Can you help me with these questions
1 answer:
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Answer:
POSTULATE
Step-by-step explanation:
<em>A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven </em>
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<em>In geometry, the theorem is considered valid or correct with which its assertion is practically not refuted by almost anyone, whether it is really true or not. </em>
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<em>This, in practice, implies that all students of the subject share the same criteria on the theory. Thus, the postulates, in short, have the following characteristics: </em>
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<em> They are presumed true by most of the scholars in the field. </em>
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<em>Its contradiction goes against the very essence of the subject. </em>
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<em>Postulate 6: If two planes intersect, then their intersection is a line.</em>
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<em>See Attachment for Details ^^</em>
<em>The image attached represents the statement given in the question (If two distinct planes intersect, then their intersection is a line)</em>
<em>Therefore</em><em>, </em>
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<em>The Geometry term that represents the statement above is POSTULATE</em>
Answer:
740
Step-by-step explanation:
The n th term of an arithmetic series is
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 7 and a₇ = (3 × 7) + 2 = 21 + 2 = 23 , then
a₁ + 2d = 7 → (1)
a₁ + 6d = 23 → (2)
Subtract (1) from (2) term by term
4d = 16 ( divide both sides by 4 )
d = 4
Substitute d = 4 into (1)
a₁ + 2(4) = 7
a₁ + 8 = 7 ( subtract 8 from both sides )
a₁ = - 1
The sum to n terms of an arithmetic series is
=
[ 2a₁ + (n - 1)d ] , thus
=
[ (2 × - 1) + (19 × 4) ]
= 10(- 2 + 76) = 10 × 74 = 740