Answer: 5/2
5/6 / 1/3 = 2.5
2.5 in fraction = 5/2
Answer:
30xy
Step-by-step explanation:
Answer:
the solution set consists of {x < -2 ∪ x > 10/3}
Step-by-step explanation:
|3x - 2| > 8 is equivalent to the following set of inequalities:
1) 3x - 2 > 8
and
2) -(3x - 2) > 8
In case 1, above, add 2 to both sides, obtaining 3x > 10, or x > 10/3.
In case 2, above, carry out the indicated multiplication first:
-3x + 2 > 8. Next, subtract 2 from both sides: -3x > 6.
Next, divide both sides by -3, remembering to reverse the direction of the inequality sign: x < -2.
Thus, the solution set consists of {x < -2 ∪ x > 10/3}
Answer:
The sum of the first 37 terms of the arithmetic sequence is 2997.
Step-by-step explanation:
Arithmetic sequence concepts:
The general rule of an arithmetic sequence is the following:
![a_{n+1} = a_{n} + d](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20a_%7Bn%7D%20%2B%20d)
In which d is the common diference between each term.
We can expand the general equation to find the nth term from the first, by the following equation:
![a_{n} = a_{1} + (n-1)*d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29%2Ad)
The sum of the first n terms of an arithmetic sequence is given by:
![S_{n} = \frac{n(a_{1} + a_{n})}{2}](https://tex.z-dn.net/?f=S_%7Bn%7D%20%3D%20%5Cfrac%7Bn%28a_%7B1%7D%20%2B%20a_%7Bn%7D%29%7D%7B2%7D)
In this question:
![a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%20-27%2C%20d%20%3D%20-21%20-%20%28-27%29%20%3D%20-15%20-%20%28-21%29%20%3D%20...%20%3D%206)
We want the sum of the first 37 terms, so we have to find ![a_{37}](https://tex.z-dn.net/?f=a_%7B37%7D)
![a_{n} = a_{1} + (n-1)*d](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7D%20%2B%20%28n-1%29%2Ad)
![a_{37} = a_{1} + (36)*d](https://tex.z-dn.net/?f=a_%7B37%7D%20%3D%20a_%7B1%7D%20%2B%20%2836%29%2Ad)
![a_{37} = -27 + 36*6](https://tex.z-dn.net/?f=a_%7B37%7D%20%3D%20-27%20%2B%2036%2A6)
![a_{37} = 189](https://tex.z-dn.net/?f=a_%7B37%7D%20%3D%20189)
Then
![S_{37} = \frac{37(-27 + 189)}{2} = 2997](https://tex.z-dn.net/?f=S_%7B37%7D%20%3D%20%5Cfrac%7B37%28-27%20%2B%20189%29%7D%7B2%7D%20%3D%202997)
The sum of the first 37 terms of the arithmetic sequence is 2997.