5 minus 3 1/3 is 1 2/3
step one: turn into improper fractions
15/3 minus 10/3
step two : answer
15/3 minus 10/3 = 5/3 =1 2/3
Answer:
f(t) = 5t
Step-by-step explanation:
distance = speed × time
d = st Insert value of speed
d = 5t
In function notation,
f(t) = 5t
Answer:
Slope = 1
This is becuase the rise is 1 and the run is 1.
Answer:
Domain:![[-1,0]\cup [1,\infty )](https://tex.z-dn.net/?f=%5B-1%2C0%5D%5Ccup%20%5B1%2C%5Cinfty%20%29)
Step-by-step explanation:
Since we know that a square root function is not defined for negative numbers. In order our function to be defined values inside radical must be greater than or equal to zero.
Our function will be defined when


or 
Now we will use number line method of solving inequalities to check whether our answer is right or not.
Let us try -2, -1/2, 1/2 and 2 to check which conditions meet our criteria.






Therefore, we can see that our function is defined when
or
and domain of f(x) is
.
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 