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3 years ago

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His isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the tr

iangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information. If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?

1 answer:

Papessa [141]3 years ago

3 0

Answer: 12.6 + b = 15.7

Step-by-step explanation:

Here a be the length of equal sides of the isosceles triangle and b be the length of the base of the triangle,

And, the given equation that model the given situation is,

2 a + b = 15.7

Since, a = 6.3,

By putting this value in the above equation,

We get,

2 × 6.3 + b = 15.7

⇒ 12.6 + b = 15.7

Which is the required equation that will use to find the base of the triangle.

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Answer:

See below

Step-by-step explanation:

By using the table 1 attached (See Table 1 attached)

We can perform all the calculations to express both, y as a function of x or x as a function of y.

Let's make first the line relating y as a function of x.

<u>y as a function of x </u>

<em>(y=response variable, x=explanatory variable) </em>

$\bf y=m_{yx}x+b_{yx}$

where

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In this case we use these formulas:

$\bf m_{yx}=\frac{(\sum y)(\sum x)^2-(\sum x)(\sum xy)}{n\sum x^2-(\sum x)^2}$

$\bf b_{yx}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2}$

n = 10 is the number of observations taken (pairs x,y)

<u>Note:</u> <em>Be careful not to confuse </em>

$\bf \sum x^2$ with $\bf (\sum x)^2$

Performing our calculations we get:

$\bf m_{yx}=\frac{(83)(95)^2-(95)(923)}{10*1277-(95)^2}=176.6061$

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So the equation of the line that relates y as a function of x is

<h3>y = 176.6061x + 0.3591 </h3>

In order to compute the standard error $\bf S_{yx}$ , we must use Table 2 (See Table 2 attached) and use the definition

$\bf s_{yx}=\sqrt{\frac{(y-y_{est})^2}{n}}$

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$\bf s_{yx}=\sqrt{\frac{39515985}{10}}=1987.8628$

Now, to find the line that relates x as a function of y, we simply switch the roles of x and y in the formulas.

So now we have:

x as a function of y

(x=response variable, y=explanatory variable)

$\bf x=m_{xy}y+b_{xy}$

where

$\bf m_{xy}$ is the slope of the line

$\bf b_{xy}$ is the x-intercept

In this case we use these formulas:

$\bf m_{xy}=\frac{(\sum x)(\sum y)^2-(\sum y)(\sum xy)}{n\sum y^2-(\sum y)^2}$

$\bf b_{xy}=\frac{n\sum xy-(\sum x)(\sum y)}{n(\sum y^2)-(\sum y)^2}$

n = 10 is the number of observations taken (pairs x,y)

<u>Note:</u> <em>Be careful not to confuse </em>

$\bf \sum y^2$ with $\bf (\sum y)^2$

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Computing our values, we get

$\bf m_{xy}=\frac{(95)(83)^2-(83)(923)}{10*743-(83)^2}=1068.1072$

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$\bf s_{xy}=\sqrt{\frac{846507757}{10}}=9200.5856$

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$\bf r=\frac{\sum xy}{\sqrt{(\sum x^2)(\sum y^2)}}$

Remark: <em>This formula for r is only true if we assume the correlation is linear. The formula does not hold for other kind of correlations like parabolic, exponential,..., etc. </em>

Computing the correlation coefficient :

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3 years ago

Read 2 more answers

The endpoints of CD are C(3,−5) and D(7, 9).<br> The coordinates of the midpoint M of CD are?

Nutka1998 [239]

Answer:

M(5,2)

Step-by-step explanation:

We use the midpoint rule:

$( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} )$

We just have to find the arithmetic mean of the x and y-coordinates.

The endpoints of CD are given as C(3,−5) and D(7, 9).

We substitute these values to get:

$( \frac{7 + 3}{2}, \frac{9 + - 5}{2} )$

$( \frac{10}{2}, \frac{4}{2} )$

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Therefore the coordinates of the midpoint M of CD are (5,2)

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