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Basic Algebra

Exploring Powers of Seven: Example Problem

If you calculate 7^90 on a TI-83+ calculator, you will get 1.145047759x10^76. This is misleading since it implies that the digit in the ones place is zero. Explore powers of seven and use what you learn to determine what digit is in the ones place in the expansion of 7^90. Note, this needs to be done without using a calcula

Factoring formula

1. How would you apply a factoring formula to completely factor the expression "x4 - 1"? 2. i. What does the symbol "i" represent? ii. Is "12.5555..." a rational or irrational number? Explain. iii. Is "2.1273685..." a rational or irrational number? Explain. iv. Is "548/799" a rational or irrational number? Explain.

Inner Product Spaces; Best Approximation; Least Squares

Please find the least squares solution of linear system Ax=b, and find the orthogonal projection of b onto the column space of A. I) Matrix 3*2 A=[1 1;-1 1;-1 2] , b=[7;0;7] II) A=[2 0 -1;1 -2 2;2 -1 0;0 1 -1] , b=[0;6;0;6] Answers: I) x1=5, x2=1/2, [11/2;-9/2;-4] II) x1=14, x2=30, x3=26; [2;6;-2;4] Find the ortho

Algebra : Math 116, Appendix F - Axia College Material

1. Suppose you are in the market for a new home and are interested in a new housing community under construction in a different city. a) The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to represent fl

Power Series Representation..

(a) Find a power series representation for f(x) = ln(1+x). What is the radius of convergence? (b) Use part (a) to find a power series for f(x) = x ln(1+x). (c) Use part (a) to find a power series for f(x) = ln (x^(2)+1).

Solving Example Algebra Word Problems

1.Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. The sum of the page numbers on the facing pages of a book is 285. Find the larger page number. 2. Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. The second an

Radical and Rational Exponents

Part 1: Using the Library, web resources, and/or other materials, find the average weight in pounds of a type of bird of your choice. Use the rational exponent equation L = 2.43 * W^0.3326 to estimate the wingspan L in feet of the bird that weighs W pounds (Rockswold, 2006). Include in your post the type of bird and the average

Mathematics Help: Factoring Polynomials

See the attached file. Find the prime factorization of this number. 72 Factor out the greatest common factor. b^3 - 52b^2 Factor this expression. (q + r)c + (q + r)d Factor this expression. 6(c - d) - a(c - d) Factor this expression completely. You may have to rearrange some terms first. ar^2 - 70brs

Solving quadratic/cubic equation

57 An equation of the form ax2 + bx + c, where a 0, is called a equation. Solve the equation. (x - 1)(x - 3) = 0 x = (smaller value) x = (larger value) Solve the equation. x2 + 38x = 0 x = (smaller value) x = (larger value) Solve the equation. x2 - 23x = 0 x = (smaller value) x =

Factoring Trinomials and Polyhnomials

#54 Factor the trinomial. 7y2 - 8y + 1 Factor the trinomial. 3c2 - 16c - 64 Factor the trinomial. 2m2 + 14m - 88 Factor the trinomial. 16x2 - 14x + 3 Factor the trinomial. 15b2 - 34bc + 15c2 Write the terms of the trinomial in descending powers of one variable. 16 - 56b + 49

Finding the Volume of a Bundle of Lumber: Example Problem

A lumber yard receives 2 X 4 studs in a bundle that contains 25 rows (or layers) of studs with 20 studs in each row. A 2 X 4 stud is actually 1 ½ inches, by 3 ½ inches, by 92 5/8 inches. Find the cross-sectional area of a bundle in square inches. Find the volume of a bundle in cubic feet. (The formula V = LWH gives the volume

Ordinal Multiplication and Exponentiation

Please provide a detailed solution to the attached problem. a) Suppose that alpha and Beta are non-zero ordinals such that alpha + Beta = w. What is alpha*Beta and alpha^Beta? b) Now suppose alpha + Beta = w + 1. What are the possible values of alpha*Beta and alpha^Beta?

Pros and Cons of Methods of Solving Quadratic Equation

I believe I have an somewhat of an understanding. I would like to get a second opinion on the pros and cons of these methods: Solving by graphing, using the quadratic formula, completing the square and factoring. when might each method be appropriate? Which method do your prefer? Explain?

Algebra - Simplex Tableau

Write the solutions that can be read from each simplex tableau. Pivot once as indicated in each simplex tableau. Read the solution from the result Please answer 12 & 16 only. Please show all work in steps. The problems are attached.

Quadratic equations solution

I would like understanding if a quadratic will have one, two or no solution? How do I find a quadratic equation if I'm only given a solution. explain. an example of one or two solution to that creates a quadratic equation. having trouble downloading info. for review, any suggestions would be great.

Further simplification in algebra

1. Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y= mx+b (3,9); 5x+y=6 The equation of the line is y = (Simplify your answer. Use integers or fractions for any numbers in the expression.) Please provide step-by-step instructions.

Math Problems

Name: 1) Solve algebraically. Trial and error is not an appropriate method of solution. You must show all your work. Learn how to type math roots and fractions by clicking on the link in the assignment list. Alternately, you may type as cuberoot(x) and show raising to the nth power as ^n, like x 3 is typed x^3. a)

Speed and Force of a Fall

An object weighing 12 pounds (mass) falls from a height of 4 feet, what is the speed at which the object falls and what is the force of the impact (it would be hitting a hard concrete or granite floor). So how fast is it falling, and how hard does it hit the floor?

Chinese remainder theorem

Solve the egg problem used to illustrate the Chinese Remainder Theorem if the remainders on division by 2,3,4,5,6 and 7 are all 1 by (i) the given procedure (ii) the "easier" way (i) the given procedure X=1(Mod2) X=1(Mod3) X=1(Mod4) X=1(Mod5) X=1(Mod6) X=1(Mod7) If and and then . We will use this r

Algebra - Logarithmics, Graphs, Word Problems

See the attached file. 1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 a

The law of exponents

I would like help understanding the following: The law of exponents 1) to raise a power to a power we can multiply the exponents with an example. 2) to raise a product to a power we can mulitply the exponents with an example. please explain how you simplified each example. How do laws work with rational exponents? with a third e

Week 8: Diagnostic for Baseline Projects 15, 16 and 17 Math Skill Diagnostic

Week 8: Diagnostic for Baseline Projects 15, 16 and 17 Math Skill Diagnostic Baseline Project 15 - The Behavior of Astronomical Masses 1.Express each of the following using scientific notation 2.Solve for x in each of the following. 3.In words, write out the steps necessary to solve for x in each of the following equatio

Algebra - Echelon Method and other problems

Use the echelon method to solve the system of three equations in three unknowns. 8) x-y+2z=-2 5x + z=0 x+2y+z=4 9) Determine the equation of the line described. Put the answer in the slope -intercept form, if possible. Through (-7,-7), parallel to 5x-4y=-19 10) Write a word or phrase that best completes each s

Simplify radicals expressions

I would like help understanding why it is important to simplify radicals expressions before adding and subtracting? How is adding radicals expressions similar to adding polynomials expressions? How is it different? also, an example of an radical expression would be great? I'm having hard time finding comprehensive information.


I need help with the following problems attached.

Postage stamp denominations

If postage stamps only had the denominations 5 cents and 7 cents, what amounts of postage could we buy? What if they were 3 cents and 5 cents? Or 15 cents and 18 cents? what generalizations can be made for stamp denominations m and n cent, where m and n are positive integers?

Consecutive sums

What kinds of numbers can be written as the sum of consecutive whole numbers? How many ways can you write a whole number as the sum of consecutive whole numbers? For instance 9 = 5+4 and 9 = 2+3+4. Is it possible to tell if a number can be written as the sum of a given number of consecutive whole numbers? For instance, can 101 b

Graphing transformations

1. graph the following transformations of f (x)= |x| a. f(x) = |x+3|-1 b. f (x)= 1/3 |x| +2 c. f (x)= -2 |x-1| -1 d. f (x) = 5 |x-1| -4 __________________________________________________________________ 2. f(x)= {-2x+3} if x>1 and f(x)=x^2+3 if x less than or equal to 1

Exponential and Reciprocal Functions

Present value calculations: 1. What is the present value of nine annual cash payments of $4000 to be paid at the end of each year using an interest rate of 6%? 2. What is the present value of $15,000 to be paid at the end of 20 years using an interest rate of 18%? 3. How much cash must be deposited in a savings accou


1)Richard's GPA is 3.7, and he made the following statement recently, "I have earned 110 credits from my college, and I earned at least an A- in each case." An A is equivalent to 4.0 and an A- is equivalent to 3.67. How many of the credits were A, and how many of the credits were A-? (To earn full credit, you need to formulat