Properties of Absolute Value and Inequalities

The video tutorial covers an introduction to calculus, focusing on number systems, inequalities, absolute values, Cartesian coordinates, and graphing equations. It explains the properties and solutions of inequalities, the concept of absolute values, and the use of Cartesian coordinates to determine distances and midpoints. The tutorial also provides techniques for graphing equations and analyzing their symmetry and intersections.

Which of the following is a characteristic of rational numbers?

• They can be expressed as repeating decimals.

• They are always whole numbers.

• They cannot be expressed as fractions.

• They are always negative.

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CCSS.6.EE.B.8

What is the main difference between an inequality and an equation?

• Inequalities have variables, equations do not.

• Equations have variables, inequalities do not.

• Equations are always true, inequalities are not.

• Inequalities express a range of values, equations express specific values.

How is a solution to an inequality typically expressed?

• As a single number.

• As a fraction.

• Using interval notation.

• Using a pie chart.

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CCSS.6.NS.C.7C

What does the absolute value of a number represent?

• The number itself.

• The distance from zero.

• The negative of the number.

• The square of the number.

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CCSS.7.NS.A.1D

Which property is true for the absolute value of a product?

• The absolute value of a product is the sum of the absolute values.

• The absolute value of a product is always negative.

• The absolute value of a product is the difference of the absolute values.

• The absolute value of a product is the product of the absolute values.

What is the correct way to combine solution sets when solving inequalities?

• Use 'and' for intersection and 'or' for union

• Use 'or' for intersection and 'and' for union

• Always use 'or'

• Always use 'and'

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CCSS.HSG.GPE.B.7

How do you calculate the distance between two points in a Cartesian coordinate system?

• Add the coordinates of the points

• Multiply the coordinates of the points

• Subtract the coordinates of the points

• Use the Pythagorean theorem

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CCSS.HSG.GPE.A.1

What is the equation of a circle with center at (h, k) and radius r?

• (x + h)^2 - (y + k)^2 = r^2

• (x - h)^2 - (y - k)^2 = r^2

• (x + h)^2 + (y + k)^2 = r^2

• (x - h)^2 + (y - k)^2 = r^2

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CCSS.8.EE.B.6

Which of the following describes a line that is perpendicular to another line with a gradient of m?

• A line with a gradient of 1/m

• A line with a gradient of -m

• A line with a gradient of m

• A line with a gradient of -1/m

What is the first step in graphing an equation?

• Plot points that satisfy the equation

• Draw the axes

• Find the intercepts

• Determine the symmetry of the graph