In a city park, three walking paths form triangle ABC. The length AB is 800 meters, the length BC is 900 meters, and the length
AC is 850 meters. Which angle of this triangle has the greatest measure?
2 answers:
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Answer:
[Vertex form]
Step-by-step explanation:
Given function:
We need to find the vertex form which is.,
where represents the co-ordinates of vertex.
We apply completing square method to do so.
We have
First of all we make sure that the leading co-efficient is =1.
In order to make the leading co-efficient is =1, we multiply each term with -3.
Isolating and
terms on one side.
Subtracting both sides by 15.
In order to make the right side a perfect square trinomial, we will take half of the co-efficient of term, square it and add it both sides side.
square of half of the co-efficient of term =
Adding 36 to both sides.
Since is a perfect square of
, so, we can write as:
Subtracting 21 to both sides:
Dividing both sides by -3.
[Vertex form]
Answer:
There are 122 one dollar bills, 11 five dollar bills and 5 ten dollar bills.
Step-by-step explanation:
There are bills of one dollar, five dollars and ten dollars on the cash drawer, therefore the sum of all of them multiplied by their respective values must be equal to the total amount of money on the drawer. We will call the number of one dollar bills, five dollar bills and ten dollar bills, respectively "x","y" and "z", therefore we can create the following expression:
We know that there are six more 5 dollar bills than 10 dollar bills and that the number of 1 dollar bills is two more than 24 times the number of 10 dollar bills, therefore:
Applying these values on the first equation, we have:
Applying z to the formulas of y and x, we have:
There are 122 one dollar bills, 11 five dollar bills and 5 ten dollar bills.