Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Certainly! Let's go through each question step-by-step:
6. Find the square of 32:
To square the number 32, you multiply 32 by itself.
[tex]\[ 32 \times 32 = 1024 \][/tex]
Therefore, the square of 32 is 1024.
7. Represent [tex]\(\frac{2}{7}\)[/tex] on the number line:
To represent the fraction [tex]\(\frac{2}{7}\)[/tex] on the number line, we first understand that this fraction is between 0 and 1. Divide the interval from 0 to 1 into 7 equal parts. Each part corresponds to a [tex]\(\frac{1}{7}\)[/tex]. The fraction [tex]\(\frac{2}{7}\)[/tex] would be located at the second mark after 0 on this interval.
Numerically, [tex]\(\frac{2}{7} \approx 0.2857142857142857\)[/tex], which helps us pinpoint the location on the number line.
8. Write Multiplicative inverse of 0:
The multiplicative inverse of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(a \times b = 1\)[/tex]. However, for zero, there is no number [tex]\(b\)[/tex] such that [tex]\(0 \times b = 1\)[/tex]. Therefore, the multiplicative inverse of 0 does not exist.
9. The product of a number and its reciprocal:
The reciprocal of a number [tex]\(a\)[/tex] (assuming [tex]\(a \neq 0\)[/tex]) is [tex]\(\frac{1}{a}\)[/tex]. The product of [tex]\(a\)[/tex] and its reciprocal is:
[tex]\[ a \times \frac{1}{a} = 1 \][/tex]
So, the product of a number and its reciprocal is always 1.
10. Write in ascending and descending order:
We are given the fractions [tex]\(\frac{4}{5}, \frac{3}{7}, \frac{-1}{5}, \frac{2}{3}, \frac{5}{7}\)[/tex].
Let's first convert these to their decimal equivalents:
[tex]\[ \frac{4}{5} = 0.8, \quad \frac{3}{7} \approx 0.42857142857142855, \quad \frac{-1}{5} = -0.2, \quad \frac{2}{3} \approx 0.6666666666666666, \quad \frac{5}{7} \approx 0.7142857142857143 \][/tex]
Now we can sort these decimals in ascending order:
[tex]\[ -0.2, 0.42857142857142855, 0.6666666666666666, 0.7142857142857143, 0.8 \][/tex]
And in descending order:
[tex]\[ 0.8, 0.7142857142857143, 0.6666666666666666, 0.42857142857142855, -0.2 \][/tex]
Thus, the fractions in ascending order are:
[tex]\[ \frac{-1}{5}, \frac{3}{7}, \frac{2}{3}, \frac{5}{7}, \frac{4}{5} \][/tex]
And the fractions in descending order are:
[tex]\[ \frac{4}{5}, \frac{5}{7}, \frac{2}{3}, \frac{3}{7}, \frac{-1}{5} \][/tex]
Hope this helps! Let me know if you have any questions.
6. Find the square of 32:
To square the number 32, you multiply 32 by itself.
[tex]\[ 32 \times 32 = 1024 \][/tex]
Therefore, the square of 32 is 1024.
7. Represent [tex]\(\frac{2}{7}\)[/tex] on the number line:
To represent the fraction [tex]\(\frac{2}{7}\)[/tex] on the number line, we first understand that this fraction is between 0 and 1. Divide the interval from 0 to 1 into 7 equal parts. Each part corresponds to a [tex]\(\frac{1}{7}\)[/tex]. The fraction [tex]\(\frac{2}{7}\)[/tex] would be located at the second mark after 0 on this interval.
Numerically, [tex]\(\frac{2}{7} \approx 0.2857142857142857\)[/tex], which helps us pinpoint the location on the number line.
8. Write Multiplicative inverse of 0:
The multiplicative inverse of a number [tex]\(a\)[/tex] is a number [tex]\(b\)[/tex] such that [tex]\(a \times b = 1\)[/tex]. However, for zero, there is no number [tex]\(b\)[/tex] such that [tex]\(0 \times b = 1\)[/tex]. Therefore, the multiplicative inverse of 0 does not exist.
9. The product of a number and its reciprocal:
The reciprocal of a number [tex]\(a\)[/tex] (assuming [tex]\(a \neq 0\)[/tex]) is [tex]\(\frac{1}{a}\)[/tex]. The product of [tex]\(a\)[/tex] and its reciprocal is:
[tex]\[ a \times \frac{1}{a} = 1 \][/tex]
So, the product of a number and its reciprocal is always 1.
10. Write in ascending and descending order:
We are given the fractions [tex]\(\frac{4}{5}, \frac{3}{7}, \frac{-1}{5}, \frac{2}{3}, \frac{5}{7}\)[/tex].
Let's first convert these to their decimal equivalents:
[tex]\[ \frac{4}{5} = 0.8, \quad \frac{3}{7} \approx 0.42857142857142855, \quad \frac{-1}{5} = -0.2, \quad \frac{2}{3} \approx 0.6666666666666666, \quad \frac{5}{7} \approx 0.7142857142857143 \][/tex]
Now we can sort these decimals in ascending order:
[tex]\[ -0.2, 0.42857142857142855, 0.6666666666666666, 0.7142857142857143, 0.8 \][/tex]
And in descending order:
[tex]\[ 0.8, 0.7142857142857143, 0.6666666666666666, 0.42857142857142855, -0.2 \][/tex]
Thus, the fractions in ascending order are:
[tex]\[ \frac{-1}{5}, \frac{3}{7}, \frac{2}{3}, \frac{5}{7}, \frac{4}{5} \][/tex]
And the fractions in descending order are:
[tex]\[ \frac{4}{5}, \frac{5}{7}, \frac{2}{3}, \frac{3}{7}, \frac{-1}{5} \][/tex]
Hope this helps! Let me know if you have any questions.
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.