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# Basic Algebra

### How much water will Jill need to add to her pool to return the water level to its original depth?

Jill has a swimming pool in her backyard. It measures approximately 16.4 feet wide and 26.25 feet long. It is an average of 5 feet deep. During a few hot weeks during the summer, some water evaporates from the pool, and Jill needs to add 10 inches of water to the depth of the pool, using her garden hose. Although her water press

### Graph and Solve the System of Inequality

See the attached file. CheckPoint 11) Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first \$190, plus 40% of the rest. Under plan B, Giselle would pay the first \$220, but only 30% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over \$220 in

### Galois Extension

** Please see the attachment for a full problem description ** Suppose that K/F is a Galois extension, the Norm of alpha is an element of K is N_K/F := (please see the attached file) and trace is Tr_K/F(alpha) = (please see the attached file). Suppose also (please see the attached file) that Gal(K/F) is cyclic and K, F are fi

### Find the Solution for Equations

See the attached file. 1) Solve algebraically and check your potential solutions: a) sqrt(t+12)-t=0 b) 3/(x-3)=x/(x-3)-3/2 ? Answer Show your work here: What potential solution did you obtain? Explain why this is not a solution. Answer: 2) a) If y=sqrt(x)-1, fill in the following table for x = 0, 1, 2, 3, 4. Round t

### Unit 2 Individual Project 2D

1a) Solve the following quadratic equation by factoring: Answers: Show work here: 1b) Solve the following quadratic equation by using the quadratic formula: Read the information in the assignment list to learn more about how to type math symbols, such as the square root. Answers: Show work here: 1c) Compute the discrimin

### Galois Group

If f(x)=x^7-2 and K is its splitting field over Q, determine the degree of [K:Q], describe K explicitly using a primitive element or by listing a set of generators over Q and find the Galois group of K/Q.

### Inequalities-Creating a shape with a coordinate plane closed figure

Creating a Shape: You will create a colored in, closed figure on a coordinate plane and then state the inequalities that allow you to create the figure. You may use the link and directions below to help you create your shape or you may use any paint program, power point, or graph the figure by hand, scan, and attach. For h

### Abstract Algebra Problems

In addition to the attached, from 3-37, the subgroup is the one generated by the 270 mapping. 3-37 In the octic group, find the cyclic subgroup generated by the 270 mapping. What is the order and index?

### Measures of poverty and income inequality

Discuss the measures of poverty and the measures of income inequality.

### Multiple algebra questions

1. Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of some traffic signs must be 68 Inches. Also, its length is 6 inches longer than its width. Find the dimensions of this sign. The width of the sign is? The Length of the sign is? 2. A hardw

### Properties of Affine Groups over Finite Fields

Let F be a field. The 1-dimensional affine group over F is the set A of all functions f: F -> F of the form f(x) = ax+b where a, b belong to F and a is a unit. Let S and T be subsets of A consisting of the scaling (s(x)=ax) and translations (t(x) = x+b) Are S and T normal subgroups? If p > 3 and F = Z/p consider the subgro

### Green Functions

I'm looking for help in solving question 3 which is attached as a PDF document to this description. The question asks for the Green Function, GF of: d(^2)y/dt(^2) +5*dy/dt + 6*y and show that's its generic sol is y(t)= e^-2t int e^2z f(z) dz - e^-3t int e^3z f(z) dz.

### Using Math Induction for Proof

Find a formula for (1/(1*2) + 1/(2*3) + ..... + 1/ (n*(n+1) ) by examining the values of this expression for small values of n. Prove the formula you found by induction Please show me stepwise in word document.

### Inequality for Convex Function

Let a < b be real numbers and f: [a,b] -> R a convex function (equivalently a concave upward function). Define F(s,t) = f (s) + f(t) - 2f((s+t)/2) Prove that F(s,t) &#8804; F(a,b) for every s,t &#8712;[a,b].

### Solvable Roots and Solvable Group

The problem is in the attachment.

### Math problems: Basic Algebra

** Please see the attached file for the complete description of the math problems **

### Identities Involving Logarithms

a) Show that if Re z1 > 0 and Re z2 > 0, then Log (z1z2) = Log z1 + Log z2 b) By choosing specific nonzero values of z1 and z2, show that expression "log(z1/z2) = log z1 - log z2" , for log (z1/z2) is not always valid when log is replaced by Log.

### Fundamental Counting Principle

Use the Fundamental Counting Principle to determine the number of 3-letter expressions possible under the following circumstances: The first letter must be a vowel (a, e, i, o, or u); the second letter can be any letter except a vowel; the third letter can be any letter of the alphabet. Remember that there are 26 letters in th

### State Review for Elementary Algebra

5. How many feet of fencing should be purchased for a rectangular garden that is 17 ft. long and 16 ft. wide? A) 272 ft. B) 132 ft. C) 66 ft. D) 33 ft. 7. Write 0.000097717 in scientific notation. A) B) C) D) 9. Write 130% as a fraction in simplified form. A) B) C)

### Algebraic Inequalities

Please solve the following inequality problems. You must give your answer using the interval notation. You must also give you answer in graphical form (using the number line). (a) (4 - x) is less than or equal to (-2) or x + 3 > 3x - 1 (b) 1 -2x <7 and (3x-2) is less than or equal to 1

### Exponential and Logarithmic Functions

The pH of a solution is given by pH = -log x, where x represents the concentration of the hydrogen ions in the solution, in moles per liter. Express answers in powers of 10 1. What is the hydrogen ion concentration of lemon juice. 2. What is the hydrogen ion con

### Logarithm and Scientific Notation

1. Imagine that every single person in your contact list has the same number of people in their contact list as you. Write this total number of all the contacts in all the phones (ignore the fact that some may repeat) as an exponential. Next, evaluate this exponential. 2. Express the value you calculated in the first problem

### Logarithms and Exponents

Exercises 1. Solve the following problems with exponents a. 25 b. 3-3 c. 115 d. 02 e. 223/4 2. Solve the following problems with roots a. (sqrt)169 b. (sqrt)50 c. 3(sqrt)82 (Cube Root of 82) 3. Write the following

### Rational Equations, Pythagorean Theorem and Quadratic Equations

1. Explain the five-steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand? Provide an example with your explanation. 2. How might the Pythagorean theorem and distance formula be used in

### Identifying Factors in Trinomials

Identify a factor of the following trinomial: 15u2 - 17u - 26 A. (u + 2) B. (u - 13) C. (u - 2) D. (u + 13) Identify a factor of the following trinomial: 17r2 - 48r + 28 A. (r - 2) B. (r - 14) C. (r + 14) D. (r + 2) Identify a factor of the following trinomial: 12u2 - 16u - 16 A. (12u + 8) B.

### You are considering the purchase of a computer

You are considering the purchase of a computer and have consulted several computer magazines that contain ratings and prices for the five models you are investigating. You decide to include price, speed, and expansion capabilities as three criteria on which you will judge the models under consideration. The ratings, with 10 bein

### Monic polynomial

Find an irreducible monic polynomial of degree 2 over the field Z_7 whose root is a primitive element GF(49).

### What is the greatest common factor?

1. What is the greatest common factor? How do you know when you have found the greatest one? Provide an example and a detailed explanation. 2. Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Use an example in your explanation. Show your answer usin

### Algebra-related Problems

1. Express in terms of i. 4 square root of -255 2. Subtract. (5x^6 + 9x^4 - 2x^3 - 3) - (8x^6 - 8x^5 + x^4 - 4) 3. Given the quadratic function f(x) = x^2 - 18x + 81, find a value of x such that f(x) = 16 4. Joe has a collection of nickels and dimes that is worth \$7.65. If the number of dimes was doubled and the numb

### Algebra; Factoring 2

1. Completely factor the following expression: 25a^2-60ab + 36b^2 2. Factor the following expression into a product of two binomials: 36x^2-84x+49 3. Use the "difference of squares" rule to factor the following expression: 16x^4-121y^4 4. Megan factored the expression12x^2+13x-14 as (3x+2)(4x-7). But when Jacob appli