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Dmitry [639]
4 years ago
12

find two consecutive negative odd integers such that the square of the lesser integer is 40 more than the square of the greater

integer
Mathematics
1 answer:
nirvana33 [79]4 years ago
7 0
(x) ,  (x + 2)  consecutive odd integers
(x)^2 = 40 + (x + 2)^2 
x^2 = 40 + x^2 - 4x + 4
x^2 = x^2 - 4x + 44
subtract x^2 from both sides
0 = -4x + 44
subtract -4x from both sides
4x = 44
divide both sides by 4
x = 11* -1 = -11
x + 2 = -11 + 2 = -9
(-11)^2 = 40 + (-9)^2
121 = 40 + 81
121 = 121 CHECKS
-11 and -9 are the two negative integers.
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Answer:

\sum_{i=1}^n x_i = 334

\sum_{i=1}^n y_i =611

\sum_{i=1}^n x^2_i =13970

\sum_{i=1}^n y^2_i =51581

\sum_{i=1}^n x_i y_i =26584

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=13970-\frac{334^2}{10}=2814.4

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=26584-\frac{334*611}{10}=6176.6

And the slope would be:

m=\frac{6176.6}{2814.4}=2.195

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4

\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1

And we can find the intercept using this:

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So the line would be given by:

y=2.195 x -12.213

Step-by-step explanation:

The data given on this case is:

x: 14,12,20,16,46,23,48,50,55,50

y: 24,24,28,30,80,30,90,85,120,110

For this case we need to calculate the slope with the following formula:

m=\frac{S_{xy}}{S_{xx}}

Where:

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}

So we can find the sums like this:

\sum_{i=1}^n x_i = 334

\sum_{i=1}^n y_i =611

\sum_{i=1}^n x^2_i =13970

\sum_{i=1}^n y^2_i =51581

\sum_{i=1}^n x_i y_i =26584

With these we can find the sums:

S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=13970-\frac{334^2}{10}=2814.4

S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=26584-\frac{334*611}{10}=6176.6

And the slope would be:

m=\frac{6176.6}{2814.4}=2.195

Nowe we can find the means for x and y like this:

\bar x= \frac{\sum x_i}{n}=\frac{334}{10}=33.4

\bar y= \frac{\sum y_i}{n}=\frac{611}{10}=61.1

And we can find the intercept using this:

b=\bar y -m \bar x=61.1-(2.195*33.4)=-12.213

So the line would be given by:

y=2.195 x -12.213

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