Answer:
We need the following three rigid motions:
i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.
Step-by-step explanation:
We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':
i) Reflection around y-axis:
(Eq. 1)
ii) Translation three units in the -y direction:
(Eq. 2)
iii) Translation four units in the -x direction:
(Eq. 3)
We proceed to proof the effectiveness of operations defined above by testing point D:
1) 
Given.
2) 
By (Eq. 1)
3) 
By (Eq. 2)
4) 
By (Eq. 3)/Result
Using the two parallel line theorems we proved that ∠8 ≅ ∠4.
In the given question,
Given: f || g
Prove: ∠8 ≅ ∠4
We using given diagram in proving that ∠8 ≅ ∠4
Since f || g, by the Corresponding Angles Postulate which states that "When a transversal divides two parallel lines, the resulting angles are congruent." So
∠8≅∠6
Then by the Vertical Angles Theorem which states that "When two straight lines collide, two sets of linear pairs with identical angles are created."
∠6≅∠4
Then, by the Transitive Property of Congruence which states that "All shapes are congruent to one another if two shapes are congruent to the third shape."
∠8 ≅ ∠4
Hence, we proved that ∠8 ≅ ∠4.
To learn more about parallel line theorems link is here
brainly.com/question/27033529
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Answer:
0.0656
Step-by-step explanation:
For each message, we have these following probabilities:
90% probability it is spam.
10% probability it is legitimate.
Compute the probability that the first legitimate e-mail she finds is the fifth message she checks:
The first four all spam, each with a 90% probability.
The fifth legitimate, with a 10% probability.
The decimal is irrational because it is not repeating.
Answer:
<u>$71.33</u>
Step-by-step explanation:
An automobile warranty costing = $856
It is required to make 12 equal payments
So, we need to divide $856 over 12
So, the average payment = 856/12 = $71.33
