Mathematical Expressions and Equations Quiz

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Questions and Answers

What is the measure of angle A if it is formed by two intersecting lines creating vertical angles?

  • 90 degrees (correct)
  • 60 degrees
  • 150 degrees
  • 45 degrees

If angle B measures 30 degrees, what is the measure of its corresponding angle on the opposite line?

  • 120 degrees
  • 60 degrees
  • 30 degrees
  • 150 degrees (correct)

What is the sum of the measures of angles C and D formed by a transversal cutting through parallel lines?

  • 180 degrees (correct)
  • 90 degrees
  • 360 degrees
  • 270 degrees

If angle E measures 120 degrees, what is the measure of the interior angle on the same side of the transversal?

<p>60 degrees (D)</p> Signup and view all the answers

What is the measure of angle F if it is an alternate interior angle corresponding to angle G, which is 75 degrees?

<p>75 degrees (B)</p> Signup and view all the answers

Flashcards

Angle Measure

The measure of an angle expressed in degrees or radians.

Complementary Angles

Two angles whose measures add up to 90 degrees.

Supplementary Angles

Two angles whose measures add up to 180 degrees.

Vertical Angles

Angles opposite each other when two lines cross; they are equal.

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Adjacent Angles

Angles that share a common side and vertex but do not overlap.

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Study Notes

Translating Words to Mathematical Expressions

  • Key words and phrases indicate mathematical operations (addition, subtraction, multiplication, division).
  • Common verbal expressions and their corresponding mathematical expressions for addition, subtraction, multiplication, division are provided.

Solving Equations from Verbal Information

  • Translate verbal sentences into equations using variables.
  • Examples demonstrate translating different types of verbal sentences.
  • Key steps for solving problems include:
    • Read the problem carefully, identify the given information.
    • Assign a variable to the unknown.
    • Write an equation using variable expressions.
    • Solve the equation.
    • State the answer with appropriate labels.
    • Check the answer in the original problem.

Solving Perimeter Problems

  • Use formulas to write equations representing perimeter of rectangles.
  • Examples demonstrate finding width and length of rectangles, given perimeter information.

Solving Percent Problems

  • Example problem showing how to find the health expenditure from 1990 given the 2015 health expenditure and increase rate.
  • Assign variables to represent unknowns.
  • Write equations based on the given information.
    
    • Solve the equations.
    • State answers with relevant units.

Solving Investment Problems

  • Use a table to organize given information for investment problems.
  • Examples demonstrate finding invested amounts at different interest rates.
  • Formula for interest is I = prt where time is 1 year.

Solving Mixture Problems

  • Use tables to solve mixture problems.
  • Example problem showing how to solve for the amount of 70% solution needed to mix with 40% solution to get a 50% solution.

Solving Problems about Angles

  • The sum of the angles in a triangle is 180 degrees.

Solving Problems about Consecutive Integers

  • Consecutive integers differ by 1.
  • Consecutive even integers differ by 2.
  • Consecutive odd integers differ by 2.
  • Example problems show how to write and solve equations involving consecutive integers.

Money Denomination Problems

  • Use variables to represent the number of coins or bills.
  • Organize information in a table for each denomination.
  • Write equations, clear parentheses and solve the equations.

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Lecture (1.3 and 1.4) (2) PDF

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