12 will be opposite to 24. Then the number of the people are sitting at the table will be 24.
<h3>What is Algebra?</h3>
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The several people are sitting evenly spaced around a circular table and the positions are labelled 1, 2, 3 and so on.
The people at positions 3 and 15 are directly opposite each other.
Then the number of the people are sitting at the table will be
1 is opposite to 13
2 is opposite to 14
3 is opposite to 15
Similarly, 12 will be opposite to 24.
Then the number of the people are sitting at the table will be 24.
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The equations would be:
x=18+3y
x+y=54
(substitute x in the second equation with 18+3y)
18+3y+y=54
(combine like terms and solve for y)
y=9
(plug y into the second equation to find x)
x+9=54
x=45
Answer:
Proved that GB ≅ AH.
Step-by-step explanation:
See the attached diagram.
Statement 1: ∠ GBH ≅ ∠ AHB
Reason 1: This is given.
Statement 2: ∠ GHB ≅ ∠ ABH
Reason 2: This is also given.
Statement 3: BH ≅ HB.
Reason 3: From the diagram. Reflexive property of congruence.
Statement 4: Δ GBH ≅ Δ AHB
Reason 4: By Angle-Side-Angle or ASA criteria of congruency.
Statement 5: GB ≅ AH
Reason 5: Corresponding sides of two congruent triangles. (Proved)
Answer:x=13
BMC=75 degrees
Step-by-step explanation:
(x+2)+(5x+10)=90 degrees
so 6x+12=90
x=13
5x+10=5x13+10=75 degrees