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Colt1911 [192]
3 years ago
13

Algebraically find three consecutive positive integers such that the square of the first is equal to the third.

Mathematics
1 answer:
dexar [7]3 years ago
7 0
Your numbers are 2, 3, 4.

The three consecutive numbers are x, x+1, x+2
The square of the first equals the third so x^2=x+2
Solve this quadratic as x^2-x-2=0
Factor into (x+1)(x-2)=0
So your answers are x=-1 and x=2
Since the question says they’re positive integers, use x=2
So the numbers are 2, 3, 4
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<em>Note: You may have missed to add the dot plots chart, so I found the chart after a little research and hence, I am attaching it and based on that dot plot chart I am solving the question which anyways would clear you concept.</em>

Answer:

''The median for the students is 2 and the median for the teachers is 3'' is the right option which compares the medians of the data.

Step-by-step explanation:

Data for students from the dot plot in order

0,\:0,\:1,\:1,\:1,\:1,\:2,\:2,\:2,\:2,\:2,\:2,\:2,\:3,\:3,\:3,\:3,\:3,\:4,\:4

Calculating Median for students:

0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

As you can see, we do not have just one middle number but we have a pair of middle numbers i.e. 2 and 2, so the median is the average of these two numbers:

Median = (2+2)/2

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Data for teachers from the dot plot in order

0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8

Calculating Median for teachers:

0, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 8

As you can see, we do not have just one middle number but we have a pair of middle numbers i.e. 3 and 3, so the median is the average of these two numbers:

Median = (3+3)/2

            =6/2

            = 3

Therefore, ''the median for the students is 2 and the median for the teachers is 3'' is the right option which compares the medians of the data.

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