Algebra - find the equation of a line

Find the equation of a line passing through (1,-3) and parallel to x+y=2.

Algebra - circles,, center and radius

(a) Consider the circle: (x+2)squared + (y-1)squared =9. Find the center and radius of the circle. (b) Consider the circles: x squared + y squared + 4x-4y-1=0 x squared + y squared -2x+4y-4=0 (i) Find the center of each circle. (ii) Find the distance between the centers if the circles are plotted on the same rectangu ...continues

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.

Solution to a recursive equation

Given a_1=1,a_2=2, a_(n+1)=2a_(n)-a_(n-1),n>=2, find a_n, for n>=1

Linear algebra

Q.63. For each i,j ≥ 0, define P (i,j) as follows : P (0,0) = 0, and , for (i,j) ≠ (0,0) , P(i,j) is the least integer ≥ 0 that is not equal to P (k,l) for any (k,l) with k < i and l = j , or with k = I and l < j. Find P (2987,6592).

Quadratic Equations

Solve this equation: 3x²- 5x -1 = 0

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 ...continues

Proofs by induction

Show by induction that: a) Sum(n^2/[(2n-1)*(2n+1)],n=1..) = n(n+1)/[2*(2n+1)] b) Sum( r/(r-1)!, r=1..n) = 1-1/(n+1)! c) n^3+3n^2-10n is divisible by 3 d) 4^(2n+1) + 3^(n+2) is divisible by 13 See attached file for full problem description.

Roots of a rational function

Q: Consider the polynomial function f(x)=4x^4-13x^2+9 a. What is the maximum number of real roots you would expect and why? b. Find the real roots of the polynomial function. Using factoring by substitution, or substitution and the quadratic formula to find the real roots

Asymptotes and domain of a rational function

Q: Determine the vertical asymptote(s) and domain of the following function: f(x)=[4x^2+3x]/[4x^2+7x-2]