3. Find the domain and range of the function represented by the graph.
1 answer:
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Answer:
The correct option is A.
Step-by-step explanation:
It is given that DEFG is a parallelogram.
Draw the diagonals DF and EG. Place point H where DF and EG intersect.
In triangle HGD and HEF
,
∠HGD ≅ ∠HEF (Alternate Interior angle)
∠HDG ≅ ∠HFE (Alternate Interior angle)
By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.
DG ≅ EF (Opposite sides of parallelogram)
According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.
So, by using ASA criterion for congruence we get,
ΔDGH ≅ ΔFEH
Since corresponding sides of congruent triangles are congruent, therefore
GH ≅ EH (CPCTC)
DH ≅ FH (CPCTC)
Option A is correct.
Answer:
There are 256 ways in total.
There are 56 possible outcomes contain exactly three heads.
The possible outcomes contain at least three heads is 219.
The possible outcomes contain the same number of heads and tails are 70.
Step-by-step explanation:
Consider the provided information.
A coin is flipped eight times where each flip comes up either heads or tails.
Part (a) How many possible outcomes are there in total?
Each time we flip a coin it comes up either heads or tail.
Therefore the total number of ways are:
Hence, there are 256 ways in total.
Part (b) contain exactly three heads?
We want exactly 3 heads, therefore,
n=8 and r=3
According to the definition of combination:
Hence, there are 56 possible outcomes contain exactly three heads.
Part (c) contain at least three heads?
For 3 heads:
For 4 heads:
For 5 heads:
For 6 heads:
For 7 heads:
For 8 heads:
Now add them as shown:
56+70+56+28+8+1=219
Hence, the possible outcomes contain at least three heads is 219.
Part (d) contain the same number of heads and tails?
Same number of heads and tails means that the value of r=4.
Therefore,
Hence, the possible outcomes contain the same number of heads and tails are 70.