Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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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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### Question: Which pair of numbers are both between 6 and 7? ### Options: 1. ○ √36 and √49 2. ○ √30 and √42 3. ○ √42 and √48 4. ○ √37 and √50 ### Explanation: To determine which pair of numbers both fall between 6 and 7, we need to evaluate the square roots of the numbers provided in each option. 1. **√36 and √49**: - √36 = 6 - √49 = 7 - Thus, this pair includes one number that is exactly 6 and another that is exactly 7, so both are not between 6 and 7. 2. **√30 and √42**: - √30 ≈ 5.48 (not between 6 and 7) - √42 ≈ 6.48 (between 6 and 7) - Thus, this pair has only one number between 6 and 7. 3. **√42 and √48**: - √42 ≈ 6.48 (between 6 and 7) - √48 ≈ 6.93 (between 6 and 7) - Thus, both numbers in this pair are between 6 and 7. 4. **√37 and √50**: - √37 ≈ 6.08 (between 6 and 7) - √50 ≈ 7.07 (not between 6 and 7) - Thus, this pair has only one number between 6 and 7. ### Correct Answer: The correct pair of numbers that are both between 6 and 7 is found in option 3: - √42 and √48.
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Transcribed Image Text:### Question: Which pair of numbers are both between 6 and 7? ### Options: 1. ○ √36 and √49 2. ○ √30 and √42 3. ○ √42 and √48 4. ○ √37 and √50 ### Explanation: To determine which pair of numbers both fall between 6 and 7, we need to evaluate the square roots of the numbers provided in each option. 1. **√36 and √49**: - √36 = 6 - √49 = 7 - Thus, this pair includes one number that is exactly 6 and another that is exactly 7, so both are not between 6 and 7. 2. **√30 and √42**: - √30 ≈ 5.48 (not between 6 and 7) - √42 ≈ 6.48 (between 6 and 7) - Thus, this pair has only one number between 6 and 7. 3. **√42 and √48**: - √42 ≈ 6.48 (between 6 and 7) - √48 ≈ 6.93 (between 6 and 7) - Thus, both numbers in this pair are between 6 and 7. 4. **√37 and √50**: - √37 ≈ 6.08 (between 6 and 7) - √50 ≈ 7.07 (not between 6 and 7) - Thus, this pair has only one number between 6 and 7. ### Correct Answer: The correct pair of numbers that are both between 6 and 7 is found in option 3: - √42 and √48.
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