Share
Explore BrainMass

Basic Algebra

Solving Quadratic Equations: Example Problems

1. Solve. Let f(x) = (x - 8)^2. Find x so that f(x) = 100. 2. Write a quadratic equation having the given numbers as solutions. 7, -4 3. Complete the square by filling in the two blanks so as to produce a true equation. x^2 + 8x + __ = (x + __)^2 x^2 + 8x + 64; (x+8)^2 x^2 + 8x + 16; (x+4)^2

I need help answering all these 4 questions

1) Consider the following nine integers: -4, -3, -2, -1, 0, 1, 2, 3, 4 Which of these integers has an absolute value greater than 1? 2) Evaluate each expression using a=-1, b= 2, and c=-3. (a-c)(a+c) 3) Married filing jointly. The value of the expression 8440+0.25(x-61,300) is the 2006 federal income ta

Simplify expressions. Solve equations and inequalities.

1) A scuba driver at sea level descends 80 feet, rises 25 feet, descends 12 feet, and then rises 52 feet where he will do a safety stop for five minutes before surfacing. At what depth did he do his safety stop? For questions #2 and #3, please assume the following when solving the following expressions: a = 3 b = -5

Factoring a quadratic with leading coefficient greater

Factor the given quadratic equations. 3y^2+22y+24 3x^2-17x+22 5x^2+22x+8 Enclosed is an attachment with a sample of the type of explanation I'm getting, which I do not still understand after reviewing the explanation. The explanation seems very confusing. Please provide a more complete explanation that I can ea

Algebra: direct and inverse variations. Probability of event

1. A shipping company is shipping cargo by truckloads. The number of miles per gallon the truck averages goes down as the weight of each load goes up. What is the relationship between the miles per gallon and the weight of the trucks' loads(which variation describes the data)? Direct, Inverse, Direct as nth power, Joint o

Math: Quadratic Equations and Completing the Square

Please provide step by step calculations for the following problems. 1. x^2+5x-7=0 The solutions are______ No solutions______ 2. A. solve 4x+x(x-2)=0 B. Find the x-intercepts of f(x)=4x+x(x-2). A. What are the solutions_____? B. What are the x-intercepts_____ 3. Solve for x 4x^2=-21x-5 A

Evaluate Relations as a Function: Example Problems

Understanding Functions Determine whether each relation is a function. In addition, provide reasons for identifying a relation as a function. i. {(3, 4), (5, 9), (9, 9), (2, 3)} ii. {(0, 0), (0, 1), (1, 4), (2, 4)} iii. {(2, 1), (4, 5), (8, 4), (1, 0)} iv. {(8, 3), (8, 0), (7, 7), (4, 7)} Solve the Point-Slope Form

Precalculus questions with polynomials, exponentials, etc.

1.) If f(x) = x^3 + 3x^2 - 1, which of these is true? I. f has domain all real numbers II. f is a 1-1 function III. f is onto the set of real numbers a. Only one (could be any one b. I and II c. II and II d. I and II e. All three 2) solve e^x +2x =7 3) If log 3 = 1.4 and log5 = 3.6, find log 45 4) Find t

Perform the following operations and simplify the results

Please provide solutions. 1. Simplify the following expression. 2. Simplify the following expression. 3. Perform the operations and simplify. 4. Perform the operations and simplify. ÷ 5. Perform the operations and simplify. 6. Perform the operations and simplify. x2 - 4

Linear Growth Models - population scenarios

Develop four different population scenarios for a town. As a group, you will decide on the name of the town and the initial population. You will graph the function for each population scenario and use your model to make some decisions about the population. 1) Decide on a name of a rural town. 2) Decide on an initial popula

Economic investment options

An investor is consider 4 different opportunities, A, B, C, or D. The payoff for each opportunity will depend on the economic conditions, represented in the payoff table below. Economic Condition Poor Average Good Excellent Inves

Elementary & Intermediate Algebra

Chapter 2 of Elementary and Intermediate Algebra. I do not understand the questions below: 1.What is the difference between an equation and an expression? How does knowing how to simplify an expression help with solving an equation? 2.When is it all right to cross-multiply when solving an inequality, and what are the rul

Homework Problem

A marketing group developing online ad space is offering two payment options: Option 1: $210 set up fee plus $10/inch of the ad Option 2: No set up fee but $25/inch of the ad. Let x = inches of the proposed ad, for example, x = 2 for a column ad that is 2" long. a) Write a mathematical model representing the total ad cos

Rational and Irrational Numbers and Expressions

1. Classify each number below as a rational number or an irrational number: a) Square root of 64 b) 9 c) -41.4 d) 46.97 e) -3 sqaure root 2 f) 24+9*(15-13)/6 g) -(1-23/1)2/1-4.5 2. Evaluate the expression when a=-6 and b=4 . a-9b 3. Evaluate the expression for c=-4 c^2 + 7c - 5 4. Write an ineq

Exponential Function Amounts

1. A laptop computer is purchased for $1500. Its value each year is about 80% of its value in the preceding year. Its value in dollars after t years is given by the exponential function V(t) = 1500(0.8)^t. A)After what amount of time will the computer's value be $900? B)After what amount of time will the computer's value be

Evaluate the exponential equation for three positive values of x

1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Use th

inequality on a plane Interval notation

1)47-(2x+5)< 3(x+2)+2 = 2)Can this equation be dependent or indepdent ? Is the system consistent or inconsistent? 5x +9y=-27 -5x+9y=27 3) Write interval notation fo rthe set (x|-2 > x>-10) 4)x<2 & y>-2x +4 5)What is the solution of the system? The solution is?in an order pair 7x +4y=2 & 3x-4y=-22 6)x+y<4 gr

Valuation

Vonnegut Company and Heller Company are two identical firms that agree to merge. Both have revenues of $1500, operating margin of 15%, a tax rate of 40%, investment rate of 10%, growth rate of 11%, 5 years of supernormal growth followed by zero growth thereafter, and a 9% cost of capital. a) what are the values of the compani

Example Algebra Problems and Solutions

2-3 paragraphs Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inch)

change-of-base formula

1. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this and show your work ln x - ln (x - 4) = ln 4 2. Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this and show your work. log x = 1 3. Solve. Where a

Algebra: Quadratic Equations and Word Problems

Apply the quadratic formula to find the roots of the given function, and then graph the function. 1. f(x) = x^2 - 4 2. g(x) = x^2 - x - 12 Factor the quadratic expression completely, and find the roots of the expression. 3. 20x^2 + 13x + 2 4. 49x^2 - 14x - 3 Complete the square, and find the

Algebra: Addition, Subtraction, Multiplication & Division

1. Find all the numbers for which the rational expression is undefined. 7/v-3= 2. Solve s/10 - 10/s =0 The solutions are______ 3. Y^2 - 49 y - 7 ------------ divide sign ------ = _______ 64y + 448 56 4. 5/x-9 divide sign 16/(x-9)^2 = _____ 5. Add 7/v+1 + 7/5v =____

Assistance with an Exponential Equation

Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph. Show your wok and state if the equation of the line is asymptotic to the graph (if any). y = 3-x Evaluate the exponential equation for three positive v

Exponential and Logaithmic Equations

1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph (if any). y = 3x - 4 2. Evaluate the logarithmic equation for three values of x that

Algebra: Solve, Simplify & Factorize

1. If an expression has two terms, check to see whether the problem type is the -------- of two squares, the sum of two ------ , or the ----------- of two cubes. 2. If an expression has four or more terms, try factoring it by--------------. 3. Factor the polynomial. bc + b + cd + d 4. Factor the polynomial. 64x9 -

Linear and Quadratic Equations

1.Bill can row 3 mph in still water. It takes him 3 hours 36 minutes to go 3 miles upstream and return. Find the speed of the current. Show your work. 2.Use the discriminant to determine whether the following equations have solutions that are: two different rational solutions; two different irrational solutions; exactly one r

Quadratic equations for x-interception

1. Use the quadratic formula to determine the x-intercepts (if any) of the following function. Then evaluate the function for several values of x, and use the resulting points to graph the function. Show your work. F(x) = 7x^2 - 28x + 28 2. Use the discriminate to determine whether the following equations have solutions t

Distance and measurements still have me stumped

1.Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable and please show your work. A plane flies 400 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wi

MTH - 209, 21 questions !!! Algebra Questions 1. Using the x, y graph plot the point 2. Give an ordered pair of numbers that satisfy the following equation: 3. For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: Line 2: (x, y) Line 1 Line 2 Both Lines Neither Line (-6, 7) (-2, 4) (0, -4) 4. Graph the line whose y-intercept is 3 and whose x-intercept is 2. 5. Graph the line. 6. Graph the line. 7. Graph the line with slope passing through the point . 8. Find the slope of the line graphed below (-3, 7) and (2, -6) 9. Graph the line 10. Graph the inequality below on the number line. 11. Find the y -intercept of the line whose equation is 12. Find the x-intercept and y-intercept of the line given by the equation 13. Find the slope of the line 14. A line passes through the point and has a slope of 3 Write an equation for this line. 15. Owners of a recreation area are filling a small pond with water. They are adding water at a rate of 35 liters per minute. There are 700 liters in the pond to start. Let W represent the amount of water in the pond (in liters), and let T represent the number of minutes that water has been added. Write an equation relating W to T, and then graph your equation using the axes below. 16. Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.75. If the monthly bill for 15 HCF is $24.01, what is the monthly bill for 11 HCF? 17. The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes), as shown in the figure below. The monthly cost for 47 minutes of calls is $14.97 and the monthly cost for 100 minutes is $21.86. What is the monthly cost for 57 minutes of calls? 18. Find an equation of the line that is parallel to the line and that passes through the point . 19. The sum of two numbers is 63. The larger number is 5 more than the smaller number. What are the large number and the small number? 20. In a family there are two cars. The sum of the average miles per gallon obtained by the two cars in a particular week is 65. The first car has consumed 56 gallons during that week, and the second has consumed 25 gallons, for a total of 1325 miles driven by the two cars combined. What was the average gas mileage obtained by each of the two cars in that week? 21. A motorboat travels 595 mi in 7 hours going upstream and 484 mi in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Algebra Questions 1. Using the x, y graph plot the point 2. Give an ordered pair of numbers that satisfy the following equation: 3. For each point in the table below, decide whether it is on Line 1, Line 2, both, or neither. Line 1: Line 2: (x, y) Line 1 Line 2 Both Lines Neither Line (-6, 7) (-2,