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xxMikexx [17]
3 years ago
15

Question 28 of 42

Mathematics
1 answer:
lina2011 [118]3 years ago
5 0

Answer with explanation:

Properties of Rectangle

1. Opposite sides are equal and parallel.

2. Diagonals are equal and bisect each other.

3. Adjacent Sides are Perpendicular to each other.

→If two lines are parallel their slopes are equal and if two Lines are perpendicular, their product of slopes is -1.

→A Rectangle is a Quadrilateral also.

→Adjacent sides are perpendicular ,so , their slopes can't be equal.Product of their slopes should be equal to ,-1.

⇒Slope of AB × Slope of BC = -1

⇒Also, Slope of AB × Slope of BC = -1

Slope of AB × Slope of AD = -1

⇒ Slope of AD × Slope of CD = -1

Slope of CB × Slope of CD = -1

Option B And Option C

are statement which proves that polygon ABCD is not a rectangle.

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y~=~234.56158 ~-~ 2.95835 \cdot x

Step-by-step explanation:

The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It’s called a “least squares” because the best line of fit is one that minimizes the variance.

We have the following data:

\begin{array}{c|ccccccccc}X&50&55&50&79&44&37&70&45&49\\Y&152&48&22&35&43&171&13&185&25\end{array}

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Step 1: Find X\cdot X and X\cdot Y as it was done in the table

Step 2: Find the sum of every column:

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Step 3: Use the following equations to find a and b:

\begin{aligned}        a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} =             \frac{ 694 \cdot 26897 - 479 \cdot 32784}{ 9 \cdot 26897 - 479^2} \approx 234.56158 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2}        = \frac{ 9 \cdot 32784 - 479 \cdot 694 }{ 9 \cdot 26897 - \left( 479 \right)^2} \approx -2.95835\end{aligned}

Step 4: Assemble the equation of a line

\begin{aligned} y~&=~a ~+~ b \cdot x \\y~=~234.56158 ~-~ 2.95835\cdot x\end{aligned}

The graph of the regression line is:

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