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# Basic Algebra

### Apply the Discriminant, Quadratic Equations and Their Applications

Determine whether the following equations have a solution or not? Apply the discriminant, are the solutions real, repeated real, or complex? Steve traveled 200 mile at a certain speed, had he gone 10 mph faster, the trip would have taken one hour less, find the speed of his vehicle?

### Quadratic Equations and Negative Discrimants

What type of solution do you get for a quadratic equation where D<0? Give reasons for your answers also provide an example of such a quadratic equation and find the solution of the equation.

### Solving Equations

Please see the attached file for the fully formatted problems. 1. The volume of a cube is given by V = s3, where s is the length of a side. Find the length of a side of a cube if the volume is 800 cm3. Round the answer to three decimal places. Answer: Show your work here: a) Show the steps that you would take

Please see the attached file for the fully formatted problems. 1. 2. 3. 4. Solve algebraically and check your potential solutions: 5 Suppose that N= models the number of cases of an infection, in millions, of a disease x years from now. a) Approximately how many cases of the infection will there

Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: Integers Rational numbers Irrational numbers Do you find any striking difference between the graphical representation of quadratic equations and linear equations? Explain the differences and comment on the responses posted

### Translate the following into a quadratic equation and solve it

Translate the following into a quadratic equation and solve it, The lenght of a rectangular garden is three times it's width, if the area of the garden is 75 square meters, what are it's dimension?

### various problems on algebra and geometry

I need help in completing the following exercises. I need to use the Equation Editor in Microsoft® Word to do these problems, then submit a Word document, showing the work and answers. Attached you will find the problems to be completed. Please help me by actually working the problems with microsoft Equation Editor & replying

### Basic Algebra Problems

Section 1.1 Exercises Pages 10-12 Problems 44, 48, 92, 98, 110 Write each interval of real numbers in interval notation and graph it. 44. The set of real numbers greater than or equal to _1 and less than 6 48. The set of real numbers less than or equal to _4 Consider the following nine integers: -4, -3, -2, -1,

### Factoring Expressions and Solving Radicals

1) Simplify: (4+ √48) / 4 2) Find all real solutions: x^2= 81 3) Solve: 3√(x-2) = 4 4) Solve: 3x^2+5=11 5) Solve by factoring: x^2-4x-5=0 6)Solve: x^2= 49/36 7) Find the perfect square trinomial whose first two terms are q^2+7q. 8) solve using the quadratic formula: 2

### Solving Equations with Radicals and Exponents

Problem #1 Surface area of a cube. The formula A=6V^2/3 gives the surface area of a cube in terms of its volume V. What is the volume of a cube with surface area 12 square feet? Problem #2 Sailboat Speed. The sail area-displacement ratio S provides a measure of the sail power available to drive a boat. For a boat with a

Problem #2: sqrt(3) / sqrt((6) - 1) + sqrt(3) / sqrt((6) - 1) Problem #3: 3 + sqrtx^2-8x) = 0 Problem #4: X^-2=4

### Radicals to Determines Areas of a Triangles

Problem #1 sqrt(2t^5) * sqrt(10t^4) Problem #2 (3-2*sqrt7)(3+ 2*sqrt7) Problem #3 Area of a triangle. Find the exact area of a triangle with a base of sqrt(30) meters and a height of sqrt(6) meters. Note: sqrt is the square root

### Writing a Word Problem from a System of Equations

Details: From the following augmented matrix, first write the system of equations that represents the augmented matrix and then create a real-world word problem that would represent these equations and their unknowns. Be creative. Do not use word problems that are in the assignments or course material.

Please see the attached file for the fully formatted problems. 1. Simplify. 2. Simplify. Write your answer with only positive exponents. A) B) C) r10 D) r2 3. A triangle has sides 2x - 5, 3x + 1, and 4x + 2. Find the polynomial that represents its perimeter. A) (2x - 5)(3x + 1)(4x + 2)

### Basic Algebra Exam

1. Solve. 3(x - 2) - 2x = x - 6 A) Identity B) 0 C) No solution D) 1 2. Find the GCF for 21, 28, and 35. 3. Find the LCM for 6, 28, and 48. 4. Solve the following system of linear inequalities by graphing. x + 2y <= 3 2x - 3y <= 6 5. Evaluate. 6. Evaluate. (15 - 5) ÷ [(12 ÷ 2 ? 2)

### Basic Algebra : Graphs

Problems #'s 12, 16, 18, 20, 26, 28, 30, 32, 46 these I need help completing Find the slope and y-intercept of the line represented by each of the following equations. 12. 2x - y = 6 Write the equation of the line with given slope and y-intercept. Then graph each line using the slope and y-intercept. 16. Slope: -2

### Product and Single Powers Expressed

1. Express the following product powers of t as a single power of t 2. Write without parenthesis 3. 4. Simplify without negative exponents 5. Simplify without negative exponents 6. Multiply and simplify (4z - 2u - 2)(6z - 5u + 6) 7. Write in simplest form without parentheses

### Solving Equations

Please show work so that I can get a better understanding. Thank you. (For question 1 - find the value of y in each the formula if x = -3) 1.) y + 1 = 2(x - 5) (For question 2 - Fill the tables using the given formulas) 2.) y = 10x + 100 x y -20 -10 0 10 (For question 3 - Translate ea

### Inequalities, quadratic equations and intercepts

What is the situation when two inequalities have no solution? What is the meaning of the VERTEX of the quadratic equation? Why does the graph of a quadratic intercept the y-axis at only ONE point?

### Word Problems, Quadratic Equations and Inequalities

Word Problem Diagonal Brace: The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures &#8730;6m. Find the width and height. ************** Graph each parabola. y = -1/3*(x^2) + 5 ************** Find the vertex and intercept for each parabola. g(x) = x^2 +x-6 **

### Word Problems and Quadratic equations and inequalities

Solve each equation: 1) 2y^2 - 3y -6 = 0 2) (x-10)(x-2) = -20 Find all real or imaginary solutions for each equation: 1) W^2=-225 2) 3v^2+4v-1=0 3) sqrt (7x+29) = x+3 Word Problem Time to Swing. The period T (time in seconds for one complete cycle) of simple pendulum is related to the length L (in feet) o

### Exponential Derivatives of Composite Functions : Chain Rule and Leibnitz Notation

Please see the attached file for the fully formatted problems. The Chain Rule states how to differentiate composite functions If and be differentiable, then the derivative of the composite function is In Leibnitz notation, if and , then . For example, or The derivative of the exponential function is

### Choose one equation of each type: linear, quadratic, polynomial, rational, exponential, and log. Plot each equation on the same graph. Discuss and compare the appearance of each graph. Describe the plot's shape, the effect of any constants, and behavior for very large or very small x or y.

Choose one equation of each type: linear, quadratic, polynomial, rational, exponential, and log. Plot each equation on the same graph. Discuss and compare the appearance of each graph. Describe the plot's shape, the effect of any constants, and behavior for very large or very small x or y.

### A vendor sells hot dogs and bags of potato chips.

Please see attached file for full problem description. A vendor sells hot dogs and bags of potato chips. A customer buys 3 hot dogs and 4 bags of potato chips for \$10.25. Another customer buys 5 hot dogs and 3 bags of potato chips for \$12.50. Find the cost of each item. \$ 1.25 for a hot dog; \$ 1.75 for a bag of potato ch

### Solving Equations and Word Problems

Please see attached file for full problem description. Please show me how to get solution for problems. 1. 2. Winston can mow his dad's lawn in 1 hour less than it takes his brother Willie. If they take 2 hours to mow it when working together, then how long would it take Winston working alone? 3. Solve equation f

### Formulate three real-life problems that can be translated to quadratic equations.

Formulate three word problems from day-to-day life that can be translated to quadratic equations.

### Determining the Number of Solutions to A Quadratic Equation and Finding the Domains of Functions

1) What determines how many solutions you would have in a quadratic equation? Please explain. 2) How do you figure out the domain in a function?

### Principle of Mathematical Induction

Theory of Numbers (XVI) Principle of Mathematical Induction Prove that if n is an odd positive integer, then x + y is a factor of x^n + y^n. (For example, if n = 3, then x^n + y^n = ( x + y )( x^2 - xy + y^2 ) ) See the attached file.

### Basic Algebra Problems - What is the place value of 5?

I need help in completing the following exercises. I need to use the Equation Editor in Microsoft® Word to do these problems, then submit a Word document, showing the work and answers. (problems will be used as guide for problems I must complete on asignment) Please see attached file for full problem description. For the de

### Solving Polynomials

Please see the attached file for the fully formatted problems. Because 7 = -12 is not a true equation, the equation has no solution. If this is correct, state that there is no solution. If not, explain in detail why it is not correct, and supply the correct answer. Finally, create an equation that includes at least one set