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# 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

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

### Dave Bidini has saved 20000 for a down payment on a home and plans to save another 5000

Dave Bidini has saved 20000 for a down payment on a home and plans to save another 5000 at the end of each year for the next 5 yrs. He expects to earn 7.25% compounded annually on his savings. How much will be have in 5 years time? Calculate the FV of an ordinary annuity consisting of quarterly payments of 1200 for 5 yrs if t

### 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 -

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