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3 years ago

The sum of the interior angles of an n-sided polygon is 5400 the value of n is?

Mathematics

2 answers:

IRISSAK [1]3 years ago

7 0

Answer:

Step-by-step explanation:

180*(n-2)=5400

180*(n-2/180)=5400/180

n-2=30

n=30+2

n=32

Mandarinka [93]3 years ago

6 0

Answer:

32 sides

Step-by-step explanation:

The sum of the interior angles of a polygon is (n-2)*180 where n is the number of sides

(n-2) * 180 = 5400

Divide by 180

(n-2) * 180/180 = 5400/180

n-2 = 30

Add 2 to each side

n-2+2 = 30+2

n =32

There are 32 sides

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Solve 5x 2 - 7x + 2 = 0 by completing the square. What are the solutions?

Alexeev081 [22]

Answer:

$x=\frac{2}{5}$ or $x=1$

Step-by-step explanation:

The given quadratic equation is

$5x^2-7x+2=0$

Group the constant terms on the right hand side.

$5x^2-7x=0-2$

$5x^2-7x=-2$

Divide through by 5.

$x^2-\frac{7}{5}x=-\frac{2}{5}$

Add the square of half the coefficient of x., which is $(\frac{1}{2}\times- \frac{7}{5})^2=\frac{49}{100}$ to both sides of the equation.

$x^2-\frac{7}{5}x+\frac{49}{100}=-\frac{2}{5}+\frac{49}{100}$

The left hand side is now a perfect square.

$(x-\frac{7}{10})^2=\frac{9}{100}$

Take the square root of both sides;

$(x-\frac{7}{10})=\pm \sqrt{\frac{9}{100}}$

$x-\frac{7}{10}=\pm \frac{3}{10}$

$x=\frac{7}{10}\pm \frac{3}{10}$

$x=\frac{7-3}{10}$ or $x=\frac{7+3}{10}$

$x=\frac{4}{10}$ or $x=\frac{10}{10}$

$x=1$ or $x=\frac{2}{5}$

5 0

3 years ago

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If F(x)=2/3x^2+8x, what is the value of f(6)

Delvig [45]

Answer:

f = 2x + 24/ 3

Step-by-step explanation:

Step 1: Divide both sides by x.

fx/x = 2/3 x^2 + 8x/x

f = 2x + 24/3

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3 years ago

the length of a rectangle is 4a + 5, the width of the same rectangle is 2a -3 if the perimeter of the rectangle is 76 what is th

viktelen [127]

Answer:

Here

perimeter=76

length =4a+5

breadth=2a-3

we know,

perimeter=2(length+breadth)

76=2(4a+5+2a-3)

76=2(7a+2)

76=14a+4

76-4=14a

72=14a

72÷14=a

a=5.14

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2 years ago

Joel is twice as old as Kayla in 5 years the sum of their ages will be 55 years what are the ages of two people

stealth61 [152]

Kayla is 15 while joel is 30

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3 years ago

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The least-squares regression model y =−3.4+5.2x and correlation coefficient r=−0.66 were calculated for a set of bivariate data

Makovka662 [10]

Answer:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

Step-by-step explanation:

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

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

Where:

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

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

$\bar x= \frac{\sum x_i}{n}$

$\bar y= \frac{\sum y_i}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

And the model obtained for this case is:

$y = -3.4 +5.2 x$

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For this case the value of r = -0.66

Now we can calculate the determination coeffcient:

$r^2 = (-0.66)^2 = 0.4356$

And then we can conclude that 43.56% of the variation in y can be explained by the explanatory variable

And then 100-43.56 = 56.44 % of the variation in y that cannot be explained by the explanatory variable

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3 years ago