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3 years ago

Find all Values of b that will make the polynomial a perfect square trinomial.

Mathematics

1 answer:

weeeeeb [17]3 years ago

8 0

Answer:

10,404/334,084

Step-by-step explanation:

Given the polynomial

289r^2 - 102r + c

We are to find the value of c that will make it a perfect square

Divide through by 289

289r²/289 - 102r/289 + c/289

Half of the coefficient of r is 1/2(102/289)

Half of the coefficient of r = 102/578

Square the result

r² = (102/578)²

r² = 10,404/334,084

Hence the required constant is 10,404/334,084

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Easy question what is your favorite part of Christmas.

Ivenika [448]

Answer:

Hanging out with my family. :D

Step-by-step explanation:

6 0

3 years ago

Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client

vlada-n [284]

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:

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

So the line would be given by:

$y=2.195 x -12.213$

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:

$y=2.195 x -12.213$

5 0

3 years ago

The volume of a cylinder is 768 N in³. Find the radius of the cylinder (in inches) if the height is 3 in

yarga [219]

To find the volume of the cylinder we multiply the area of the face by the height of the cylinder. Area pi*r^2
First find area
768in^3/3in = 256in^2
Pi*r^2 = 256
r^2 = 256 / pi
radius = root of 256/pi
Hence radius = 9.027033337 in
To check answer
Pi*9.027033337^2 * 3in = 768in^3

Finalized answer to 2 d.p
Radius = 9.03 in

6 0

3 years ago

Which of the binomials below is a factor of this trinomial 3x^2+18-21

KengaRu [80]

Answer:

Step-by-step explanation:

you will get 3(x-1)×(x+1) you can get the 3 and x by itself then it would be x+3

4 0

3 years ago

What is information given in numbers called? A) facts B)data C) figures D)estimates

yKpoI14uk [10]

Answer:

B) Data

Step-by-step explanation:

Data has to do with numbers.

3 0

4 years ago

Read 2 more answers