Please help!
1. Evaluate the function for x = 2 and x = 7, when f(x) = -4x + 61
2. Tell whether the sequence is arithmetic. If it is, identify the common difference. ( 1/2, 1/3, 1/6, 0 … )
3. Tell whether the sequence is arithmetic. If it is, identify the common difference. (-3, -7, -10, -14 …)
4. You have a cafeteria card worth $50. After you buy lunch on Monday its value is $46.75. After you buy lunch on Tuesday, its value is $43.50. Write a rule to represent the amount on money left on the card as an arithmetic sequence. What is the value of the card after you buy 12 lunches?
5. What is the seventh term of an arithmetic sequence represented by the rule A(n) = -9 + (n-1)(.5)?
6. New grass seeds grow rapidly. A grass seed has grown to 0.3 millimeters tall. Tomorrow it will be 0.9 millimeters tall, the next day it will be 1.5 millimeters tall, and on the next day it will be 2.1 millimeters tall. Write a rule to represent the height of the bean plant as an arithmetic sequence. How tall will the plant be in 15 days?
So does anyone have the answers?
bruh
Sure! I can help you with these questions. Let's solve each one step by step:
1. To evaluate the function f(x) = -4x + 61 for x = 2, substitute x = 2 into the function and calculate the result:
f(2) = -4(2) + 61
= -8 + 61
= 53
To evaluate the function for x = 7, substitute x = 7 into the function and calculate the result:
f(7) = -4(7) + 61
= -28 + 61
= 33
2. To determine if the sequence (1/2, 1/3, 1/6, 0...) is arithmetic, check if there is a common difference between consecutive terms. To find the common difference between the terms, subtract each term from the next term:
Common difference = (1/3) - (1/2) = -1/6
Since there is a common difference of -1/6, the sequence is arithmetic.
3. To determine if the sequence (-3, -7, -10, -14...) is arithmetic, check for a common difference. Subtract each term from the next term:
Common difference = -7 - (-3) = -4
= -10 - (-7) = -3
= -14 - (-10) = -4
Since there is a common difference of -4, the sequence is arithmetic.
4. To write a rule to represent the amount of money left on the cafeteria card as an arithmetic sequence, we observe the pattern of decreasing amounts. Let's find the common difference:
Common difference = 46.75 - 50 = -3.25
43.50 - 46.75 = -3.25
The common difference is -3.25, and the initial value of the sequence is $50. So the rule to represent the amount of money left on the card as an arithmetic sequence is:
A(n) = 50 - 3.25n, where n represents the number of lunches bought.
To find the value of the card after buying 12 lunches, substitute n = 12 into the sequence:
A(12) = 50 - 3.25(12)
= 50 - 39
= $11
Therefore, the value of the card after buying 12 lunches is $11.
5. The arithmetic sequence is represented by the rule A(n) = -9 + (n - 1)(0.5). To find the seventh term, substitute n = 7 into the rule:
A(7) = -9 + (7 - 1)(0.5)
= -9 + 6(0.5)
= -9 + 3
= -6
Therefore, the seventh term is -6.
6. To write a rule to represent the height of the grass plant as an arithmetic sequence, we observe that the growth is consistent and increasing by 0.6 millimeters each day. So the rule to represent the height of the plant as an arithmetic sequence is:
A(n) = 0.3 + (n - 1)(0.6), where n represents the number of days.
To find the height of the plant in 15 days, substitute n = 15 into the sequence:
A(15) = 0.3 + (15 - 1)(0.6)
= 0.3 + 14(0.6)
= 0.3 + 8.4
= 8.7 millimeters
Therefore, the plant will be 8.7 millimeters tall after 15 days.
I hope that helps! Let me know if you have any further questions.
these problems look familiar. No ideas on any of them?
They are all just linear functions or arithmetic sequences.