Absolute value
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Absolute value is defined as the distance from zero, which is always a positive number. While it is impossible to walk a negative distance in feet, one can refer to negative locations such as elevations below sea level or floors below ground. The concept of absolute value is useful when adding and subtracting integers, as it provides the distance regardless of what number is positive or negative.
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Absolute Value
The document provides an overview of absolute value functions and how to solve absolute value equations and inequalities. It defines absolute value, discusses evaluating absolute value expressions, and solves absolute value equations by isolating the absolute value. It also explains how to solve absolute value inequalities by considering whether the absolute value is less than, greater than, or equal to the right side of the inequality and interpreting the solutions. Examples of each type of problem are worked out step-by-step.
Integers and Absolute Value
This document discusses integers and absolute value. It defines integers as positive and negative whole numbers and explains how to graph and order integers on a number line. It also defines absolute value as the distance from zero and how to evaluate the absolute value of integers, including that the absolute value of a number can never be negative. Examples are provided for graphing, ordering, and finding opposites and absolute values of integers.
Absolute Value
This document provides an introduction to absolute value, including definitions of key terms like positive and negative numbers. It explains that the absolute value of a number is the distance from zero, so the absolute value of positive numbers is the same as the number itself, while the absolute value of negative numbers is the positive version of that number. Examples are provided of absolute value equations with both positive and negative solutions. Real-world applications like banking debts are discussed.
Add and subtract pos and neg numbers 4 parts
This document provides an introduction to integers through five parts:
Part I defines key integer vocabulary like positive and negative numbers. It discusses integer properties like opposites and compares/orders integers on number lines. Real world applications like temperature, sea level, and money are explored.
Part II covers integer addition rules - signs the same means keep the sign, signs different means subtract the numbers and keep the larger absolute value sign. Number lines demonstrate adding integers visually.
Part III explains that subtracting a negative number is the same as adding a positive number through changing operation and number signs. More examples solidify this rule.
Part IV proves this subtraction rule is true by using the same checking method as regular subtraction equations
Numberline notes
- Integers include whole numbers and their opposites on the number line including zero. Positive numbers are greater than zero, while negative numbers are less than zero.
- Integers can be compared and ordered on a number line, with numbers to the left being less than those to the right. Their absolute values represent distances from zero.
- Integers are used to represent real-world concepts like temperature, elevation, and financial amounts, with positive integers for gains and negative for losses or amounts owed.
Absolute value functions
1. Absolute-value functions can be transformed through translations, reflections, stretches, and compressions. Translations move the graph up/down or left/right and change the vertex. Reflections flip the graph across an axis. Stretches and compressions make the graph wider/narrower or taller/shorter.
2. Examples show how to write the rule for a transformed absolute-value function g(x) based on an original function f(x). The transformations can be vertical/horizontal shifts, reflections, or vertical/horizontal stretches/compressions.
3. Graphs confirm that the transformations are applied as expected to f(x), resulting in the graph of g(x) with the
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The document discusses the surface area formula for cylinders. It can be found by adding the area of the two circular bases and the lateral rectangular area. The total surface area is given as 2πrh + 2πr^2. Several examples are provided to demonstrate calculating the surface area of cylinders using given radii and heights. One example asks if 175 in^2 of gift wrap will be enough to cover a gift with a cylindrical container that has a height of 18 in and diameter of 3 in.
Scientific notation explaination positve
The document discusses scientific notation, which is a way to write very large or small numbers in a more compact form using two factors - a number between 1 and 10 multiplied by a power of 10. It provides examples of converting numbers between standard form and scientific notation, such as 2.3 x 103 representing 2300. The Andromeda Galaxy contains at least 200 billion stars, which can be written more concisely in scientific notation as 2 x 1011 stars.
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Absolute Value
The document provides an overview of absolute value functions and how to solve absolute value equations and inequalities. It defines absolute value, discusses evaluating absolute value expressions, and solves absolute value equations by isolating the absolute value. It also explains how to solve absolute value inequalities by considering whether the absolute value is less than, greater than, or equal to the right side of the inequality and interpreting the solutions. Examples of each type of problem are worked out step-by-step.
Integers and Absolute Value
This document discusses integers and absolute value. It defines integers as positive and negative whole numbers and explains how to graph and order integers on a number line. It also defines absolute value as the distance from zero and how to evaluate the absolute value of integers, including that the absolute value of a number can never be negative. Examples are provided for graphing, ordering, and finding opposites and absolute values of integers.
Absolute Value
This document provides an introduction to absolute value, including definitions of key terms like positive and negative numbers. It explains that the absolute value of a number is the distance from zero, so the absolute value of positive numbers is the same as the number itself, while the absolute value of negative numbers is the positive version of that number. Examples are provided of absolute value equations with both positive and negative solutions. Real-world applications like banking debts are discussed.
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This document provides an introduction to integers through five parts:
Part I defines key integer vocabulary like positive and negative numbers. It discusses integer properties like opposites and compares/orders integers on number lines. Real world applications like temperature, sea level, and money are explored.
Part II covers integer addition rules - signs the same means keep the sign, signs different means subtract the numbers and keep the larger absolute value sign. Number lines demonstrate adding integers visually.
Part III explains that subtracting a negative number is the same as adding a positive number through changing operation and number signs. More examples solidify this rule.
Part IV proves this subtraction rule is true by using the same checking method as regular subtraction equations
Numberline notes
- Integers include whole numbers and their opposites on the number line including zero. Positive numbers are greater than zero, while negative numbers are less than zero.
- Integers can be compared and ordered on a number line, with numbers to the left being less than those to the right. Their absolute values represent distances from zero.
- Integers are used to represent real-world concepts like temperature, elevation, and financial amounts, with positive integers for gains and negative for losses or amounts owed.
Absolute value functions
1. Absolute-value functions can be transformed through translations, reflections, stretches, and compressions. Translations move the graph up/down or left/right and change the vertex. Reflections flip the graph across an axis. Stretches and compressions make the graph wider/narrower or taller/shorter.
2. Examples show how to write the rule for a transformed absolute-value function g(x) based on an original function f(x). The transformations can be vertical/horizontal shifts, reflections, or vertical/horizontal stretches/compressions.
3. Graphs confirm that the transformations are applied as expected to f(x), resulting in the graph of g(x) with the
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The document discusses the surface area formula for cylinders. It can be found by adding the area of the two circular bases and the lateral rectangular area. The total surface area is given as 2πrh + 2πr^2. Several examples are provided to demonstrate calculating the surface area of cylinders using given radii and heights. One example asks if 175 in^2 of gift wrap will be enough to cover a gift with a cylindrical container that has a height of 18 in and diameter of 3 in.
Scientific notation explaination positve
The document discusses scientific notation, which is a way to write very large or small numbers in a more compact form using two factors - a number between 1 and 10 multiplied by a power of 10. It provides examples of converting numbers between standard form and scientific notation, such as 2.3 x 103 representing 2300. The Andromeda Galaxy contains at least 200 billion stars, which can be written more concisely in scientific notation as 2 x 1011 stars.
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Rectangular and triangular prisms have formulas to calculate their volume (V).
For a rectangular prism, V = (bh)h, where b is the width, h is the height, and the product bh gives the area of the rectangular base.
For a triangular prism, V = (1/2)bh, where b is the base, h is the height. The area of the triangular base is calculated as (1/2)bh.
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Absolute value
- 1. Absolute Value Can you demonstrate walking a distance of a negative 2 feet????
- 2. Walking a negative distance is impossible! You can walk to a negative location…for example you can walk to an elevation of 10 feet below sea level…you can walk to the 3rd story below ground…you can swim 10 feet under water….but you cannot walk a negative distance.
- 3. Definition The absolute value of a number is the distance from zero. Distance is always a positive number The symbol used for absolute value looks like this:
- 4. We will use the concept of absolute value when we add and subtract integers
- 5. Examples – find the value of… 3- 8 7--
- 6. Compare 6 7- 5 2-- 1 1--
- 7. Compare 6 7- 5 2-- 1 1--