Answer:
A) 21
Step-by-step explanation:
Mean:
(23 + 18 + 24 + 15 + 25)/5
105/5
21
Answer:
2. congruent
3. congruent
Step-by-step explanation:
Segments will be congruent if their lengths are the same. Their lengths will be the same if the sum of squares of the x- and y-differences of their endpoint coordinates are the same.
2. B-A = (-4-(-4), 8-1) = (0, 7)
D-C = (5-(-2), -5-(-5)) = (7, 0)
The total of 0² and 7² is the same as the total of 7² and 0², so these segments are congruent. (They are both of length 7.)
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3. B-A = (2-4, 6-1) = (-2, 5)
D-C = (-4-(-2), -3-2) = (-2, -5)
The sum of (-2)² and 5² is the same as the sum of (-2)² and (-5)², so these segments are congruent. (They both are of length √29.)
The total number of marbles = 6 + 5 + 2 = 13 marbles
Orange= 2 marbles
The probability of getting the first marble out of the hat is
2 / 13
The probability of getting the second marble out of the hat is
1 / 12 The total has been reduced by one and the number of orange marbles has been reduced by one.
2/13 * 1/12 = 2 / 156 = 1/78
Answer:
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Step-by-step explanation:
Answer:
See Below.
Step-by-step explanation:
We are given that ΔAPB and ΔAQC are equilateral triangles.
And we want to prove that PC = BQ.
Since ΔAPB and ΔAQC are equilateral triangles, this means that:
Likewise:
Since they all measure 60°.
Note that ∠PAC is the addition of the angles ∠PAB and ∠BAC. So:
Likewise:
Since ∠QAC ≅ ∠PAB:
And by substitution:
Thus:
Then by SAS Congruence:
And by CPCTC:
