Solving Inequalities

Solve: -4 (x+6) < -4 -4x Is the answer, x< -10; x> -10; all real numbers or no solution? Please show step by step how to solve the inequality. Also, I came up with "x<0" but I do not know if this means "no solution" or "all real numbers" Can you please explain step by step h ...continues

Factoring, 4-terms, NOT factored by grouping

4-terms - NOT factored by grouping. Factor out greatest common factor. 2-terms together. Get down to 3 terms first. 4t(xt+yt)+4t(x+y)-24x-24y

Proof: Upper and lower limits

Please see the attached file for the fully formatted problems. Let be a sequence of real numbers. We define and I’m having trouble with the following three proofs: 1) Show that 2) Show that if the limit of only exists when , then . 3) Show that if , then the limit exists, and .

Linear Algebra : Vectors - Inner Products

Given a vector w, the inner product of R^n is defined by: =Summation from i=1 to n (xi,yi,wi) [a] Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T Show that x and y are orthogonal with respect to this inner product. Compute the values of ...continues

Linear Algebra: Vectors - Inner Product

Show that the functions x and x^2 are orthogonal in P5 with inner product defined by ( =sum from i=1 to n of p(xi)*q*(xi) ) where xi=(i-3)/2 for i=1,...,5. Show that ||X||1=sum i=1 to n of the absolute value of Xi. Show that ||x||infinity= max (1<=i<=n) of the absolute value of Xi. Thank you for your explanation.

Scientific notation

A human being has about 2.5 X 10(to the 13th power) red blood cells in her bloodstream. There are about 2 white blood cells for every 1,000 red blood cells. How many white blood cells are in a human's bloodstream? Please show your answer in scientific and standard notation.

Scientific notation

A number written in scientific notation is doubled. Explain why the exponent of 10 may or may not change.

Polynomials

Here is what the problem asks for: Give an example of a polynomial function f of degree 5 such that the only real roots of f(x) are -2,1,6 and f(2)=32. Show that your example works and leave f(x) in factored form.

Rational Expression : Addition

Please see the attached file for the fully formatted problems. Add the rational expression 5x/x-3 + 2/x - 6/x^2-3

Add the rational expression

5/x-3 + 2/x-2 - 6/x+1