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# Basic Algebra

### 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.

Algebaic word problems (please see attachment)

### Algebra word problems

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. x - 2y = 6 4--------------find the slope of each line. 5--------------- 6---------------Graph the line with the given point and slope. The line through (-2, 5) with slope -1 7--------------- Draw l1 through (-4, 0) and (0, 6). What is the slope of any line parallel to l1? Draw l2 through the origin and parallel to l1. 8-----------------Write an equation for each line. Use slope-intercept form if possible. 9------------ 10-------------Find the slope and y-intercept for each line that has a slope and y-intercept. X+2y=3 11----------- Y+4x=8 12----------determine whether the lines are parallel, perpendicular, or neither. Y=x+7 Y=-x+2 13------------Write each equation in slope-intercept form. Y+3=-3(x-6) 14------------Find the equation of the line that goes through the given point and has the given slope. (-1, -5), -8 15-------¬Find the equation of each line. Write each answer in slope intercept form. The line is parallel to -3x + 2y = 9 and contains the point (-2, 1). 16------------Find the equation of each line in the form y = mx + b if possible. The line through (3, 2) with undefined slope 17----------------Write a formula that expresses the relationship described by each statement. Use k for the constant in each case. m varies directly as p. 18------------ Write a formula that expresses the relationship described by each statement. Use k for the constant in each case. u varies inversely as n. 19-----------------Find the variation constant, and write a formula that expresses the indicated variation. c varies inversely as d, and c = 5 when d = 2. 20-------------------- Solve each variation problem n varies directly as q, and n = 39 when q = 3. Find n when q = 8.

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.

### laws of vector algebra

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

### Time Card & Net Pay Calculation

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

### Average Annual Return Equation

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.

### What are the lengths of the sides of a rectangle?

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?

### linear equation mathematical models

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?

### Solving Quadratic Equations and Substitutions

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 formula D(p) for the monthly demand c) Find D(3000)

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

### "Squares everywhere" Determine the Perimeter

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.

### Equations and inequalities

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

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

### Factoring by grouping

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

### Difference of Two Squares formula Discussion Question.

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?

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?

### An interest word problem using the polynomial.

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%

### Solving for Unknowns

(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

### Several algebra problems

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

### Mathematics - Algebra - Transforming Graphs

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?

### Mathematics - Algebra - Word Problem

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

### An expression for expenditures and receipts

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

### Algebra - Equations and Matrices

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

### Quadratics: Appendix F - Ticket Sales Living in or near a metropolitan area has some advantages. Entertainment opportunities are almost endless in a major city. Events occur almost every night, from sporting events to the symphony. Tickets to these events are not available long and can often be modeled by quadratic equations. Application Practice Answer the following questions. Use Equation Editor to write mathematical expressions and equations. First, save this file to your hard drive by selecting Save As from the File menu. Click the white space below each question to maintain proper formatting. 1. Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the ... (See the attached file)

Looking at graphs of quadratics: (See the attached file)

### Mathematics in Investing Rate

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

### Cumulative Equation Problems

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