A recipe uses 114 cups of sugar for a batch of brownies. Tommy makes 10 batches of cookies for a bake sale. How many cups of sug
2 answers:
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Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:
Where is the area of the regular hexagon
is the side length of the regular hexagon
Also, it's Perimeter is given by:
Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.
A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.
Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.
Let us now find the distance between the points D and E using the distance formula which is as:
Where is the distance.
and
are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance
)
Applying the above formula we get:
We know that this distance is the side length of the given regular hexagon.
Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:
Thus, the area of the smaller hexagon will be:
unit squared
and the new smaller perimeter will be:
unit
Which are the required answers.
Two options are given to Tina. We find how much she pays for each option, and the one in which she pays less offers the better value.
Tina sends 12 text messages each day in June
June has 30 days, so in June, Tina sent 12*30 = 360 text messages.
Package A:
First 100 messages cost 3p, the next 100 cost $2 and after that each costs $1.
She sends 360 messages, with:
The first 100 costing 3p.
The next 100 costing 2p.
The final 360 - 200 = 160 costing 1p.
She pays:
Package B:
2p for each message, 360 messages, so:
360*2p = 720p.
Which package is better?
Package A costs less, thus, it offers her the better value for money in 30 days.
Another example of a problem in which a person has to choose between two packages is given in brainly.com/question/10693932