### Quadratic formula and Completing the square.

Solve the equation x2 + 8x - 2 = 0 using both 1) The quadratic formula 2) Completing the square Write a paragraph or two comparing and contrasting the two methods. Explain which method you prefer and why.

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Solve the equation x2 + 8x - 2 = 0 using both 1) The quadratic formula 2) Completing the square Write a paragraph or two comparing and contrasting the two methods. Explain which method you prefer and why.

Marginal revenue. A defense attorney charges her client $4000 plus $120 per hour. The formula R =120n + 4000 gives her revenue in dollars for n hours of work. What is her revenue for 100 hours of work? What is her revenue for 101 hours of work? By how much did the one extra hour of work increase the revenue? (The increase i

Complete each ordered pair so that it satisfies the given equation. 1---- y = 2x + 5: (8, ), (-1, ), ( ,-1) Use the given equations to find the missing coordinates in the following tables. 2------ y= -x+4 X Y -2 0 2 0 -2 3-------------Graph each equation. Plot at least five points for each equation.

Draw appropiate figures to give geometric proofs for the following laws of vector algebra: (a+b)+c = a +(b+c) lambda(a+b) = lambda(a) + lambda (b) : lambda is any scalar a(b+c) = ab + ac .................................................................... a,b,c do not need to be coplanar. Full solution please

Practice Questions Complete the following time card. Janice earns time and a half overtime when she works more than eight hours on a weekday or on Saturday. She earns double time on Sundays and holidays. Calculate Janice's net pay if she earns $9.75 per hour, is married, and claims one withholding allowance. Challenge Proble

Venture capital. Henry invested $12,000 in a new restaurant. When the restaurant was sold two years later, he received $27,000. Find his average annual return by solving the equation 12,000(1 + r)2 = 27,000.

Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

A butcher charges $2.80 for 2.5 pounds of hamburger. How do I write a mathematical model (linear equation) that allows the calculation of the cost of the hamburger based on buying any number of pounds?

1. An interesting method for solving quadratic equations came from India. The steps are: (a) Move the constant term to the right side of the equation (b) Multiply each term in the equation by four times the coefficient of the x2 term (c) Square the coefficient of the original x term and add it to both sides of the equation (d)

Demand for pools. Tropical pools sells an above ground model for p dollars each. The monthly revenue for this model is given by the formula R(p) = -0.08P^2+300P Revenue is the product of the price p and the demand (quantity sold) a) Factor out the price on the right- hand side of the formula b) Write a f

The figure has been divided into nine squares, the smallest one, darkly shaded, has sides of length one and the lightly shaded squares has side of length x. Determine x and also determine the perimeter of the large figure. See Attached

See the attached file. Solve each equation using the quadratic formula. 1. x^2 + 5x + 2 = 0 2. 3x^2 = 6x - 1 Show your work step by step. Compute the discriminant. Then determine the number and type of solutions for the given equation. 1. 4x^2 - 2x + 3 = 0 2. 3x^2 + 4x - 2 = 0.

Show your work step by step. Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Write and factor the trinomial. 1. x^2 + 16x 2. x^2 + 5x 3. x^2 + 4 x 5 Show your work step by step. Solve each equation by completing the sq

Factor out the common factor. (5x - 2)2 + (5x - 2) Completely factor the expression. x4 - 3x3 + x2 - 3x Write the rational expression in simplest form. 4x2y xy - y Write the rational expression in simplest form. 9x2 + 9x 8x + 8 Write the rational expression in simplest form. x2 - 9 3 - x

What is factoring by grouping ? When factoring a trinomial by grouping , why is it necessary to write the trinomial in four terms ?

Some people say that the Difference of Two Squares formula helps them to multiply large numbers without a calculator. How would you use this formula to multiply 201 by 199? Find at least one more pair of numbers that can be multiplied this way.

Choose three integers a,b,and c.(negative numbers are welcome ).Now use a,b,and c to create a trinomial ax^2 +bx+c. Can you factor this trinomial? How would you create a trinomial that will factor?

Please see the attached file.

P dollars is invested at an annual interest rate R for one year. If the interest is compounded semi-annually, then the polynomial P (1+ r/2)^2 represents the value of the investment after one year. Re write this expression without parentheses. Evaluate the polynomial if P = $200 & R = 10%

(1) A forensic scientist uses the expression 72.6 + 2.5T to estimate the height in centimeters of a female with a tibia of length T centimeters. If a female skeleton has a tibia of length 32.4 cm, then what was the height of the person? Find the length of your tibia in centimeters, and use the expression from this exerc

2. 3. 4. Find the coordinates of the x-intercept. 2x + y = -6 (-6, 0) (0, -3) (0, -6) (-3, 0) 5. 6. Janet invested $26,000, part at 6% and part at 3%. If the total interest at the end of the year is $1,080, how much did she invest at 6%? $11,000 $10,0

I understand that when you transform y = f(x) to y = f(ax) it is a stretch in the x direction of scale factor 1/a, but I can't find any reasoning as to why the scale factor is 1/a and not just a. Can you explain?

You are a high school math teacher and are introducing matrices to the classroom next week. It is very important to you to make a connection between the real world and this topic, so you decide to research in which applications matrices are used. To your surprise, you find several very useful applications, such as decoding and e

How do I create an expression for expenditures and for receipts on this problem? How many chips must be sold to produce a profit? To make x thousand computer chips requires fixed expenditures of $352 plus $42 per thousand chips. Receipts from the sale of x thousand chips amount to $130 per thousand.

I have a customer that is purchasing purchasing a item packed 6,0000 per case @ 19.00 per case. they are buying 281,000 cases per year. I would like to sell them our new items that is packed 10,800 per case. 1. How many cases would be new items reduce their inventory by 2. If I sold the new item for $32.00, how

See Attached Exercise 5.5 25. Supply and Demand The supply function for a product is given by p=q²+2q+122 and the demand function for this product is p=650-30q, where p is the price in dollars and q is the number of hundreds of units. Find the price that gives market equilibrium and the equilibrium quantity. 29. Break-Ev

Hi can some help me with the below questions? 1. What does 200% mean? If you have a job making $5 an hour and you receiva a 200% raise how much will you be making after the 200% raise? 2.Is is better to invest your money where it will earn interest at a rate of 7% per year or to invest it where it will be multiplied by 2/3

Ch. 10 Cumulative Problems 1) solve (X - 4)2 = 3 2) solve 5 (X - 2)2 = 3 3) solve - 9 (X - 3)2 = - 7 4) solve by completing the square 2 X2 - 8 X - 9 = 0 5) solve by completing the square 4 X2 + 2 X - 3 = 0 6) solve by using the quadratic formula 4 X2 - 3 X + 3 = 0 7) solve by using the quadratic formula 5