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arissahyp73x7x
17.11.2020 •
Mathematics
How many diagonals can be constructed from one vertex of an n-gon? State your answer in terms of n and, of course, justify your answer.
IM REPOSTING THIS QUESTION, BUT THIS TIME FOR 15 POINTS
PLEASE HELP :)
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Ответ:
Step-by-step explanation:
A diagonal is defined in geometry as a line connecting to two non adjacent vertices.
Therefore, the minimum number of sides a polygon must have in order to have a diagonal n - 3 sides as the 3 comes from the originating vertex and the other two adjacent vertices
Given that the polygon has n sides, the number of diagonals that can be drawn from each of those n sides gives the total number of diagonals as follows;
Total possible diagonals = n × (n - 3)
However, half of the diagonals drawn within the polygon are the same diagonals drawn in reverse. Therefore, the total number of distinct diagonals that can be drawn in a polygon is given as follows;
Ответ:
Part A = B. 1 ÷ 1/3 = 3
Part B = 27 brownies
Step-by-step explanation:
Part A
From the ingredients given in above question:
1/3 cup of butter = 1 batch of brownies
Hence: 1 cup of butter = x
Cross Multiply
1/3 cup of butter × x = 1 cup of butter × 1 batch of brownies
x = 1 cup of butter × 1 batch of brownies/1/3 cup of butter
x = 1 batch of brownies ÷ 1/3
x = 1 batch of brownies × 3/1
x = 3 batches of brownies
Hence, the number brownies Jackson can make with 1 cup of butter Is 3 batches of brownies
Therefore, the equation you can use to solve the problem is Option B. 1 ÷ 1/3 = 3
Part B
If each brownie is 1/9 of a batch, how many brownies did he make?
We know from Part A that Jackson made 3 batches of brownies hence:
1/9 of a batch of brownies = 1 brownie
3 batches of brownies = x
Cross Multiply
1/9 of a batch of brownies × x = 1 brownie × 3 batches of brownies
x = 1 brownie × 3 batches of brownies/ 1/9 of a batch of brownies
x =( 3 ÷ 1/9) brownies
x = ( 3 × 9/1) brownies
x = 27 brownies
Therefore, the number of brownies he made was 27 brownies.