Fitzgerald Wagner
07/09/2023 · Elementary School

Determine whether the following divisibility statement is true of false. Justify your solution. \[ 9 \mid 1017 \] False, because the sum of the digits of 1017 is not divisible by 9. True, because the sum of the digits of 1017 is divisible by 9. False, because the last two digits do not form a number that is divisible by 9. True, because the last two digits form a number that is divisible by 9.

UpStudy ThothAI Solution

Tutor-Verified Answer

Step-by-step Solution

To determine whether \( 9 \mid 1017 \) (which means "9 divides 1017"), we can use the rule of divisibility for 9. According to this rule, a number is divisible by 9 if the sum of its digits is divisible by 9. Let's calculate the sum of the digits of 1017: - The digits of 1017 are 1, 0, 1, and 7. - The sum of these digits is: \[ 1 + 0 + 1 + 7 = 9 \] Now, we check if this sum (9) is divisible by 9: \[ 9 \div 9 = 1 \] Since 1 is an integer, 9 is indeed divisible by 9. Thus, the statement \( 9 \mid 1017 \) is **true**. The correct justification is: **True, because the sum of the digits of 1017 is divisible by 9.**

Quick Answer

The statement \( 9 \mid 1017 \) is true because the sum of the digits of 1017 is divisible by 9.
Answered by UpStudy AI and reviewed by a Professional Tutor
UpStudy ThothAI
Self-Developed and Ever-Improving
Thoth AI product is constantly being upgraded and optimized.
Covers All Major Subjects
Capable of handling homework in math, chemistry, biology, physics, and more.
Instant and Accurate
Provides immediate and precise solutions and guidance.
Try Now
Ask Tutors
Ask AI
10x
Fastest way to Get Answers & Solutions
By text

Enter your question here…

By image
Re-Upload
Uploaded Files
xxxx.png0%
Submit
📸 STUDY CAN BE A REAL STRUGGLE
Why Not UpStudy It?
Select your plan below
Premium

You can enjoy

  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to answer and
    solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic
  • Limited Solutions