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Basic Algebra

Least Common Multilpes

A. Find the LCM (Least common multiple) (84, 108). Show how you obtained your answer. B. Suppose LCM (18,A) = 72. What are the possible values, if any, for A? Explain your answer.

Equivalence and Simplification

A. Show that 693/858 and 42/52 are equivalent in THREE different ways. B. Simplify 3^5 X 24^3 divide by 12^3 X (6^3)^2 ^ means exponent.

Algebra : Graphing Functions

Please see the attached file for the fully formatted problems. Can you please assist me with the problems listed below? P. 237 1. a) #6, b) #18 2. a) #22, b) #24 3. a) #32, b) #46 P.253 4. a) #1, b) #2, c) #3. d_ #4 5. a) #10, b) #12 6. a) # 28, b) #30 7. P.260, Matched Problem 1 P.271 8. # 2 - 22 (Eve

Intervals

Please see the attached file for full problem description Find ten real numbers in the closed interval [0,1] such that for each value m from 2 to 10, the numbers lie so that there is one of them in each of the open intervals [Note that these conditions for m = 1,2......,10 all have to hold simultaneously for your

Proving that an equality is false.

I have two sets of 64 numbers (1.1 to 7.4). Both number sets are created using the same equation for values of i from 0 to 63. m = 1.1 + ( i * 0.1 ) n = 1.1 + ( i * 0.1 ) I am trying to understand if the following equality is false in all cases except when the terms in each expression are equal (e.g. m^-12 = n^-12 and

Quadratic Equations

The graph of the quadratic equation x^T Ax = [0,0,1]x, where A = [ 1/(alpha^2) 0 0 ] [ 0 -1/(beta^2) 0 ] [ 0 0 0 ] is a(n): A. ellipse B. hyperbola C. elliptic paraboloid D. parabolic cone E. hyperbolic paraboloid

Linear Algebra (Inner Products)

Let f1, f2, f3 be unit vectors in R3 such that < f1, f2 >= 1/2. Give a necessary and sufficient relationship between x =< f1, f3 > and y =< f2, f3 >. Please be sure to be rigorous and as detailed as possible.

Log

E^x*e^x+1=e^x-1

Algebra with Indicies

Given that S=(R+D)^(1/3) and T=(R-D)^(1/3) where D= square root(R^2+Q^3), show that ST=-Q

How does sqrt128 become 8sqrt2?

Hi, can someone please explain to me how sqrt (square root of)128 becomes 8sqrt2 ; or sqrt68 becomes 2sqrt17? ; or sqrt45 becomes 3sqrt5? Thank you

Simpify the expression.

Simplify the following expressions: a. 3x-2/2x2+x-3 Divide by 9x-6/2x-2 b.(108)1/2- (48)1/2+ (192)1/2 (should be exponent 1/2) c. (20x3+3x2-4x+5)/(4x2+3x-7) (should be exponent 3 and 2,2).

Factoring

Factor the following: a. 81a4- 16b4 (should be exponent 4) b. 12x2+ x- 35 (should be exponent 2)

Word problem in Algebra about ages

3 years ago, Liz's age was 1/3 of her mother's age. Now, 7 years later, her age will be 1/2 of her mother's age. How old are Liz and her mother?

Help with setting up problem

Please see the attached file for full problem description. I would like to get some assistance in setting up this problem. A=1.645 and they give the answer of x as .56506 Thank You

Algebra - Composition of Functions

For the given functions f and g, find: (a)  the composition of (f o g) (4) (b) (g o f) (2)  (c)( f o f) (1)  (d) (g o g) (0) f(x) = 2x; g(x) = 3xsquared + 1

Algebra - Functions and Domains

For the given functions f and g, find the following functions and state the domain of each. (a) f + g   (b)f - g  (c)f x g  (d) f / g f(x)= square root of x + 1;  g(x) = 2 / x

Algebra - Graphing a Function

Sketch the graph of each function.  Be sure to label three points on the graph. If f(x) = integral (2x), find: (a) f(1.2)  (b) f(1.6)  (c) f(-1.8)

College Algebra

Please help me with #4, #10, and #16. I am having trouble woth these. Please show your work so that I may better understand the process.