Algebra and Trigonometry
Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Textbook Question
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Chapter 1.2, Problem 10TI

Write each number in scientific notation.

  1. U.S. national debt per taxpayer (April 2014): $152,000
  2. World population (April 2014): 7,158,000,000
  3. World gross national income (April 2014): $85,500,000,000,000
  4. Time for light to travel 1 m: 0.00000000334 s
  5. Probability of winning lottery (match 6 of 49 possible numbers): 0.0000000715

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Chapter 1 Solutions

Algebra and Trigonometry

Ch. 1.1 - Write each of thefollowing as a rational number....Ch. 1.1 - Write each of the following rational numbers as...Ch. 1.1 - Determine whether each of the following numbers is...Ch. 1.1 - Classify each number as either positive or...Ch. 1.1 - Classify each number as being a natural number...Ch. 1.1 - Use the order of operations to evaluate each of...Ch. 1.1 - Use the properties of real numbers to rewrite and...Ch. 1.1 - List the constants and variables for each...Ch. 1.1 - Evaluate the expression 113y for each value of y....Ch. 1.1 - Evaluate each expression for the given values....
Ch. 1.1 - A photograph with length L and width W is placed...Ch. 1.1 - Simplify each algebraic expression....Ch. 1.1 - If the amount P is deposited into an account...Ch. 1.1 - Is 2 an example of a rational terminating,...Ch. 1.1 - What is the order of operations? What acronym is...Ch. 1.1 - What do the Associative Properties allow us to do...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, simplify the given...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, solve for the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - For the following exercises, simplify the...Ch. 1.1 - REAL-WORLD APPLICATIONS For the following...Ch. 1.1 - REAL-WORLD APPLICATIONS For the following...Ch. 1.1 - For the following exercises, solve the given...Ch. 1.1 - For the following exercises, solve the given...Ch. 1.1 - For the following exercises, consider this...Ch. 1.1 - For the following exercises, consider this...Ch. 1.1 - For the following exercise, solve the given...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - For the following exercises, use a graphing...Ch. 1.1 - If a whole number is not a natural number, what...Ch. 1.1 - Determine whether the statement is true or false:...Ch. 1.1 - Determine whether the statement is true or false:...Ch. 1.1 - Determine whether the simplified expression is...Ch. 1.1 - Determine whether the simplified expression is...Ch. 1.1 - The division of two whole numbers will always...Ch. 1.1 - What property of real numbers would, simplify the...Ch. 1.2 - Write each of the following products with a single...Ch. 1.2 - Write each of the following products with a single...Ch. 1.2 - Write each of the following products with a single...Ch. 1.2 - Simplify each expression using the zero exponent...Ch. 1.2 - Write each of the following quotients with a...Ch. 1.2 - Write each of the following quotients with a...Ch. 1.2 - Simplify each of the following quotients as much...Ch. 1.2 - Simplify each of the following quotients as much...Ch. 1.2 - Simplify each expression and write the answer with...Ch. 1.2 - Write each number in scientific notation. U.S....Ch. 1.2 - Convert each number in scientific notation to...Ch. 1.2 - Perform the operations and write the answer in...Ch. 1.2 - An average human body contains around...Ch. 1.2 - Is 23 the same as 32 ? Explain.Ch. 1.2 - When can you add two exponents?Ch. 1.2 - What is the purpose of scientific notation?Ch. 1.2 - Explain what a negative exponent does.Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify each...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, write each expression...Ch. 1.2 - For the following exercises, write each expression...Ch. 1.2 - For the following exercises, write each expression...Ch. 1.2 - For the following exercises, write each expression...Ch. 1.2 - For the following exercises, write each expression...Ch. 1.2 - For the following exercises, write each expression...Ch. 1.2 - For the following exercises, express the decimal...Ch. 1.2 - For the following exercises, express the decimal...Ch. 1.2 - For the following exercises, convert each number...Ch. 1.2 - For the following exercises, convert each number...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - To reach escape velocity, a rocket must travel at...Ch. 1.2 - A dime is the thinnest coin in U.S. currency. A...Ch. 1.2 - The average distance between Earth and the Sun is...Ch. 1.2 - A terabyte is made of approximately...Ch. 1.2 - The Gross Domestic Product (GDP) for the United...Ch. 1.2 - One picometer is approximately 3.3971011in....Ch. 1.2 - The value of the services sector of the U.S....Ch. 1.2 - For the following exercises, use a graphing...Ch. 1.2 - For the following exercises, use a graphing...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.2 - For the following exercises, simplify the given...Ch. 1.3 - 225 b. 81 c. 259 d. 36+121Ch. 1.3 - Simplify 50x2y3z .Ch. 1.3 - Simplify 50x2x assuming x0 .Ch. 1.3 - Simplify 2x29y4 .Ch. 1.3 - Simplify 9a5b143a4b5 .Ch. 1.3 - Add 5+620 .Ch. 1.3 - Subtract: 380x445x .Ch. 1.3 - Write 1232 in simplest form.Ch. 1.3 - Write 72+3 in simplest form.Ch. 1.3 - Simplify. 2163 380454 69,0003+75763Ch. 1.3 - Write 952 as a radical. Simplify.Ch. 1.3 - Write x(5y)9 using a rational exponent.Ch. 1.3 - Simplify 8x13(14x65) .Ch. 1.3 - What does it mean when a radical does not have an...Ch. 1.3 - Where would radicals come in the order of...Ch. 1.3 - Every number will have two square root? What is...Ch. 1.3 - Can a radical with a negative radicand have a real...Ch. 1.3 - For the following exercises, simplify the given...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify the given...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - A guy wire for a suspension bridge runs from the...Ch. 1.3 - A car accelerates at a rate of 64tm/s2 where tis...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.3 - For the following exercises, simplify each...Ch. 1.4 - Identify the degree, leading term, and leading...Ch. 1.4 - Find the sum. (2x3+5x2x+1)+(2x23x4)Ch. 1.4 - Find the difference. (7x37x2+6x2)(4x36x2x+7)Ch. 1.4 - Find the product. (3x+2)(x34x2+7)Ch. 1.4 - Use FOIL to find the product. (x+7)(3x5)Ch. 1.4 - Expand (4x1)2.Ch. 1.4 - Multiply (2x+7)(2x7) .Ch. 1.4 - Multiply (3x1)(2x+7y9) .Ch. 1.4 - Evaluate the following statement: The degree of a...Ch. 1.4 - Many times, multiplying two binomials with two...Ch. 1.4 - You can multiply polynomials with any number of...Ch. 1.4 - State whether the following statement is true and...Ch. 1.4 - For the following exercises, identify the degree...Ch. 1.4 - For the following exercises, identify the degree...Ch. 1.4 - For the following exercises, identify the degree...Ch. 1.4 - For the following exercises, identify the degree...Ch. 1.4 - For the following exercises, identify the degree...Ch. 1.4 - For the following exercises, identify the degree...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the sum or...Ch. 1.4 - For the following exercises, find the product. 18....Ch. 1.4 - For the following exercises, find the product. 19....Ch. 1.4 - For the following exercises, find the product. 20....Ch. 1.4 - For the following exercises, find the product. 21....Ch. 1.4 - For the following exercises, find the product. 22....Ch. 1.4 - For the following exercises, find the product. 23....Ch. 1.4 - For the following exercises, expand the binomial....Ch. 1.4 - For the following exercises, expand the binomial....Ch. 1.4 - For the following exercises, expand the binomial....Ch. 1.4 - For the following exercises, expand the binomial....Ch. 1.4 - For the following exercises, expand the binomial....Ch. 1.4 - For the following exercises, expand the binomial...Ch. 1.4 - For the following exercises, expand the binomial....Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - For the following exercises, multiply the...Ch. 1.4 - A developer wants to purchase a plot of land to...Ch. 1.4 - A prospective buyer wants to know how much grain a...Ch. 1.4 - For the following exercises, perform the given...Ch. 1.4 - For the following exercises, perform the given...Ch. 1.4 - For the following exercises, perform the given...Ch. 1.5 - Factor x(b2a)+6(b2a) by pulling out the GCF.Ch. 1.5 - Factor x27x+6 .Ch. 1.5 - Factor. 2x2+9x+9 6x2+x1Ch. 1.5 - Factor 49x214x+1Ch. 1.5 - Factor 81y2100 .Ch. 1.5 - Factor the sum of cubes: 216a3+b3. .Ch. 1.5 - Factor the difference of cubes: 1,000x31 .Ch. 1.5 - Factor 2(5a1)34+7a(5a1)14 .Ch. 1.5 - If the terms of a polynomial do not have a GCF,...Ch. 1.5 - A polynomial is factorable, but it is not a...Ch. 1.5 - How do you factor by grouping?Ch. 1.5 - For the following exercises, find the greatest...Ch. 1.5 - For the following exercises, find the greatest...Ch. 1.5 - For the following exercises, find the greatest...Ch. 1.5 - For the following exercises, find the greatest...Ch. 1.5 - For the following exercises, find the greatest...Ch. 1.5 - For the following exercises, find the greatest...Ch. 1.5 - For the following exercises, factor by grouping....Ch. 1.5 - For the following exercises, factor by grouping....Ch. 1.5 - For the following exercises, factor by grouping....Ch. 1.5 - For the following exercises, factor by grouping....Ch. 1.5 - For the following exercises, factor by grouping....Ch. 1.5 - For the following exercises, factor by grouping....Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - 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For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, consider this...Ch. 1.5 - REAL-WORLD APPLICATIONS Charlotte has appointed a...Ch. 1.5 - For the following exercises, consider this...Ch. 1.5 - For the following exercise, consider the following...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.5 - For the following exercises, factor the...Ch. 1.6 - Simplify x6x236 .Ch. 1.6 - Multiply the rational expressions and show the...Ch. 1.6 - Divide the rational expressions and express the...Ch. 1.6 - Subtract the rational expressions: 3x+51x3Ch. 1.6 - Simplify: xyyxyCh. 1.6 - How can you use factoring to simplify rational...Ch. 1.6 - How do you use the LCD to combine two rational...Ch. 1.6 - Tell whether the following statement is true or...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, simplify the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, multiply the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, divide the rational...Ch. 1.6 - For the following exercises, add and subtract the...Ch. 1.6 - For the following exercises, add and subtract the...Ch. 1.6 - 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The...Ch. 1.6 - The area of Sandy’s yard is 25x2625ft2 . A patch...Ch. 1.6 - Aaron wants to mulch his garden. His garden is...Ch. 1.6 - For the following exercises, perform the given...Ch. 1.6 - For the following exercises, perform the given...Ch. 1.6 - For the following exercises, perform the given...Ch. 1.6 - For the following exercises, perform the given...Ch. 1 - For the following exercises, perform the given...Ch. 1 - For the following exercises, perform the given...Ch. 1 - For the following exercises, perform the given...Ch. 1 - For the following exercises, solve the equation....Ch. 1 - For the following exercises, solve the expression....Ch. 1 - For the following exercises, simplify the...Ch. 1 - For the following exercises, simplify the...Ch. 1 - For the following exercises, identify the number...Ch. 1 - For the following exercises, identify the number...Ch. 1 - For the following exercises, identify the number...Ch. 1 - For the following exercises, identify the number...Ch. 1 - For the following exercises, simplify the...Ch. 1 - For the following exercises, simplify the...Ch. 1 - For the following exercises, simplify the...Ch. 1 - 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