What scale factor was used when going from the grey triangle to the yellow triangle
2 answers:
Answer:
It was used as scale factor.
Step-by-step explanation:
The scale factor is the ratio of two corresponding side lengths of similar figures. Similar figures have the same shape but are of different sizes.
To find the scale factor that was used when going from the grey triangle to the yellow triangle we can work with any of the three sides of the grey triangle.
Let's work with the below side.
The below side is extended from the point to the point
The length of this side is 9 units.
In the yellow triangle, we can see that the below side is extended from the point to the point
The length of this side is 3 units.
Working with the lengths and the scale factor ⇒
We find that the scale factor that was used when going from the grey triangle to the yellow triangle is
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The correct answers are:
(1) 6, 11, 16, 21, 26 (Option B)
(2);
(Option A)
(3) (Option D)
Explanations:
(1) Given Sequence:
Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.
For n=1:
For n=2:
For n=3:
For n=4:
For n=5:
Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)
(2) Given Sequence:
8, 6, 4, 2, …
Now to find the recursive definition, we need to adopt trial-and-error approach.
As, (meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:
--- (1)
Where, n = the index of the number in a sequence
d = difference between two consecutive numbers = 8-6 = 2
Now,
The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):
Since , therefore,
(correct)
Hence the correct answer is ;
(Option A)
(3) Given Sequence:
−2, 1, 4, 7, …
To find the explicit definition, use the following formula:
--- (X)
Where,
Plug in the values in (X):
(X)=> (Option D)