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# Algebra

### the solution set solved

(x+7)(x-11)(x+5)>0 A. The solution set is {x| }. (Use at least one inequality or compound inequality to express your answer.) B. The solution is all real numbers. C. There is no solution.

### Find all solutions of x^16 = 1 Mod 19

Solve the equation x^6 = 1 in F_19. Do not use brute force. I know I can just substitute in x=0 ... x=18, but rather than doing that, I would like to know a more clever method so I can solve such equations easily in general.

### Square size

Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?

### Decide how you would prefer to commute to work each day.

Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in days, is graphed on a rectangular coordinate system where time is on the horizontal axis. Further suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C=p*a^t where p is the number of cars on the roa

### Solve the equations for the different bicycle models that can be made daily, with any of the techniques - graphing, substitution, elimination, and matrix.

As a business owner, there are many decisions that you need to make on a daily basis, such as ensuring you reach the highest production levels possible with your company's products. Your company produces two models of bicycles: Model A and Model B. Model A takes 2 hours to assemble. Model B takes 3 hours to assemble. Model

### How many solutions can be created from a specific amount of numbers/characters/digits

How many passwords can be created from the 36 alpha-numeric characters (26 alpha characters and 10 numerical digits 0 to 9), assuming passwords can be 8 or 9 alpha-numeric characters in length with a minimum of 2 characters being numerical digits? Explain each step of the process by which you arrived at the answer, showing th

### Various Methods and Deciding Consistency

Write equation slope intercept line satisfying the following condition. The line passes though (-6, 4) and is perpendicular to the line that has an x intercept 3 and a y intercept -9 Solve each system or state the system is inconsistent or dependent. x/2= y+8/4, x+3/2=y+5/4 Solve by using the substitution method. x/4

### Calculating Total Distance

Eva enters a walkathon that covers a total distance of 12 miles. She runs part of the distance at a rate of 6 mph and walks the remaining distance at a rate of 4 mph, completing the course in 2 hours and 30 minutes. How far did Eva run? How many hours did she spend running?

### Existing Slopes and Pairs of Points

The math Problems that I need help with are below. #1) Find the slope, if it exist, of the line containing the pair of points. (8,10) and (9,-6) The slope m= What? #2 Find the slope and the y- intercept F(x) = -10x -3 The slope is what? The y- intercept is (0, what o

### Algeba Word Problem

Flying against the wind, an airplane travels 6030 km in 9 hours. Flying with the wind, the same plane travels 7600km in 8 hours. What is the rate of the plane in still air and what is the rate of the wind?

### Determing Unions, Intersections, and Subsets

Set X = {5, 7, 11, 16, 21, 702}, Set Y = {2, 5, 8, 11, 19, 702} a. What is the union of Sets X and Y? b. What is the intersection of Sets X and Y c. Create your own set Z that is a subset of Set X.

### Desalination Exponential Equation

1. Desalination. More cities are supplying some of their fresh water through desalination, the process of removing the salt from the ocean water. The worldwide desalination capacity has grown exponentially from 15 million m^3 per day in 1990 to 55 million m^3 per day in 2007. a) Find the exponential growth rate k and write an e

### Null and convergent sequences

Please show all the work. (a) Use the definition of a null sequence to prove that the sequence {an} given by an = (-1)^(n+1) / (n^3 - 3) , n = 1, 2, ... is null. (b) Determine whether or not each of the attached sequences {an} converges. Find the limit of each convergent sequence.

### Area of a Square and Polynomial Region

88. Area of a square. Find a polynomial A(x) that represents the area of the shaded region in the accompanying figure. 96. Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)^2 represents the value of the investment af

### Renting a Condo

A Condo is renting at \$1,100 per month. I have two options, if I sign up for 12 month, I get 1 month free offer. Or I can use the money from that 1 month and spread it throughout the 12 month. My question is, if I would to go ahead and use that free month (\$1100) and spread it to 12 month, what would my newly adjusted monthly re

### Solving various algebraic equation problems

1. Find the value of x, 52 degrees, 137 degrees 2. find the x- intercept and y- intercept of the line given by the equation 9x - 5y = 13 3. find the points line 1- 3x + 13y = 12 line 2- 3x + 5y = 12

### Population Growth.

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2015. Please show th

### 2-4 Paragraphs.... Research Solve equations with radicals and exponents

Part 1: Using the Library, web resources, and/or other materials, find the gas mileage of your dream car or any car of your choice. Let x be the number of miles driven on 60 gallons of gas. By setting up and solving a proportion involving x, find the value of x for the car that you have chosen. State the type of car, the mile

### Computing elasticity of demand

Question 1. The demand equation for a certain brand of metal alloy audio cassette tape is: 100 x^2 + 9 p^2 = 3600, where x represents the number (in thousands) of ten-packs demanded each week when the unit price is \$p. How fast is the quantity demanded increasing when the unit price per ten-pack is \$14 and the selling price is d

### Word problem

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1600 after 1 day, what is the size of the colony after 4 days? How long is there until there are 20,000 mosquitoes? What is the size of the colony after 4 days? Approximately ___mosquitoes. (Do no

### Word problem

The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1500 after 1 day, what is the size of the colony after 2 days? How long is there until there are 30,000 mosquitoes? What is the size of the colony after 2 days? Approximately ___mosquitoes. (Do no

### Problems involving graphing a line

Question #6 / 24 Graph the line. We use the table x y -3 4.00 -2 4.33 -1 4.67 0 5.00 1 5.33 2 5.67 3 6.00 4 6.33 5 6.67 6 7.00 The graph is given by Question #7 / 24 Graph the line. We use the table x y -3 -2.75 -2 -2.50 -1 -2.25 0 -2.00 1 -1.75 2 -1.50 3 -1.25 4 -1.00 5 -0.75 6 -0.50

### Sum of Terms of Arithmetic Sequence

Find SUM_(k=10)^15 tk for an arithmetic sequence with 10th term being -10 and 20th term being 15, where tk represents the kth term of this arithmetic sequence.

### Solve the system of equations by graphing

1. Determine whether the given ordered pair is a solution of the equation. (-5,1); 2p - 3q = -13 2. For the equation, find the intercepts, Then use the intercepts to graph the equation. 4x - 3y = 12 3. Find the slope of a treadmill. 0.4ft by 5ft 4. Find an equation of the line containing the given poi

### Equation Model and Compount Interest Formula

1. Given the equation model F(x) = 62 + 35 log(x) - 4 where x represents a girl's age from 5 to 15 years. F(x) represents the percentage of adult height. Determine approximately what percentage of her adult height would the girl be at age 13? 2. Use the compound interest formula A = p(1+r/n)^(nt) to solv

### Area of the Segment of a Circle

Find the area of the segment of a circle with radius of 6 cm bounded by a 132 degree arc. The area of the segment can be found by first finding the area of the sector of the circle and then finding the area of triangle APB and subtracting the two.

### Two types of strictly increasing sequences of ordinals

I need help on the following problem (from Notes on Set Theory -Yiannis Moschovakis): [Let me know if you have a question on notation; I have a pdf file of this book] Give examples of strictly increasing sequences of ordinals such that ,

### Volume of the Box - Types of Equations

.Solve the problem. A yardstick measures 0.5 by 2 by 36 inches. How many yardsticks will fit in a box 3 inches wide and 36 inches high, if the length of the box is 14 inches? 2. Gerard wants to replace his from door with a solid wood door. The solid wood door will be shaped like a rectangular solid and will measure 78 1/2 in

### Length of a Rectangle

Suppose that the width of a rectangle is 5 inches shorter than the length and that the perimeter of the rectangle is 50 inches. The formula for the perimeter of a rectangle is P=2L+2W. a) Set up an equation for the perimeter involving only L, the length of the rectangle. Answer: b) Solve this equation algebraically to fin

### Algebra

Lets say Costco price club claims that they sell a 6 pack of Coors Beer at the wholesale price plus an additional 5% off. But with Costco, you also have to pay a yearly membership fee of \$60 just to have the privilege of shopping there. The wholesale price of Coors at Costco is \$3.50 a six pack. The 5% discount is taken at th