Triangles FGH and ABC are congruent because of the: AAS congruence theorem.
<h3>What is the AAS Congruence Theorem?</h3>
The AAS congruence theorem states that when two angles and one non-included side in one triangle are congruent to corresponding two angles and one non-included side in another triangle, then both triangles are congruent.
In the proof given, it is established that both triangles have two corresponding congruent angles, and also, BC ≅ GH which are non-included sides.
Therefore, both triangles are congruent because of the AAS congruence theorem.
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Answer:
The coordinates of the circumcenter of triangle ABC is 
.
Step-by-step explanation:
The circumcenter of triangle ABC is the point of intersection of any two perpendicular bisectors of any two sides of the given triangle.
The equation of the perpendicular bisector of side B(3,0) and C(3,2) is 
.
Since the midpoint of AB is 
and its slope is undefined. The perpendicular bisector has a slope of zero. The equation of such line is 
.
Also the equation of the perpendicular bisector of A(0,0) and B(3,0) is 
. The reason is that the midpoint of AB is 
and its slope is zero. The perpendicular bisector will have an undefined slope. The equation of such line is given by 
.
These two perpendicular bisectors will intersect at . These are the coordinates of the circumcenter of the triangle.
Answer:
C with 3000 successes of 5000 cases
Step-by-step explanation:
In test statistics the number of samples goes a long way in determining the result of a test.
Using the z score formula
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size
po = Null hypothesized value
p^ = Observed proportion
Therefore the z score is directly proportional to the square root of the sample size.
z ∝ √n
The higher the sample size, the higher the z score, the higher the evidence of confirming the alternative hypothesis.
Since the all have the same proportion (0.6), and options c has the highest sample size (5000 cases), it will give the strongest evidence for the alternative hypothesis
Answer:
T.
Step-by-step explanation:
The ordered pair (-2,-1) can also be represented by (x,y). To check the inequality we can substitute the values into the given inequality.
After substituting the values, we then have a clear view that -1 is Greater than -3.1622.
