4. Using the given information, which lines, if any, can you conclude are parallel? Justify your conclusion with a theorem or postulate. Angle 1 is supplementary to angle 4. 9/11 v 1/5 2/6 10/12 b A 3/7 4 8 1 O || m by Converse of the Corresponding Angles postulate Oa || b by Converse of the Corresponding Angles Postulate Ollm by Converse of the Same-Side Exterior Angles Theorem Oa || b by Converse of the Same-Side Exterior Angles Theorem
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Answer:
Option (4)
Step-by-step explanation:
It has been given in the question that angle 1 is supplementary to angle 4.
m∠1 + m∠4 = 180°
∠2 and ∠3 are the interior consecutive angles.
Since, same side of the theorem says "Exterior angles formed on the same side of the parallel lines and the transversal line are supplementary".
Therefore, by converse of the same side Exterior angles theorem 'a' and 'b' will be parallel.
Option (4) will be the answer.
Final answer:
Given that Angle 1 and Angle 4 are supplementary, no lines can be concluded to be parallel as according to the Converse of the Corresponding Angles Postulate, the angles need to be congruent (equal), not supplementary, to infer parallel lines.
Explanation:
From the given information, it is mentioned that Angle 1 is supplementary to Angle 4. In geometry, supplementary angles are two angles that add up to 180 degrees. By the converse of the corresponding angles postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.
In the context of your question, since the angles given are supplementary, they add up to 180 degrees and hence are not congruent. This implies, according to the corresponding angles postulate, that no lines can be concluded to be parallel based on the provided information. This is because the postulate only holds for congruent (equal), not supplementary angles.
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A=π(R+r)(R-r) is the factorization of the polynomial.
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Factorizing completely we get:
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Hope this helped!
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Answer:
Rotation about 90° counter clockwise (x , y) →→ ( -y, x ).
Step-by-step explanation:
Given : Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices X'(–3, 1), Y'(0, 0), and Z'(–2, –1).
To find : Which rule describes the transformation.
Solution : We have given
vertices X(1, 3) →→ X'(–3, 1)
Y(0, 0) →→ Y'(0, 0),
Z(–1, 2) →→ Z'(–2, –1).
Here , we can see in each coordinates value of y become -x and x become y.
(x , y) →→ ( -y, x ) this the rule of rotation about 90° counter clockwise.
Therefore, rotation about 90° counter clockwise (x , y) →→ ( -y, x ).
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Answer: C received 20% of the votes so C would be your answer
Answer:
Step-by-step explanation:
Let C received x% votes. Then B received 3x% votes. B and C together received 80% of votes because A received the remaining 20%.
x + 3x = 80
4x = 80
x = 20
Answer: c) 20%
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Answer:
The approximate time that it will take Mary to save R40000 is 29 years
Step-by-step explanation:
A= p(1+r/n)^nt
t = log(A/P) / n[log(1 + r/n)]
A = R40000
n = 4
P = R400
r = 16%
t = log(A/P) / n[log(1 + r/n)]
= log(40,000 / 400) / 4{log(1+0.16/4)}
= log(100) / 4{log(1+0.04)}
= 2 / 4{log(1.04)}
= 2 / 4(0.0170)
= 2 / 0.068
= 29.41
t = 29.41 years
Approximately 29 years
The approximate time that it will take Mary to save R40000 is 29 years