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Basic Algebra

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.

Groups and Integers

Let m be the smallest positive integer such that @^m=E for all @eS_n. Show that m=lcm(2,3,4,5,...,n). note: e denotes element of

Simplifying Expressions : Number Properties

Simplify each of the following expressions further and identify the number property(ies) used in each. 1. 2 x (15+8)= (2 x 15)+ (2 x 8)= 2. 5/2 x (3/4 x 2/5)= (5/2 x 2/5)x 3/4=

Binomial Expansion : Finding Coefficients

Please see the attached file for the fully formatted problems. Find the following: a) The coefficient of x in the expansion of b) The coeffiecient of in the expansion of c) The coefficient of in the expansion of d) The coefficient of in the expansion of is equal to the coefficient of in the

Arithmetic / Geometric Progressions

Three numbers are in arithmetic progression. The sum of the three numbers is 30 and the sum of their squares is 398. What are the three numbers? b) An arithmetic series is such that its first term is a and its third term is b. The sum of the first n terms is Sn . Find S4 in terms of a and b. Given that S4, S5 , S7 are con

Induction

Prove by induction where n is a positive integer. (The questions are attached).

Dependent variables

Find a new dependent variable such that the equation becomes linear in that variable. Then solve the equation: 1/(y^2 + 1) y' + 2/x tan^-1 y =2/x

Exact equations

First determine if the equation is exact. If it is exact, find the general solution, or at least a relation that defines the solutions implicitly: [cos(x^2 + y) - 3xy^2]y' + 2x cos(x^2 + y) - y^3=0

Algebra problem and rectangles

If the perimeter of a rectangle is 10 inches, and one side is one inch longer than the other, how long are the sides? Can you show me the steps to take to work out this and similar problems.

Investigation (Diagonals in a Rectangle)

Diagonals in a Rectangle. In the case of a 2 X 2 rectangle, or a 3 X 5 rectangle, we can simply count. However, can we make a decision about a 100 X 167 or a 3600 X 288 rectangle? In general, given an N X K rectangle, how many grid squares are crossed by its diagonal?

Algebra - Circle center, radius, equation

The endpoints of the diameter of a circle are P=(-3,2) and Q=(5,-6) Find: (i) the center of the circle (ii) The radius of the circle (iii) the equation of the circle.