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# Algebra

### Polynomials and Rational Theorem Algebra Questions

See 7 questions attached.

### Vertex, Intercept, Domain, Range of Quadratic Function

1. Given the quadratic equation y=-x^2+2x+8, find: a) the vertex b) the axis of symmetry c) the intercepts d) the domain e) the range f) the interval where the function is increasing and g) the interval where the function is decreasing h) graph the function y=-x^2+2x+8 2. The following polynomial represents a profit

### Transformations Investigated Graphically and Algebraically

Use transformations of f(x)=x^2 to graph the following function 1. g(x)=x^2+3 2. g(x)=(x-4)^2+4 3. g(x)=4(x+3)^2-2 4. g(x)=-3(x+5)^2+3 Find the function that is finally graphed the following transformations are applied to the graph of y=sqrt of x in the order listed 1. shift up 9 units 2. Reflect about the x-axis 3. R

### Mixed Algebra Questions Solved

PLEASE HELP SOLVE THE FOLLOWING QUESTIONS 1. Elsie is making a quilt using quilt blocks like the one in the diagram. a. How many lines of symmetry are there? Type your answer below. b. Does the quilt square have rotational symmetry? If so, what is the angle of rotation? Type your answers below.

### simultaneous eqns & concrete strength

1. Solve graphically the following simultaneous equations: y = 10 - 2x y = x - 1 2. Plot the graph of: y = x^2 - 2x - 4 for values of x from x = -2 to x = 4 at intervals of 1 and use the graph to solve the quadratic equation x^2 - 2x - 4 = 0. 3. The following grouped frequency table shows the compres

### Equation of Lines and Modeling

Select and graph a point (with coordinates) in the x-y plane, not on the x- or y-axis; then, (a) Graph the line that passes through the selected point and is parallel to the x-axis. (b) Write the equation of the line drawn in Part (a) (c) What is the slope of the line drawn in Part (a)? (d) Graph the line that passes throu

### deriving formulas to meet certain conditions

1) Derive a formula to find all numbers that meet the following conditions: • Divide by 3 the remainder is 1 • Divide by 29 the remainder is 6 2) What are the first 20 solutions to Sun Tsu's Chinese Remainder problem? 3) Derive a formula to find all numbers that meet the following conditions: • Divide by 3 the r

### Standardized Mortality Ratio

Please show the calculation for how the numbers in red where determined. Using Table 4, calculate the expected number of deaths for each age and latency category, and then an overall standardized mortality ratio (SMR) for each latency group. To determine if 10 years latency is indeed needed to develop ASL, we split latency i

### Solve the given problems by using TMV concepts.

1. How much should Elton John invest at the end of each year for six years if he expects to earn 6% and he wants to accumulate \$150,000 in order to buy a new grand piano six years from today? 2. How much must Elton John invest today if he expects to earn 6% compounded semiannually and he wants to accumulate \$

### Mathematical Modeling: Equations

How is an equation a breakdown of a specific model, where it has the x-value as its input and a y-value as its output?

### Fundamental Mathematics Sequences

FUNDAMENTAL MATHEMATICS II Question 1. Say that a sequence (an) is a Cauchy sequence (named after the French mathematician Cauchy) if it has the following property: For every  > 0 there is a number M (depending on ) such that |an - |am <  for all n, m >= M. (1) * Show that the sequences ( 1/n) and (n + 1/2n) and Cauchy s

### Sports Activities in 1998

The following table gives participation in selected sports activities in 1998, in thousands, for persons living in the U.S. age 7 or older. (Source: Statistical Abstract of the United States 2000, 120th Edition Exercise Bicycle Sport Walking Swimming Equipment Ridi

### High School Math Examples

See the attached file. Help solve the following: 1. Find the Greatest Common Factor (GCF) of 18X3 and 30X5. (18X raise to the power 3) and (30X raise to the power 5) A. 90X3 (90X raise to the power 3). B. 90X5 (90X raise to the power 5). C. 6X5 (6X raise to the power5). D. 6X3 (6X raise to the power3). 2. Write 6.

### Residency After Departure from Canada - Taxation

At the end of the current year, Simon Farr departed from Canada in order to take a permanent position in Ireland. He was accompanied by his wife and children,as well as all his property. Due to depressed real estate prices in his region, he was unable to sell his residence at a satisfactory price. However, he was able to rent it

### Savings Account and Deposit Techniques

Suppose you open a savings account at an interest rate of 1.5 percent per year, compounded monthly. You make an initial deposit of \$1,000 and, starting one month after you open the account, you deposit \$100 each month and do not make any withdrawals. Identify which problem-solving techniques you would use to answer the question:

### Slopes and Functions

#12 Determine the slope of each line Explanation of what I see here: There is a graph with a line going vertical from Y, 3, 1 and -1 Then there is a line above the numbers: -1, 1, 2, 3, x A blue line goes between the 3 and 1 (sorry I don't know how to the graph I am looking at) #22 The Coordinate Formula for Slope Fin

### Violent crimes equation

The number of violent crimes reported in the U.S. in 1995 was 1,798,790, and decreased to 1,682,280 in 1996. Assume that the function that relates the number of violent crimes as the dependent variable, with the year that the number of crimes occurred as the independent variable, is linear. Write an equation for the line. I

### Slope of the line and linear relationship

A wireless phone service charges 14.99 as a monthly charge and 0.30 per minute for local calls. How much would you pay in a month when you made ten local calls of three minutes each? Let C represent your total monthly cost assuming you made only local calls, did not receive any calls and the total number of minutes you wer

### Price of Gold

Suppose the current price of gold is \$650 an ounce. Hotshot consultants advises that gold prices will increase at an average rate of 12% for the next two years. After the growth rate will fall to a long-run trend of 3% per year. What is the price of 1 million ounces of gold produced in eight years? Assume that gold prices have a

### Mixed Algebra Questions

1. Insurance settlement. Gary invested one-third of his insurance settlement in a CD that yielded 12%. He also invested one-third in Tara's computer business. Tara paid Gary 15% on this investment. If Gary's total income from these investments was \$10,800 for 1 year., then what was the amount of his insurance settlement? 2.

### Commutative & Associative Properties

#12 (Commutative & Associative Properties) -8 + 12 - 9 - 15 + 6 - 22 + 3 #34 (Distributive Property) Use distributive property to write each sum or difference as a product. 7b - 49 #54 Multiplication Property of Zero x * 5 = 5x #26 (Using the Properties in Computation) Perform each computation. Make use of appropri

### Sylow's Theorem Problems

Verify that if H is a subgroup of G, and a ? G, then aHa^-1 is a subgroup of G. Prove that if H is a finite subgroup of G, and a ? G, then |aHa^-1| = |H|. (Suggestion: The mapping h ? aha^-1 is one-to-one.) Explain why if H is a Sylow p-subgroup of a finite group, then so is each conjugate of H. Prove that if a finite g

### Find the Equation of the Line

Find an equation of the line passing through the pair of points. Write the equation in the form Ax + By = C. Show Work. (-7,6),(-8,-4) A. -10x-y = 76 B. x+y = 76 C. -10x + y = 76 D. 10x + y = -76

### Simplifying Equations and Solving Functions

1. Simplify: (-5a^3b^2)^4 a^12b^5/b^-7 2. let f(x)=3x^2 and g(x)=x-4 -Find the composite function (f o g)(x) and simplify -Find (f o g)(-1) 3. Find the exact solutions and simplify as much as possible 4x^2+5=4x

### Investments and Interval Notation

1. Suppose \$8,500 is invested in an account at an annual interest rate of 3.7% compunded continuosly.How long (to the nearest tenth of a year) will it take the investment to double in size? 2. Solve, and write the answer in interval notation x+5/x-7 ? 0 3. Solve: ?3x+10=-x

### Operations with Functions

1. Solve: 7^3x-4=49 2. Let f(x)=x^2+10x40 -find vertex -state the range of the function -on what interval is the function increasing? 3. Multiply and Simplify (7+6i)(2+9i) Write the answer in the form a+bi, where a and b are real numbers.

### Concentration of a Solution for Water Distribution

1. The total weight of a container and liquid is 14.40 lbs. The tare weight of the container is 6.10 lbs. If 97% of the liquid is water, what is the weight of the chemical added to it? Multiple Choice: a) 0.25 lbs b) 0.28 lbs c) 2.50 lbs d. 8.05 lbs. 2. How many gallons of water should be mixed with 2 lbs of dry

### Capacity Word Problem

The two NCAA stadiums with the largest capacities are beaver Stadium (Penn State) and Michigan Stadium (Univ. of Michigan). Beaver Stadium has a capacity of 1081 more than Michigan Stadium. If the combined capacity for the two stadium is 213,483, find the capacity for each stadium.

### Fundamental Math: Algebraic Number Theory

See the attached file. 1) Compute the Cayley tables for the additive group Z and for the multiplicative group Z of non-zero elements in Z. 2) Let G be a group written additively. Recall that the order of an element a is the minimal natural number n such that na = 0. If such n does not exits then one says that the order

### Population Growth Analysis

Population growth in Ethiopia: In 2006, the estimated population in Ethiopia was 75 million people with a relative growth rate of 2.3%. a. Write an equation that models the population growth in Ethiopia, letting 2006 be year 0. b. Based on the model, what is the expected population in Eithiopia (to the nearest million) in