### Equality of gcd's

Show that if gcd(a, b) = 1, then gcd(ac, b) =gcd(b, c).

Explore BrainMass

- Anthropology
- Art, Music, and Creative Writing
- Biology
- Business
- Chemistry
- Computer Science
- Drama, Film, and Mass Communication
- Earth Sciences
- Economics
- Education
- Engineering
- English Language and Literature
- Gender Studies
- Health Sciences
- History
- International Development
- Languages
- Law
- Mathematics
- Philosophy
- Physics
- Political Science
- Psychology
- Religious Studies
- Social Work
- Sociology
- Statistics

- Mathematics
- /
- Algebra
- /

Show that if gcd(a, b) = 1, then gcd(ac, b) =gcd(b, c).

An integer n is called k-perfect if σ(n) = kn (note that a perfect number is 2-perfect). (a) Show that 120 = 23? ? ? 3 ? ? ? 5 is 3-perfect. (b) Show that if n is 3-perfect and gcd(3, n) = 1, then 3n is 4-perfect.

Show that if and , then . (This shows that the function g is well-defined from to ) Note: g is defined as follows: g: Where is the multiplicative inverse of m1 modulo m2 and conversely. Please see the attached file for the fully formatted problems.

Suppose that X and Y are finite sets, with m and n elements respectively. Suppose further that the function f : X → Y is one-to-one and the function g : X → Y is onto. (i) Use the function f to show that m ≤ n. (ii) Use the function g to show that m ≥ n. (iii) Is f : X → Y onto? Justify your as

How many functions are there from S = {1,2,...,10} to T = {1,2,3,4,5}? How many of these functions are onto?

Decide whether the relation is a function. 1- (6,5), (4,3), (-2,3), (0,-1) , (-1,2), (-4,-5), (-3,4) 2- (4,4), (3,3), (-1,1), (6,6), (1,-2) make an input-output table for the function rule. Use a domain of -10,-5,0,5, and 10. Identify the range. y=8x+1 y=-6x y=x square 2+5 write a function that relates and x and

Given a 2 x 2 matrix sample = 2.0000 + 3.0000i 1.0000 + 2.0000i 4.0000 + 5.0000i 2.0000 + 1.0000i >> std(sample(:)) ans = 2.1213 >> According to matlab the answer is 2.1213. I'm not arriving at that answer. I need to see all work on how to achieve said result.

The following theorem could be used to write the proof. A theorem states that if d:D-->R is uniformly continuous on D iff the following condition is satisfied: If un and vn are both sequences in D, then lim as n-->infinity (f(un)-f(vn))=0 Show f is not uniformly continuous on D making use of the sequent

Identify the type of graph with the equation x- 4y^2 - 8y = 0.

Identify the type of graph with the equation x^2 = 4y - 8.

Y+7=4(x+3)^2

Identify the type of graph that each equation has without actually graphing. x=3y^2 + 5y - 6 Equations may need to be simplified first.

A roof rises 7.25 ft over a horizontal distance of 13.71 ft. What is the slope of the roof to the nearest hundredth? A) 1.89 B) 0.53 C) 1.87 D) 0.77

Please review attachment

A hyperbola is given the equation x^2/25 - y^2/9 = 1 A) Find the coordinates of the foci and the equations of the asymptotes. B) Find the point of intersection with the line y=4-x c) Graph the hyperbola, the line, and the point of intersection. Please explain how to graph this because I dont understand it and

(See attached file for full problem description)

Please answer the following questions ASAP: Match each description of a graph with an equation. The graphs are all described in relation to the graph y = x^2 shifted 3 units upward shifted 3 units to the left shifted 3 units downward stretched out and flipped upside down shifted 3 units to the right

Given the information in the attachment, please sketch the graph.

Given the quadratic function (see attached file) a.) Does the graph open up or down? b.) What is the equation of the axis of symmetry? c.) What are the coordinates of the vertex? d.) Give the y intercept e.) Give the x intercept(s) f.) sketch the graph

1. Find an equation of variation where y varies jointly, directly as the cube of x and cube root of z, and inversely as the square of w, and y = 4 when x = 2 and z = 8 and w = 4. 2. Perform the indicated operation and simplify. y2 + 3y y2 -y y - 1 y2 -5y + 6 (y-3)(y+2)

For the rational function (see attached), give the intercepts and asymptotes and sketch the graph.

(See attached file for full problem description with proper equations) --- The problems need to be solved in full and to show all work 1a) Find the following derivative implicitly with respect to x If, Y=(1+xy)^(1/xy). Find dy/dx! without simplifying the derivative. Compute dy/dx at (1, 1). b) find the formul

Determine algebraically whether the given function is even, odd, or neither. Function: f(x) = sqrt (1 - x^2) Make sure to show all of your work.

Consider the given function: Function: f(x) = x^3 - 2x^2 Is this function even, odd or neither? Make sure to show all work.

Find an equation for the line with y-intercept 3 that is perpendicular to the line y=2/3x-4 a. 2y = 6 − 3x b. 2y = 3x + 6 c. 3y = 9 − 2x d. 3y = 2x + 9

3. Let be a function that models the temperature change in a certain valley from 6:00 PM one day to 8:00 AM the following morning. Let the origin represent the temperature at 6:00 pm. ________________ ________________ a. Find, and then sketch, the first and second derivatives of on

The linear equation is y-2.68=m(x-2006). The slope m=(2.68-1.80)/(2006-1975)=0.0284, therefore the formula of the mean average of gas is: y-2.68=0.0284(x-2006) OR y=0.0284x-54.2904 (slope-intercept form) Can you tell me what the x represents??? Thank you

(See attached file for full problem description) Is this function analytic? Why? I can't find the value to show it.

(See attached file for full problem description) --- 1. Find the domain of f: f(x) = (x - 1) / (1 - 4x)1/2. 2. If f(x) = x1/2 and g(x) = |x|, find fg, f/g, and their domains. 3. Given g(x) = x2 + 3 and f(x) = (x - 3)1/2, find fog(x), gof(x), and fog(-4). 4. Graph f(x) = | (x+1)2 + 2 |. Use rules of transformation

Perform the indicated operation and simplify. See attached file for full problem description.