Fill in the blanks to rewrite the following statement with variables: Is there an integer with a remainder of 1 when it is divid
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The area of the parallelogram whose vertices are (-4 , 9), (11 , 9), (5 , -1)
and (-10 ,-1) is 150 units²
Step-by-step explanation:
Let us revise some important facts:
1. Horizontal lines passe through points have same y-coordinates
2. The length of a horizontal segment is the difference between
the x-coordinates of its end-points
3. vertical lines passe through points have same x-coordinates
4. The length of a vertical segment is the difference between
the y-coordinates of its end-points
In the parallelogram whose vertices are
(-4 , 9), (11 , 9), (5 , -1) and (-10 ,-1)
∵ The vertices (-4 , 9) and (11 , 9) have same y-coordinates
∴ The side whose joining them is a horizontal side
∴ Its length = 11 - (-4) = 11 + 4 = 15 units
∵ The vertices (5 , -1) and (-10 , -1) have same y-coordinates
∴ The side whose joining them is a horizontal side
∴ Its length = 5 - (-10) = 5 + 10 = 15 units
∴ The two horizontal sides are parallel and equal
∵ The area of a parallelogram = ×
∵ The perpendicular distance between two parallel horizontal
sides is the difference between their y-coordinates
∵ The y-coordinate of the 1st horizontal side = 9
∵ The y-coordinate of the 2nd horizontal side = -1
∴ The vertical distance between the parallel sides = 9 - (-1) = 9 + 1
∴ The vertical distance between the parallel sides = 10 units
∵ = 15 units
∵ = 10 units
∴ The area of the parallelogram = 15 × 10 = 150 units²
The area of the parallelogram whose vertices are (-4 , 9), (11 , 9),
(5 , -1) and (-10 ,-1) is 150 units²
Learn more:
You can learn more about area of parallelograms in brainly.com/question/6779145
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Given that normally distributed data set has a mean of 55 and 99.7% of data fall between 47.5 and 62.5.
Let s be the standard deviation of data set.
Since 99.7% data fall within 3 standard deviations of mean, z-value for 47.5 and 62.5 has an absolute value of 3.
That is |z|=3
But z=
Let us plugin x=47.5 and mean =55 and equate it to 3.
That is
Since x is always positive ( being standard deviation),
Hence
We will get same value with 62.5 as well.
Hence standard deviation of data set is 2.5.