Assume that the initial coordinates are (x,y) and that the dilated coordinates are (x',y').
The dilation is therefore:
(x,y) ............> (x',y')
Now, let's assume that the dilation factor is k.
Therefore:
x' = kx
y' = ky
Based on the above, all the student has to do is get the initial coordinates and the final ones and then substitute in any of the above two equations to get the value of k.
Example:
Assume an original point at (2,4) is dilated to coordinates (4,8). Find the dilation factor.
Assume the dilation coefficient is k.
(x,y) are (2,4) and (x',y') are (4,8)
Therefore:
x' = kx .........> 4 = k*2 ..........> k = 2
or:
y' = ky ..........> 8 = k*4 .........> k = 2
Based on the above, the dilation coefficient would be 2.
Hope this helps :)
This is a positive temperature.
Answer:
a). r = 
b). At least 5 terms should be added.
Step-by-step explanation:
Formula representing sum of infinite geometric sequence is,

Where a = first term of the sequence
r = common ratio
a). If the sum is seven times the value of its first term.


7(1 - r) = 1
7 - 7r = 1
7r = 7 - 1
7r = 6
r = 
b). Since sum of n terms of the geometric sequence is given by,

If the sum of n terms of this sequence is more than half the value of the infinite sum.
> 







n[log(0.85714)] < log(0.5)
-n(0.06695) < -0.30102
n > 
n > 4.496
n > 4.5
Therefore, at least 5 terms of the sequence should be added.
Answer:
x = -13
Step-by-step explanation:
Let the number be x. ATQ,

The above equation shows Three-fourths of the difference of a number and 7 is negative fifteen. We need to find the number.
cross multiplying both sides,

So, the number is -13.