There are nine 'different' slots we can fill in for each value. Thus, we get 9! different ways, including repetition.
Now, we need to account for repetition. This can be visualised as separate letters as below:
s₁ u c₁ c₂ e₁ s₂ s₃ e₂ s₄
We can arrange them like this, and we'd never know the difference:
s₁ u c₂ c₁ e₂ s₃ s₂ e₁ s₄
s₄ u c₁ c₂ e₁ s₁ s₃ e₂ s₂
Thus, we have overcounted by a factor of 2! (c's can change in 2! ways), 2! (e's can change in 2! ways), and 4! (s' can change in 4! ways).
Therefore, our final number of permutations becomes:
Answer: to wirte and solve for a missing side length of a rectangle, do your perimeter equation backwards, hope this helps
Step-by-step explanation:
Answer:
The quadrilaterals ABCD and A'B'C'D' are congruent only if k = 1.
The corresponding side lengths are related by k(CB) = C'B'.
Step-by-step explanation:
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
Dilation is the increase or decrease in size of a figure by a factor k. If k > 1, the figure is increased, if k < 1, the figure is reduced and if k = 1, the figure does not changes shape. The image of an dilated figure is similar to the original image.
a) If k = 1, then the resulting image produced by dilating ABCD is congruent. Hence, The quadrilaterals ABCD and A'B'C'D' are congruent only if k = 1.
b) Dilation produce image similar to the original figure, hence quadrilaterals ABCD and A'B'C'D' are similar only if k ≥ 1 and k < 1.
c) Since ABCD is dilated by a factor of k to produce A'B'C'D', hence A'B' = k(AB).
d) C'B' = k(CB)
Answer:
<em>The birch tree needs 12 years</em>
Step-by-step explanation:
<u>Proportional Relationship</u>
Two variables t and d are proportional if they have the relationship described by the equation:
d = kt
Where k is the constant of proportionality.
From the graph on the question, we recognize the proportionality of the age of a birch tree and its diameter because the line passes through the origin (0,0). To find the equation, we need to recognize a clear point on the graph. We select the point (2,7). Substituting in the equation:
7 = 2k
Thus:
The equation is:
For the birch to have a diameter of d=42 inches, the time needed can be calculated by solving the equation:
t = 12 years
The birch tree needs 12 years
I don’t know. Need for information about it. Is this a book