Quincy is starting a new exercise program. On the first day, he does 10 push-ups. On the third day, he does 20 push-ups. On the sixth day, he does 35 push-ups. Is the relationship between the day and the number of push-ups a linear relationship? Choices: (A)yes (B)no Now, justify your answer. Choices: (A)There is not a clear relationship between the day and the number of pushups. (B)The number of push-ups increased at a rate of 10 push-ups per day. (C)The number of push-ups increased by a different amount each day. (D)The number of push-ups increased at a rate of 5 push-ups per day.

Question

Quincy is starting a new exercise program. On the first day, he does 10 push-ups. On the third day, he does 20 push-ups. On the sixth day, he does 35 push-ups. Is the relationship between the day and the number of push-ups a linear relationship?   Choices: (A)yes (B)no  Now, justify your answer.   Choices: (A)There is not a clear relationship between the day and the number of pushups. (B)The number of push-ups increased at a rate of 10 push-ups per day. (C)The number of push-ups increased by a different amount each day. (D)The number of push-ups increased at a rate of 5 push-ups per day.

Bytelearn · Accepted Answer

Identify Days & Push-ups:  Step 1: Identify the days and corresponding push-ups done by Quincy. Day 1: 10 push-ups, Day 3: 20 push-ups, Day 6: 35 push-ups. Calculate Rate of Increase:  Step 2: Calculate the rate of increase in push-ups between the days. From Day 1 to Day 3 (2 days), the increase is 20 - 10 = 10 push-ups. From Day 3 to Day 6 (3 days), the increase is 35 - 20 = 15 push-ups. Check Consistency of Rate:  Step 3: Check if the rate of increase is consistent. Rate from Day 1 to Day 3 is 10 push-ups/2 days = 5 push-ups per day. Rate from Day 3 to Day 6 is 15 push-ups/3 days = 5 push-ups per day.

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