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# Basic Algebra

### Description of Factoring a Polynomial

Factor the following polynomial completely, given that the binomial following it is a factor of the polynomial. x^3 + 2x^2 - 5x - 6, x + 3

### Factor differences or sum of cubes

Factor each difference or sum of cubes. u^3 - 125y^3

### Factor polynomial

Factor the following polynomial completely. -36a^2b + 21ab^2 - 3b^3

### Logarithme, Volumes and Graphs Problem Set

1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function and

X>-2y and x-3y<6

### Important Information About Graphing and Solving Systems of Inequalities

X + 8y > 8 and x - 2y < 10

### Logarithm Transformation

The logarithm transformation can be used A. to overcome violations of the autocorrelation assumption B. to test for possible violations of the autocorrelation assumption C. to change a linear independent variable into a nonlinear independent variable D. to change a nonlinear model into a linear model

1) Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is

### Solve the equation y = x2 - 6x + 8 = 0

Using the quadratic equation y = x2 - 6x + 8 = 0, perform the following tasks: a)Solve by factoring, b)solve by completing the square, c)solve by using the quadratic formula

### Algebra and Trigonometry (16 Problems)

1. Write an equation for the circle that passes through the points: (1, -1), (-5, 7), and (-6, 0). 2. Express the polar equation in rectangular form. 3. Find the total area enclosed by the graph of the polar equation r = 1 + cos 2&#952;. 4. Write the equation of the line tangent to the parametric curve x = tcos t, y

### Fixed point of function on compact metric space

Assume that (X, d) is a compact metric space, and let f: X -> X be a function such that the inequality d(f(x), f(y)) < d(x, y) holds for all distinct elements x, y in X. Show that f has a unique fixed point. See attached file for full problem description.

### Graphing and Solving Systems of Inequalities

1. Graph the inequality. y &#61619; 1 2. Graph the inequality. y &#61619; 3x 3. Given f(x) = 4x + 1, find f(3). 4. Given f(x) = 5x2 - 3x + 1, find f(-2). A) -13 B) 15 C) -25 D) 27 5. Given f(x) = x2 + 5x + 3, find f(0). 6. Rewrite the equation 4x - 10y = 11 as a function of x. A) B) C)

### Using the index of a series as the domain and the value of the series as the range, is a series a function?

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: -Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? -Which one of the basic functions (linear, quadratic, ra

### Logarithms

Please answer the following questions: 1. Find the domain of the function f(x) = ln(x - 7). 2. Simplify: log 1000 3. Write as a single logarithm (DO NOT find approximations): 2 log 4 + log x - log2. 4. Expand and simplify: ln(e^x). 5. Solve for x: log(x - 4) + log 2 = 1.

### Sequences and Series

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the su

### Radicals and Rational Exponents

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign. ADDITIONAL INSTRUCTOR COMMENTS/REQUIREMENTS For unit

### Please solve these equations related to arithmetic sequence and geometric sequence

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the

### Arithmetic Sequences

A. what is d, the difference between any 2 terms? answer: show work in this space. b. using the formuls for the nth term of a arithmetic sequence, what is 101st term? answer: show work in this space. c. using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? answer: show work in

### Volume, Interest and Logarithms

2) The volume of a cylinder (think about the volume of a can) is given by V = &#960;r2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters. a) " in the function's equation.&#61552; Write h as a function of r. Keep " Answer as interest is c

### Simple math

(See attached file for full problem description) 1. Which of the ordered pairs (3, 1), (0, -4), (-4, 0), (-3, -7) are solutions for the equation x - y = 4? A) (0, -4), (-4, 0), and (-3, -7) B) (-4, 0) and (-3, -7) C) (0, -4) and (-3, -7) D) (3, 1) and (-4, 0) 2. Give the coordinates of the point graphed below.

### Writing Complex numbers in polar form and working with Logarithmic functions.

(See attached file for full problem description with proper symbols) --- 1/ If the amplitude ratio, N in decibels, of an electrical system is given by the formula. N = 10log And the power is given by P = Show that for matched input and output resistances the output voltage Vo is related to the input voltag

### Important Information About Fixed Rate

For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, A=P [1+r/n}^nt, let r = 10%, P=1, and n= 1 and give the coordinates (t,a) for the points where t= 0,1,2,3,4. Round the A value to the tenth's place. a. show coordinates in this space.

### Suppose you deposit \$10,000 for 2 years at a rate of 10%. Calculate the return (A) if the bank compounds quarterly (n=4). Round your answer to the hundredth's place. Now calculate the return (A) if the bank compounds monthly (n=12). Now calculate the return (A) if the bank compounds daily (n=365)

Suppose you deposit \$10,000 for 2 years at a rate of 10%. Calculate the return (A) if the bank compounds quarterly (n=4). Round your answer to the hundredth's place. Now calculate the return (A) if the bank compounds monthly (n=12). Now calculate the return (A) if the bank compounds daily (n=365) Show all your work.

### Volume of open top box

An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x donate the length of each side of the square to be cut out. find the function V that represents the volume of the box in terms of x.

### Primitive Roots

(See attached file for full problem description with all symbols) --- Suppose that n is odd and a is a primitive root modulo n. (a) Show that there exists and integer b such that and . (b) Show that b is a primitive root modulo 2n.

### Radical and rational exponents

Explain an advantage of rational exponents over the radical sign and give an example.

### Racicals and Rational Exponents

While the radical symbol is widely used, converting to rational exponents has advantages. Explain an advantage of rational exponents over the radical sign. Include in your answer an example of an equation easier to solve as a rational exponent rather then a radical sign.

### Quadratic Functions: Explain what the value of the discriminant means to the graph of y = ax2 + bx + c.

When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

### Algebra Word Problems : Maximizing Volumes, Compounding Interest and Logarithms

1) An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer b) Graph this fun

### Radicals and Rational Exponents

While the radical symbol is widely used, converting to rational exponents has advantages. Could you help me understand an advantage of rational exponents over the radical sign. What could be an example of an equation easier to solve as a rational exponent rather then a radical sign.