Short answer: Yes.
Each member of the sequence is multiplied by 5 to get to the next member of the sequence.
Find the general equation.
tn = a*5^(n - 1)
Example
t4 = 1*5^(4 - 1)
t4 = 1*5^3
t4 = 125 just as the sequence shows.
t5 = 1^5^4
t5 = 625 Any member of the sequence can be found this way.
Answer:BC=68
DE=36
CE=34
Step-by-step explanation:
Since D, E and F are the midpoints, they follow the midpoint theorm which states that "The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side." As for others, it's just the calculation.
Step-by-step explanation:
step one:
given that the sample space is
red, yellow, green, white, and black. i.e (1+1+1+1+1)= 5
the sample size is 5
the probability of picking a colored card at random is
Pr(a colored card)= 1/5
step two:
without replacement, after the first event, the sample size is now 4
then the probability of picking a colored card at random is
Pr(a colored card)= 1/4
Answer:
A translation of 3 units to the right and a translation of one unit upwards.
Step-by-step explanation:
When we analyze translations of whole figures, all the points in the figure suffer the same translation, then we only need to analyze the translation of one of the points.
This means that we can only see the translation from A to A'
First, let's find the coordinates of each point:
A (2, 3)
A' (5, 4)
The translation is given if we calculate the difference between these coordinates:
A' - A = (5, 4) - (2, 3) = (5 - 2, 4 - 3) = (3, 1)
The change in the x-value is 3.
The change in the y-value is 1.
Then we can conclude that:
A' is 3 units at the right of A
A' is 1 unit above A.
Then the translation is:
A translation of 3 units to the right and a translation of one unit upwards.
Answer:
see below
Step-by-step explanation:
To find the coordinates of the midpoints, add the x's and divide by 2 and add the y's and divide by 2.
The coordinates of D, the midpoint of AB, (1+3)/2 will be the x-coordinate and (4+0)/2 will be the y-coordinate.
D (2,2)
You could also see this on a graph, see image.
E, the midpoint of AC has the x-coordinate (1+-3)/2, which is -1 and y-coordinate (4+-2)/2 which is 1.
E is (-1,1)
Then we are able to calculate the slope of DE and BC.
To calculate slope, subtract the y's and put that on top of a fraction and subtract x's and put that on the bottom of a fraction. If the slopes are the same the segment are parallel.
Slope of DE:
(2-1)/(2--1)
= 1/3
Slope of BC:
(0--2)/(3--3)
=2/6
=1/3
The slopes of BC and DE are equal, so the segments are parallel.
(Alternatively, you could show that Triangle ABC and Triangle ADE are similar. Then find the segments parallel because corresponding angles are congruent.)
