Hi, I just had an assignment in mathematics and I was wondering if someone could check my answers. Thanks!
1. Find the next three terms in the sequence.
3, 12, 21, 30, ...
My answer - C) 39, 48, 57
2. Identify the sequence as arithmetic, geometric, or neither.
1.6, 0.8, 0.4, 0.2, ...
My answer - B) geometric
3. 5 * 3^n
My answer - D) 15, 45, 135, 405
4. Scientists estimate the rate of a wildebeest running at full speed to be 66 feet per second. Write a function rule to describe the relationship between the time, t, and the distance, d, a wildebeest travels when running at full speed.
My answer - D) d = 66t
5. Find the slope of the line through (-9, -10) and (-2, -5).
My answer - I am not sure whether it is 5/7 or -7/5. My mom says it is -7/5, but i am not sure.
6. Do the data in the table represent a linear function? If so, write a rule for the function.
My answer - D) no
7. Use the slope and two points to write a linear function rule for the graph.
(^ It will not let me post the image of the graph on here.)
My answer - B) y = 2x - 6
^ I'm not sure if all of them are correct or not, but I would feel much better if someone checked them for me. Thank you to anyone who helps. :)
- Merlana
1. yes d = 9
2. yes, r = .5
3. yes
4. yes
5. dY = -5+10 = 5, dX = -2+9 = 7 dY/dX = 5/7
6. no idea
7. no idea
But your mother only got 6/7 :)
Thanks again Damon! :)
Hi Merlana! I'd be happy to help you check your answers. Let's go through each question and I'll explain how to arrive at the correct answers.
1. To find the next three terms in the sequence 3, 12, 21, 30, ..., you need to determine the pattern in the sequence. Look at the differences between consecutive terms: 12 - 3 = 9, 21 - 12 = 9, and 30 - 21 = 9. You can see that the difference is always 9. So, to find the next term, add 9 to the last term in the sequence. That gives you 30 + 9 = 39. Similarly, the next two terms would be 39 + 9 = 48 and 48 + 9 = 57. Your answer, C) 39, 48, 57, is correct.
2. The sequence 1.6, 0.8, 0.4, 0.2, ... decreases by a factor of 0.5 each time. This means the sequence is geometric. Your answer, B) geometric, is correct.
3. The expression 5 * 3^n represents a geometric sequence. Given that n is the term number, you correctly identified the first four terms as 15, 45, 135, and 405. Your answer, D) 15, 45, 135, 405, is correct.
4. The relationship between the time, t, and the distance, d, a wildebeest travels when running at full speed can be described by the formula d = 66t, where 66 is the rate in feet per second. Your answer, D) d = 66t, is correct.
5. To find the slope of the line through (-9, -10) and (-2, -5), you can use the formula for slope: (change in y) / (change in x). So, the slope is (-5 - (-10)) / (-2 - (-9)) = 5 / 7. Therefore, your answer, 5/7, is correct. Your mom is right!
6. You need to analyze the data in the table to determine if it represents a linear function. If the change in the y-values for every change in the x-values is constant, then it is a linear function. Without the data, I cannot confirm your answer, D) no, but make sure to check if there's a constant rate of change between the x and y values.
7. Without the graph, I cannot verify your answer, but using the slope and two points, a linear function rule can be written. Your answer, B) y = 2x - 6, might be correct, but it's difficult to judge without seeing the graph.
Overall, your answers seem to be correct based on the explanation provided. Keep up the good work! Let me know if there's anything else you need help with.