Let number of cranberries did Carissa eat on Thanksgiving Thursday = x
Given that she ate 7 cranberries on each following day so that seems she is following arithmetic sequence.
Whose first term is a = x
common difference d = 7
Given that on following Wednesday night, she had eaten a
total of 161 cranberries for the whole week.
Wednesday means on 7th day from thanksgiving day.
Then sum of 7 terms of the sequence is 161
S7=161
Sum of arithmetic sequcen is given by formula:
![S_n=\frac{n}{2}(2a+(n-1)d)](https://tex.z-dn.net/?f=%20S_n%3D%5Cfrac%7Bn%7D%7B2%7D%282a%2B%28n-1%29d%29%20)
![S_7=\frac{7}{2}(2*x+(7-1)*7)](https://tex.z-dn.net/?f=%20S_7%3D%5Cfrac%7B7%7D%7B2%7D%282%2Ax%2B%287-1%29%2A7%29%20)
![161=\frac{7}{2}(2x+6*7)](https://tex.z-dn.net/?f=%20161%3D%5Cfrac%7B7%7D%7B2%7D%282x%2B6%2A7%29%20)
![161=\frac{7}{2}(2x+42)](https://tex.z-dn.net/?f=%20161%3D%5Cfrac%7B7%7D%7B2%7D%282x%2B42%29%20)
![161*2=7(2x+42)](https://tex.z-dn.net/?f=%20161%2A2%3D7%282x%2B42%29%20)
![322=14x+294](https://tex.z-dn.net/?f=%20322%3D14x%2B294%20)
322-294=14x
28=14x
2=x
Hence Carissa ate 2 cranberries on Thanksgiving Thursday.
Now we have to find the number of day on which Carissa will eat 499 cranberries.
So we will use nth term formula
![t_n=a+(n-1)*d](https://tex.z-dn.net/?f=%20t_n%3Da%2B%28n-1%29%2Ad%20)
![499=2+(n-1)*7](https://tex.z-dn.net/?f=%20499%3D2%2B%28n-1%29%2A7%20)
![499=2+7n-7](https://tex.z-dn.net/?f=%20499%3D2%2B7n-7%20)
![499=7n-5](https://tex.z-dn.net/?f=%20499%3D7n-5%20)
![499+5=7n](https://tex.z-dn.net/?f=%20499%2B5%3D7n%20)
![504=7n](https://tex.z-dn.net/?f=%20504%3D7n%20)
72=n
Hence final answer is 72nd day.
Answer:
x² - 3x - 6
Step-by-step explanation:
One way to divide is to use the divisor as a factor in the numerator
Consider the numerator
= x²(x - 2) + 2x² - 5x² + 5
= x²(x - 2) - 3x(x - 2) - 6x + 5
= x²(x - 2) - 3x(x - 2) - 6(x - 2) - 12 + 5
= x²(x - 2) - 3x(x - 2) - 6(x - 2) - 7
quotient = x² - 3x - 6, remainder = - 7
Answer:
(0,10.2)
Step-by-step explanation:
If you could add a picture or tell me what the picture shows that would be great!