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# Basic Algebra

### Step by Step Algebra Solutions

Solve 2(x-4)=2[x-3(x-1)+2] Solve x-2 - x+5 =5x-2 3 6 9 The cell phone service for the CEO of a small company is \$39.99 a month plus \$0.10 per minute for long distance. In a month when the company's phone bill was \$75.19, how many minutes of long distance did the CEO use? Set up an equation a

### Equations

Determine whether the following equations have a solution or not? Justify your answer. a) 5x2 + 8x + 7 = 0 b) (7)1/2y2 - 6y - 13(7)1/2 = 0 c) 2x2 + x - 1 = 0 d) 4/3x2 - 2x + 3/4 = 0 e) 2x2 + 5x + 5 = 0 f) p2 - 4p + 4 = 0 g) m2 + m + 1 = 0 h) 3z2 + z - 1 = 0 If x = 3 and x = -5, then form a quadr

### Basic Algebra Simplest Form

Please see the attached file for the fully formatted problems. Name: __________________________ Date: _____________ 1. Write in simplest form. 2. Simplify. 3. Multiply. 4. Solve. 5. Add. Express your answer in simplest form. 6. What values for x must be

### Algebra

Please see the attached file for the fully formatted problems. Problem #6 Write the following geometric expression using the given symbol. times pi times the cube of the radius (r) Problem #7 Do you think multiplication is distributive over subtraction? ½ (16 - 10) and ½ x 16 - ½ x 1

### Algebra Compound Fractions in Lowest Terms

2. Write in lowest terms 3. Express compound fraction in lowest terms 4. Write as a single rational expression 5. Add and simplify 6. Reduce to lowest terms 7. Reduce rational expression to lowest terms 8. Solve for z 9. Solve all values of w 10.

### Solving Equations and Inequalities

1. Solve for X: 12 - 3(x+1) = x+17 The value of x is a. A number less than -2 b. At least -2 but less than 0 c. At least 0 but less than 2 d. At least 2 but less than 4 e. At least 4 2. Solve for P: 7(3P+4) = 8(2P+5) + 13 The value of P is a. a number less than 0 b. at least 0 but less than 3 c. at least 3 bu

### Algebra Word Problems and Questions

Please see attached file for full problem description. Please show all work when solving the two problems. 1. Why bother factoring a quadratic equation before you solve it? 2. Why are there usually two solutions in a quadratic equation? 3. Under what conditions would one or more solutions of a rational equation be un

### Word Problems with formulations and calculations

I need the following word problems answered and explained with formulations and calculations. Solve each inequality. State the solution set in interval notation and sketch its graph. -3/5<1/5-2/15w<-1/3 -3<or equal x <or equal -1= Solve by using an inequality. 1. Car Selling. Ronald wants to sell his car through

### Amount of concentration in chemicals

Chandra has 5 liters of a 24% solution of sodium hydroxide in a container. What is the amount and concentration of sodium hydroxide solution she must add to this in order to end up with 8 liters of 27% solution?

### review of factoring method

See attached file for full problem description. Factor 1. 2x^2 -19x +25 2. 60w^3 + 85w^2 -25w 3. 125 + 27z^3 4. Find the least common multiple of the two expressions: 9t^3wy and 5t^4w 5. Factor: uw - 6z - wz + 6u 6. Factor: -2x +wx - 4w +2w^2 7. Factor quadratic expression: t^2 +10

### Logarithms and Simultaneous Equations

1. Given that x and y are both positive, solve the simultaneous equations log(xy) =7 log(x/y) =1 Answers given: x = 10000 y = 1000 2. log (p - q +1) =0 log (pq) + 1 = 0 Show that p = q = 1/square root 10 3. Solve the following equation for x: 2^2x + 1

Please see attached file for full problem description. 1. Evaluate , if possible. 2. Use a calculator to approximate to the nearest hundredth. 3. Simplify. 4. Simplify. 5. Simplify. Assume x represents a positive number. 6. Simplify. 7. Simplify. 8. Simplify. 9. Simplify.

### Abstract Algebra: Mappings and Partitions

Suppose that f is an onto mapping from A to B. Prove that if { B_lambda } , lambda is an element of the set β, is a partition of B, then { f^-1( B_lambda)}, lambda element of β, is a partition of A. Don't get confused by the index "lambda". If it helps, you can take the partition to be B1,B2,...,Bn. The reason they have tha

### Abstract Algebra : Equivalence Relations

Please help with the following problem. A relation R is defined on the set Z of all integers. In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and list at least four members of each. 1- xRy if and only if x^2+y^2 is a multiple of 2. **Write x^2+y^2 as (x+y)^2-2xy 2- x

### Word problems with time and distance

1. Calculate distance in inches that a bicyclist travelling 35 mph moves in 1/125 of a second? 2. Notice the bicyclist is riding along a white line. Suppose the length of this white line captured in a photograph is 14 ft. Use proportions to calculate the distance the bicyclist will appear to move in a photograph of this sc

### Basic Mathematical problems (Algebra) Help

Attached you will find the problems to be completed. 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. 1. List the factors of each of the following numbers. 66 Use the following list of n

### Simplifying Polynomials and Coefficient Operations

What is the basic principle that can be used to simplify a polynomial? What is the relevance of the order of operations in simplifying a polynomial? What operations can you associate with coefficients? What operations can you associate with exponents?

### Algebra Equations

See attached file for full problem description.

### Applications of Exponential and Logarithmic Functions

Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents. Find the hydrogen ion content of a substance of your choice. Using this hydrogen ion content, show how to find the pH of the substance using th

### Algebra : Applications of Logarithms

Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents. Find the hydrogen ion content of a substance of your choice. Using this hydrogen ion content, show how to find the pH of the substance using th

### graphing inequality and evaluate function

Please see the attached file for complete description Sec 7.4 In exercises 8, we have graphed the boundary line for the linear inequality. Determine the correct half-plane in each case, and complete the graph. See attached file for full problem description. y > 3 Graph each of the following inequalities. 16. 4x + y > =

### Exponential and Logarithmic Functions: MTH133: Unit 5 Individual Project - B

See attached file for full problem description. 1) Find the domain of the following: a) f(t) = log(t -5) b) g(x) = 5 *e^x c) g(x) = ln(t + 4) d) g(t) = 5^t 2) Describe the transformations on the following graph of f(x) = e^x. State the placement of the horizontal asymptote and y-intercept after the transformation. Fo

1. Work with a partner to decide all values of b in the following equations that will give one or more real number solutions. A. 3x^2 + bx-3= 0 B. 5x^2 + bx+1= 0 C. -3x^2 +bx-3= 0 D. Write a rule for judging if an equation has solutions by looking at it in standard form. *What is your conclusion?* 2. Solve the fol

### Logarithmic functions

Logarithmic functions have an interesting history. Although John Napier is credited for popularizing logs, there are earlier developments that include another mathematician who developed logs earlier and independently. Furthermore, logarithms became especially important for allowing difficult calculations prior to the developmen

### Examples of scientific data that are measured and reported using log scales

Many different kinds of data can be modeled or measured easily using exponential and logarithmic functions. For example, consider ideal gases: Pressure versus volume give a curved plot, but a log graph of pressure versus volume provides a linear plot that is easier to interpret. Log plots are also used in the study of the rates

### Various Algebra Problems

Write in simplest form 1) 5x - 20 ___________ 7x - 28 2) 9x^10 _________ 63x^18 Multiply 3) 7x^2 16 ____ * ____ 4 x^4 4) 2x - 4 3x _____ * _____ x^2 - 4x 2 - x Divide 5) 2x - 6

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 tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffin

### Metric Measurements for a Spa

Suppose you wish to build a spa on a wood deck. The deck is to be built 4 ft above level ground. It is to be 50 ft by 30 ft and is to contain a spa that is circular with a 14-ft diameter. The spa is 4 ft deep. a. How much water will the spa contain, and how much will it weigh? Assume that the spa itself weighs 550 lb. b.

### Variable Representing Positive Real Numbers

Find the square root. Assume that all of the variables represent positive real numbers. 1. The square root 25x^12 Find the cube root. 2. ^3 square root 512 Simplify the radical expressions. Assume that all variables represent positive real numbers. 3. the square root of 72 multiply the square root of 2 4. the square