Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
To determine which expressions properly show the prime factorization of the number 90, we need to check each expression individually.
1. Expression: [tex]\(2 \times 3 \times 15\)[/tex]
- Let's simplify: [tex]\(2 \times 3 \times 15\)[/tex]
- Calculation: [tex]\(2 \times 3 = 6\)[/tex], then [tex]\(6 \times 15 = 90\)[/tex]
- This product equals 90. Therefore, expression 1 is correct.
2. Expression: [tex]\(2^2 \times 3 \times 5\)[/tex]
- Let's simplify: [tex]\(2^2 \times 3 \times 5\)[/tex]
- First, calculate [tex]\(2^2 = 4\)[/tex], then [tex]\(4 \times 3 = 12\)[/tex], and finally [tex]\(12 \times 5 = 60\)[/tex]
- This product equals 60, not 90. Therefore, expression 2 is incorrect.
3. Expression: [tex]\(2 \times 3^2 \times 5\)[/tex]
- Let's simplify: [tex]\(2 \times 3^2 \times 5\)[/tex]
- First, calculate [tex]\(3^2 = 9\)[/tex], then [tex]\(2 \times 9 = 18\)[/tex], and finally [tex]\(18 \times 5 = 90\)[/tex]
- This product equals 90. Therefore, expression 3 is correct.
4. Expression: [tex]\(2 \times 5 \times 9\)[/tex]
- Let's simplify: [tex]\(2 \times 5 \times 9\)[/tex]
- First, calculate [tex]\(2 \times 5 = 10\)[/tex], then [tex]\(10 \times 9 = 90\)[/tex]
- This product equals 90. Therefore, expression 4 is correct.
5. Expression: [tex]\(2 \times 3 \times 3 \times 5\)[/tex]
- Let's simplify: [tex]\(2 \times 3 \times 3 \times 5\)[/tex]
- First, calculate [tex]\(2 \times 3 = 6\)[/tex], then [tex]\(6 \times 3 = 18\)[/tex], and finally [tex]\(18 \times 5 = 90\)[/tex]
- This product equals 90. Therefore, expression 5 is correct.
By evaluating each expression, we find that the prime factorizations showing the number 90 correctly are:
[tex]\[ \boxed{2 \times 3 \times 15} \][/tex]
[tex]\[ \boxed{2 \times 3^2 \times 5} \][/tex]
[tex]\[ \boxed{2 \times 5 \times 9} \][/tex]
[tex]\[ \boxed{2 \times 3 \times 3 \times 5} \][/tex]
Thus, the correct expressions from the provided list that show the prime factorization of 90 are: [tex]\(2 \times 3 \times 15\)[/tex], [tex]\(2 \times 3^2 \times 5\)[/tex], [tex]\(2 \times 5 \times 9\)[/tex], and [tex]\(2 \times 3 \times 3 \times 5\)[/tex].
1. Expression: [tex]\(2 \times 3 \times 15\)[/tex]
- Let's simplify: [tex]\(2 \times 3 \times 15\)[/tex]
- Calculation: [tex]\(2 \times 3 = 6\)[/tex], then [tex]\(6 \times 15 = 90\)[/tex]
- This product equals 90. Therefore, expression 1 is correct.
2. Expression: [tex]\(2^2 \times 3 \times 5\)[/tex]
- Let's simplify: [tex]\(2^2 \times 3 \times 5\)[/tex]
- First, calculate [tex]\(2^2 = 4\)[/tex], then [tex]\(4 \times 3 = 12\)[/tex], and finally [tex]\(12 \times 5 = 60\)[/tex]
- This product equals 60, not 90. Therefore, expression 2 is incorrect.
3. Expression: [tex]\(2 \times 3^2 \times 5\)[/tex]
- Let's simplify: [tex]\(2 \times 3^2 \times 5\)[/tex]
- First, calculate [tex]\(3^2 = 9\)[/tex], then [tex]\(2 \times 9 = 18\)[/tex], and finally [tex]\(18 \times 5 = 90\)[/tex]
- This product equals 90. Therefore, expression 3 is correct.
4. Expression: [tex]\(2 \times 5 \times 9\)[/tex]
- Let's simplify: [tex]\(2 \times 5 \times 9\)[/tex]
- First, calculate [tex]\(2 \times 5 = 10\)[/tex], then [tex]\(10 \times 9 = 90\)[/tex]
- This product equals 90. Therefore, expression 4 is correct.
5. Expression: [tex]\(2 \times 3 \times 3 \times 5\)[/tex]
- Let's simplify: [tex]\(2 \times 3 \times 3 \times 5\)[/tex]
- First, calculate [tex]\(2 \times 3 = 6\)[/tex], then [tex]\(6 \times 3 = 18\)[/tex], and finally [tex]\(18 \times 5 = 90\)[/tex]
- This product equals 90. Therefore, expression 5 is correct.
By evaluating each expression, we find that the prime factorizations showing the number 90 correctly are:
[tex]\[ \boxed{2 \times 3 \times 15} \][/tex]
[tex]\[ \boxed{2 \times 3^2 \times 5} \][/tex]
[tex]\[ \boxed{2 \times 5 \times 9} \][/tex]
[tex]\[ \boxed{2 \times 3 \times 3 \times 5} \][/tex]
Thus, the correct expressions from the provided list that show the prime factorization of 90 are: [tex]\(2 \times 3 \times 15\)[/tex], [tex]\(2 \times 3^2 \times 5\)[/tex], [tex]\(2 \times 5 \times 9\)[/tex], and [tex]\(2 \times 3 \times 3 \times 5\)[/tex].
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
