Find the length of side x in simplest radical form with a rational denominator.
1 answer:
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When a triangle is rotated, it must be rotated through a center of rotation.
Assume the coordinate of LMN is
The rule of 180-degree rotation is:
So, we have:
See attachment for the graphs of LMN and L'M'N
<u>(a) Describe the transformation</u>
When triangle LMN is rotated 180 degrees across the origin, the x and y coordinates of LMN are negated to form triangle L'M'N'
<u>(b) Lines LL' and MM'</u>
The distance between point L and the center of origin is the same as the distance between point M' and the center of origin
Similarly, the distance between point L and the center of origin is the same as the distance between point M' and the center of origin
<u>(c) Line NN'</u>
Line NN' will assume the same characteristics as lines LL' and MM'
Read more about transformations at:
Question:
A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability that the sum of the two integers will equal 9?
A. 0.15
B. 0.20
C. 0.25
D. 0.30
E. 0.33
Answer:
Option B: 0.20 is the probability of the sum of the two integers.
Explanation:
The sample space for selecting 2 numbers is given by
We need to determine the probability that the sum of two integers will be equal to 9.
Hence, we need to add the two integers from the sets A and B such that their sum will be equal to 9.
Hence, the sets are
Thus, the total number of sets whose sum is equal to 9 = 4
The probability that the sum of the two integers will equal 9 is given by
Thus, the probability that the sum of the two integers will equal 9 is 0.20
Hence, Option B is the correct answer.