the square of its height and inversely as its length. If a beam 1/4 foot wide, 1/2 foot high, and 16 feet long can support 30 tons, find how much a similar beam can sup

### Payoff and Opportunity Loss Tables

In the following payoff and opportunity loss tables circle and label the payoff or loss associated with the following decision-making criteria under uncertainty. a. maximax b. maximin c. equally likely d. minimax Payoff Table State of Nature Alternatives A

### Inequality in the criminal justice system concerning race

A discussion on inequality in the criminal justice system concerning race. Analyzed are the three videos listed below. Links: - http://www.nytimes.com/video/2012/06/12/opinion/100000001601732/the-scars-of-stop-and-frisk.html - http://abcnews.go.com/video/playerIndex?id=6953414 - http://www.youtube.com/watch?v=VQHdbW36XjE

### Divisibility property in mathematics

One of the most often misunderstood concepts in math is divisibility. Divisibility is a different operation than division and the two are often confused. The solution describes the seven key properties of divisibility and proves them mathematically to show the reader that they are true and why they are important. The seven

### Mathematics: Fundamental Algebra and Graphing

1. The cost, c, in dollars of a car rental is 10 + , where m is the number of miles driven. Graph the equation and use the graph to estimate the cost of car rental if the number of miles driven is 34. A) About 24 dollars B) About 15 dollars C) About 36.5 dollars D) About 19 dollars 2. Graph the two lines x + 2y

### Explanation of Mathematical Expressions Using Examples

I am confused with the concept of mathematical expressions. How can I tell when a collection of operations and numbers is an expression? Is "234x + - ÷ 14 - 23 46 -" an expression? Can you help me understand this concept? Thanks

### Applying Algebraic Formulas

1. Against the wind small plane 858 miles in 2 hours an 10 min. Return trip took 1 hr. and 50 min. What was the speed of the wind? What was the speed of the plane in still air? 2. A basketball scored 12 times during 1 game. He scored a total of 19 points, 2 for each 2 point shot, and 1 for each free throw. How many 2 pt.