Check the picture below.
notice the red rise/run slopes, are the same, thus those two lines are parallel, and also notice the green one for the other two lines, meaning both pair of lilnes are parallel.
The sum of the series 
is 44.
Step-by-step explanation:
The given series is 
To find the sum of the series, we need to substitute the values for k in the series.
![\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right]](https://tex.z-dn.net/?f=%5Csum_%7Bk%3D1%7D%5E%7B4%7D%5Cleft%282%20k%5E%7B2%7D-4%5Cright%29%3D%5Cleft%5B2%281%29%5E%7B2%7D-4%5Cright%5D%2B%5Cleft%5B2%282%29%5E%7B2%7D-4%5Cright%5D%2B%5Cleft%5B2%283%29%5E%7B2%7D-4%5Cright%5D%2B%5Cleft%5B2%284%29%5E%7B2%7D-4%5Cright%5D)
Now, simplifying the square terms, we get,
![[2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4]](https://tex.z-dn.net/?f=%5B2%281%29-4%5D%2B%5B2%284%29-4%5D%2B%5B2%289%29-4%5D%2B%5B2%2816%29-4%5D)
Multiplying the terms,
![[2-4]+[8-4]+[18-4]+[32-4]](https://tex.z-dn.net/?f=%5B2-4%5D%2B%5B8-4%5D%2B%5B18-4%5D%2B%5B32-4%5D)
Subtracting the values within the bracket term, we get,
Now, adding all the terms, we get the sum of the series,
Thus, the sum of the series is
Answer:
8 1/30
Step-by-step explanation:
Calculate by converting into improper fractions.
Answer:
Her net annual salary is of $58,788
Step-by-step explanation:
The gross monthly salary is the salary earned before deductions are applied.
The net monthly salary is the salary after deductions are applied.
In this problem:
Gross monthly salary of a manager is $5875.
Deductions of $976
So net monthly salary = 5875 - 976 = $4899
Net yearly salary:
An year has 12 months. So
12*$4899 = $58,788
Her net annual salary is of $58,788
Answer:
60
Step-by-step explanation:
135 = (2x+15)
120 = 2x
x = 60
