Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Which expressions show the prime factorization of 90?

Check all that apply.

A. [tex]\(2 \times 3 \times 15\)[/tex]

B. [tex]\(2^2 \times 3 \times 5\)[/tex]

C. [tex]\(2 \times 3^2 \times 5\)[/tex]

D. [tex]\(2 \times 5 \times 9\)[/tex]

E. [tex]\(2 \times 3 \times 3 \times 5\)[/tex]

Sagot :

GinnyAnswer
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].
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.