Quadratic Equation : Proof by Completing the Square

1. Prove the Quadratic Formula by completing the square on ax^2+bx+c=0 2. A picture that is 14 in by 20 in is to have an even border. If the area of the picture and the border is 352 in^2, how wide will the border be?

Business Math : Revenue and Total Cost

The Revenue and Total Cost eqations for a glove company are R(x)=35x and C(x)=0.25x^2 + 30.5x + 10, where x is in hundreds of gloves and R(x) and C(x) are in thousands of dollars. What is the Revenue and production Cost for 700 gloves, the profit for this problem, the number of gloves that will produce the maximum profit, the ...continues

Graphs : Regression and Forecasting

Using the following information answer the following questions. Year Population 1860 379, 994 1870 560, 247 1880 864, 694 1890 1,213, 398 1900 1,485, 053 A) What is the linear regression function for this data? Write all decimal points. B) What does the model predict ...continues

Solve the Equations

(x-4)/2 - (3x+1)/3 = (4y+5)/6 (three fractions) 7(3-4x)-10(x-2) = 19(5-2x)

Quadratic Equations : Discriminants and Solving

For the equation 24x^2 + 68x + 28 = 0 a) Find the discriminant b) If the discriminant tells you that you can factor, do so. c) Solve the equation by completing the square(HINT: at some point during the process, you will come to a point which looks like (x+(17/12))^2 = (121/144) d) solve the equation by using the quadrati ...continues

Factoring

Factor 15x^2y^3 - 20xy^4 - 5xy^2

The length of a rectangle is 3 less than twice its width.

The length of a rectangle is 3 less than twice its width. If the area of the rectangle is 65 square inches, find the dimensions of the rectangle.

Graphing a Piecewise Function

Graph the piecewise function: f(x) = {x+1 if x less than or equal to -2 {-1 if x>-2

Solving functions

Given f(x)= 4x squared - 3x + 2 and g(x)= 3x - 2, find each of the following. simplify the expression if possible. a. f(-5) b. f(x+h) - f(x)/ h c. (f o g)(x)

Graphs : Equations of Lines through a Point

Suppose point P has coordinates (1/2 , 2/3) a. What is the equation of the vertical line through P? b. What is the equation of the horizontal line through P?