A dilation is a transformation, with center O and a scale factor of k
that is not zero, that maps O to itself and any other point P to P'.
The center O is a fixed point, P' is the image of P, points O, P and P'
are on the same line.
Thus, a dilation with centre O and a scale factor of k maps the original figure to the image in such a way that the<span>
distances from O to the vertices of the image are k times the distances
from O to the original figure. Also the size of the image are k times the
size of the original figure.
In the dilation of triangle TUV</span>, It is obvious that the image <span>T'U'V' is smaller than the original triangle TUV and hence the scale factor is less than 1.
</span>The ratio of the
distances from A to the vertices of the image T'U'V' to the distances
from A to the original triangle TUV is the scale factor.
The scale factor = 3.2 / 4.8 = 2/3
First, the difference is 7/2 - 6/4 = 14/4 - 6/4 = 8/4
Now multiply it: 8/4 x (-2/5) = -16/20 = -4/5
Answer: option B is the correct answer.
Step-by-step explanation:
Susan drove at an average speed of 30 miles per hour for the first 30 miles of a trip.
Time = distance/speed
This means that time spent by Susan in travelling the first 30 miles would be
Time = 30/30 = 1 hour
He travelled at an average speed of 60 miles per hour for the remaining 30 miles of the trip.
Time = 30/60 = 0.5 hours
Total distance travelled is 30 + 30 = 60 miles.
Total time spent = 1 + 0.5 = 1.5 hours
Speed = distance/time
Average speed = 60/1.5 = 40 miles per hour.
Answer:
3.
Step-by-step explanation:
This is a geometric series so the sum is:
a1 * r^n - 1 / (r - 1)
= 1 * (2^101 -1) / (2-1)
= 2^101 - 1.
Find the remainder when 2^101 is divided by 7:
Note that 101 = 14*7 + 3 so
2^101 = 2^(7*14 + 3) = 2^3 * (2^14)^7 = 8 * (2^14)^7.
By Fermat's Little Theorem (2^14) ^ 7 = 2^14 mod 7 = 4^7 mod 7.
So 2^101 mod 7 = (8 * 4^7) mod 7
= (8 * 4) mod 7
= 32 mod 7
= 4 = the remainder when 2^101 is divided by 7.
So the remainder when 2^101- 1 is divided by 7 is 4 - 1 = 3..
