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Answer:
a) ∆ABC ~ ∆EDC by AA similarity
b) ED/AB = 3/4
c) 15 cm
Step-by-step explanation:
a) Two angles in each triangle are the same, so the AA similarity postulate can be used to declare the ∆ABC ~ ∆EDC. (Each triangle includes a right angle and angle C.)
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b) Corresponding sides are ED/AB, DC/BC, EC/AC. The ratio of corresponding sides is ED/BC = (12 cm)/(16 cm) = 3/4.
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c) Using the ratios identified above, we have ...
DC/BC = 3/4 = x/(20 cm)
x = 3/4(20 cm)
x = 15 cm
Answer:
okay thank you for free points
Answer:
Recall that a relation is an <em>equivalence relation</em> if and only if is symmetric, reflexive and transitive. In order to simplify the notation we will use A↔B when A is in relation with B.
<em>Reflexive: </em>We need to prove that A↔A. Let us write J for the identity matrix and recall that J is invertible. Notice that 
. Thus, A↔A.
<em>Symmetric</em>: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that 
. In this equality we can perform a right multiplication by 
and obtain 
. Then, in the obtained equality we perform a left multiplication by P and get 
. If we write 
and 
we have 
. Thus, B↔A.
<em>Transitive</em>: We need to prove that A↔B and B↔C implies A↔C. From the fact A↔B we have and from B↔C we have 
. Now, if we substitute the last equality into the first one we get
.
Recall that if P and Q are invertible, then QP is invertible and 
. So, if we denote R=QP we obtained that
. Hence, A↔C.
Therefore, the relation is an <em>equivalence relation</em>.
Answer:
= 9.2 cm
Step-by-step explanation:
D = C ÷ π
= 29cm ÷ 3.14
= 9.2356
= 9.2 cm
Answer:
Whelan
Step-by-step explanation:
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