Rationalize the denominator

Rationalize the denominator. (1+ (2^1/2))/(3- (5 x 2^1/2))

Solve the Algebraic Equation

Please see the attached file for the fully formatted problem. Solve the algebraic equation. (x-6)^1/2 = (x+9)^1/2 - 3

Graph and label the vertex and the line of symmetry

Graph and label the vertex and the line of symmetry. See attachment.

Quadratic Function: Vertex, Symmetry and Maximum/Minimum Value

For each quadratic function find: a. the vertex b. the line of symmetry c. the maximum or minimum value Then graph the function. Please show your work. y = -4x^2 - 7x + 2 Please see the attached file for the fully formatted problems.

Solving for a variable in a logarithmic equation.

Solve for w. log (3w-1) + log w = 1

Solving an equation in a complex field.

Solve the following equation. x^4 + 13x^2 + 36 = 0

Logarithm Equation: Solve for x

Find a solution for the following equation logx + log(x-3)-1=0

Finding a Polynomial Function

Find a polynomial function of the attached graph and find solutions to the following parts.

Proving an inequality.

Prove the inequality. (1+x)^3 >= 1+3x for x>=0

Dependent and independent variables

Suppose you were interested in determining the effect of lighting on the morale of your employees. How would you go about obtaining data for your research? What would be your dependent and independent variables? How would you determine the ideal amount of lighting? Please use a real life situation, like an Insurance office ...continues