Translations are transformations that change the position of the graph of a function. The general shape of the graph of a function is moved up, down, to the right or to the left. The translations are considered rigid transformations.
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
We have then:
f (x) = 2 ^ x
g (x) = f (x) + k
if k = 2
then,
the graph of g (x) is shifted vertically 2 units up
Answer:
the graph of g (x) is shifted vertically 2 units up
Answer:
degrees apart in latitude: 91.22
degrees apart in longitude: 147.95
Step-by-step explanation:
Liverpool and Melbourne are two cities that are located very far away from each other. Liverpool is located in the northwestern part of England, while Melbourne is located in the southeastern part of Australia, so understandably their latitudes and longitudes are very different. In order to get to the distance in degrees between these two cities in latitude and longitude, we just simply need to sum the degrees of both of them and we will get to the result. The reason why simple summing will do the job is because they are on separate hemispheres, with Liverpool being on the Northern and Western Hemisphere, while Melbourne being on the Southern and Western Hemisphere.
Latitude distance:
53.41 + 37.81 = 91.22
Longitude distance:
2.99 + 144.96 = 147.95
Answer:
Sum of the sequence will be 648
Step-by-step explanation:
The given sequence is representing an arithmetic sequence.
Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6
3 - (-3) = 3 + 3 = 6
Since last term of the sequence is 81
Therefore, by the explicit formula of an arithmetic sequence we can find the number of terms of this sequence
where a = first term of the sequence
d = common difference
n = number of terms
81 = -9 + 6(n - 1)
81 + 9 = 6(n - 1)
n - 1 = 
n = 15 + 1 = 16
Now we know sum of an arithmetic sequence is represented by
Now we have to find the sum of the given sequence
![S_{16}=\frac{16}{2}[-9 + (16-1)6]](https://tex.z-dn.net/?f=S_%7B16%7D%3D%5Cfrac%7B16%7D%7B2%7D%5B-9%20%2B%20%2816-1%296%5D)
= 8[-9 + 90]
= 8×81
= 648
Therefore, sum of the terms of the given sequence will be 648.
We first notice that the sequence of numbers:
12, 21, 30, 39, 48 increases by 9 ($ per day).
We see that these values, related to the days 0, 1, 2, 3, 4 can be written as follows:
12=0*9+12
21=1*9+12
30=2*9+12
39=3*9+12
48=4*9+12
Thus, the price to pay for renting a lawn mower x days is y=9x+12.
Answer: y=9x+12
Yes because it has the multiples of 7&1
Hope this helps
