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# Basic Algebra

### 25 Algebra Problems

Please see the attached file for the complete list of problems (25 in all) 1. Find the greatest common factor for the following sets of terms. 12a^3b^2 , 18a ^2b^3, 6a^4b^4 2. Factor the following polynomial. 4s + 6st - 14st ^4 3. Find the GCF of (6y^2 - 3y)(y + 7) 4. Geometry: The area of a rectangle of length x is give

### Algebra: Solving Equations and Word Problems

1) Evaluate 6*5+2-24 divided by4*2 2) Given f(x)=3x+3, find f(a+1) 3) Use your calculator to evaluate the following expression if x=9.69, and y= -8.02 x-5y Round your answer to the nearest tenth 4) A bus leaves a station at 1P.M., traveling west at an average rate of 44 mi/h. At 2P.M. on the same day a second bus leav

### Solution of Quadratic Equations by completing the square, quadratic formula, square root method, factoring.

Solve the following quadratic equations by factoring and name the techniques used Example : completing the square, quadratic formula, square root method, factoring. See attached file for full problem description.

### Tips for New Algebra Students

What type of Algebra problems covered in an Algebra 1 course do you find to be the most challenging? Why? What did you learn from the experience of an Algebra 1 course and how did you overcome this challenge? If you could provide some tips or advice to new Algebra 1 students, what would you share with them?

### Practice Algebra Problems

Show all steps. Explain each step as much as you can. Find the prime factorization for each integer. #6. 200 Find the greatest common factor for each group. #10. 6a2b, 9ab2, 15a2b2 Complete the factorization of each binomial. #14. a2 - a = - a( ) Factor each polynomial by factoring out the GCF. #20. 2a2 -

### Evaluating and Solving Expressions

Please see the attached file for the fully formatted problems. Write 54 as a product of prime factors. Evaluate the six expressions below. Write each response as an integer or as a fraction. (-8)^2 (-2)^4 (1/5)^3 4^2/5 (-1/2)^2 -6^2 Evaluate. Evaluate the expression when and

### Sequences and Series: 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, quadrati

### Arithmetic and Geometric Sequences, Series and Functions

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, quadrati

### 15 Basic Algebra Problems

1. Reduce if possible: (p^2 + 5p + 6)/(p^2 + 2p - 3) 2. Multiply: (x^2 - 3x + 2)/(x^2 - 4x + 4) times (x^2 + x - 6)/(x^2 - 1) 3. For what values of p is #1 undefined? 4. For what values of x is #2 undefined? 5. Find the LCD of the following: 1/(x + 2) and 1/(x^2 + 2x). 6. Find the LCD of the following: 1/(x^2 +

### Sequence and Series

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, quadra

### Fixed Point Equations

The chapter in question is about Iteration.(x2 means x squared). It talks about the Fixed point rule. It describes a fixed opint equation as x2 + 1/8 = x; that is x2 - x + 1/8 = 0 It then gives another example: Determine the fixed points of the function f(x) = -1/8x2 + 11/8x + 1/2 and states that the fixed point equation

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.

### Basic Algebra

Practice skills- 16 Problems Each correct answer is worth 6-1/4 points 1. Write in simplest form. A) -2r3s2t B) C) D) 2. Write in simplest form. A) B) C) 4a4b D) 3. Multiply. A) B) C) D) 4. Multiply. A) B) C) -n2 +

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.

### Writing Equations from Word Problems

The equation for the distance of the room is: d=20+5t and the equation for the distance of Peter is d=vt =10t Such that setting the two equations together we see that at t=4 seconds, the distance that Peter travelled is the same as the distance of the room 40ft. However, here he only drops of one paper and he must go back

1. Decide whether each of the following is a quadratic equation or not. a. 3 - X^2 = 9x b. X^3 - 8 = 0 c. 2X^2 - 7X + 1 d. -5 - X^2 + 8X = 0 e. 6 + 5X - X^2 2. Find f(-3) if f(x) = -2x^3-8x^2+2x-1 3. Do the math and express without negative exponents: x^(-7) * x^3 4. Do the math and express without negative expon

### Evaluating Exponential Functions

Human populations can be modeled using an exponential growth function. Use the Library for research or other resources to find the following: Current world population Current U.S. population Current growth rate of the world population Current growth rate of the U.S. population Starting in the current year, determine

### Modeling with Polynomial Functions

Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileag

### Algebra Word Problems : 'Together and Alone' Problems

Problem 1:Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours . How long would it take the two painters together to paint the house? Problem 2: Two trains leave the same train station at the same time , but in opposite direction. The faster train travels at an average ra

### Logarithms and Exponents

For problems 1 -3, use the algebraic definition of the logarithm to evaluate (simplify) the expression by hand and state the property number used. All work must be shown. 1. log8 (8^(x-1) 2. log4 ((1/16)^7) 3. log (0.0001) For problems 4 - 6, solve for x exactly by hand. 4. log5 (x - 1) = 1 5. log2 (1/8) = x 6. lo

### Integers and Real Numbers

Draw the real line and label from about -5 to 5 in increments of 1. There are an infinite amount of integers on the real line. Based on your sketch you'll also agree with me that there are twice as many total integers as there are positive integers, right? But how many positive integers are there? That's it... an infinite am

### Quadratic equations, discriminant, and graph

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 +

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 +

### Graphs of Exponential and Logarithmic Functions

Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 2x y = log2x Plot the graphs of the following functions. Scan the graphs and post them to the Facilitator along with your response. f(x)=6x f(x)=3x - 2 f(x)=(1/2)x f(x)= log2x

### Quadratic Equations : Vertex Form

1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the line of symmetry for the grap

### Evaluating Functions: Example Problem

Evaluate each of the functions below at x = 1, 2, 4, 8, and 16. Plot the graph of each function. Classify each as linear, quadratic, polynomial, exponential, or logarithmic, and explain the reasons for your classifications. Compare how quickly each function increases, based on the evaluations and graphs, and rank the functions f

### Use polynomial, rational, exponential and logarithmic functions.

Human populations can be modeled using an exponential growth function. Use the Library for research or other resources to find the following: current world population current U.S. population current growth rate of the world population current growth rate of the U.S. population Starting in the current year, determine th

### Modeling Exponential Functions

Many different kinds of data can be modeled using exponential and logarithmic functions. For example, exponential functions have been used by Thomas Malthus to describe the growth of human populations. Exponential growth has also been used to indicate how property values grow in strong real estate markets. Create a set of dat