Questions and Answers
Which of the following is an irrational number?
Name the property illustrated by the following equation: 3x+(2y+x)=3x+(x+2y)
Commutative Property of Addition
Which of the following sets is closed under the given operation?
How many terms does 3xy^2 + 4x + 4y have?
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Simplify 6 ÷ 2 · 3 - 6^2 ÷ 2^2 - 3^2.
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State the degree and classification of the following polynomial: 3xy^3 + 9xy^2z^2 + 3.
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Simplify 5x(2x + 4) - 2(4x - 9).
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If x - z = y, then express x in terms of y and z.
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Which equation would be used to find three consecutive even integers whose sum is 78?
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How fast is the westbound train traveling if two trains leave at the same time from stations that are 480 mi apart and travel toward each other on parallel tracks, passing each other 6 hours later?
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How many pounds of peanuts costing $1.75/lb should be mixed with raisins costing $2.50/lb to make 3 lb of a mixture that costs $2.00/lb?
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Which of the following are rational numbers?
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Study Notes
Irrational Numbers
- The square root of 12 is classified as an irrational number.
Properties of Addition
- The equation 3x + (2y + x) = 3x + (x + 2y) illustrates the Commutative Property of Addition.
Set Closure
- Positive odd integers are closed under multiplication, meaning the product of any two positive odd integers remains a positive odd integer.
Polynomial Terms
- The polynomial 3xy² + 4x + 4y has a total of three terms.
Simplification of Expressions
- The expression 6 ÷ 2 · 3 - 6² ÷ 2² - 3² simplifies to -9.
Polynomial Classification
- The polynomial 3xy³ + 9xy²z² + 3 has a degree of 5 and is classified as a trinomial.
Simplifying Algebraic Expressions
- The expression 5x(2x + 4) - 2(4x - 9) simplifies to 10x² + 12x = 18.
Algebraic Equations
- If x - z = y, then rearranging gives x = y + z, demonstrating the use of addition.
Consecutive Even Integers
- The equation to find three consecutive even integers whose sum is 78 is 3n + 6 = 78.
Train Speed Problem
- In a scenario where two trains travel towards each other from 480 miles apart, if the eastbound train travels 10 mph slower than the westbound train and they meet after 6 hours, the westbound train travels at 45 mph.
Mixing Products
- To create a 3 lb mixture costing $2.00/lb from peanuts costing $1.75/lb and raisins costing $2.50/lb, 2 lb of peanuts should be used.
Rational Numbers
- Rational numbers include -3.2, the square root of 4, and the decimal 3.0277777..., each with a definitive fractional representation.
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Description
Test your understanding of key concepts in Algebra 2 Chapter 1 with this quiz. It covers topics such as irrational numbers, properties of addition, and the closure of sets under operations. Perfect for reviewing essential algebra concepts.
