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scoundrel [369]
3 years ago
8

Geometry help! Please prove the following is a square with full explanation, I'm really lost.

Mathematics
1 answer:
Hoochie [10]3 years ago
5 0

We have to show that this is a square, meaning all the sides are perpendicular and the same distance.  

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope.  We don't have to bother to take the square root.  We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6).   slope=-6/-1=6  AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1).  slope=1/-6=-1/6.   BC²=(-6)²+1²

CD=D-C=(1, 6).   slope=6/1=6    CD²=1²+6²=37

DA=A-D=(6,-1)   slope=-1/6     DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides.  We see they all have squared distance 37.  Equal perpendicular sides proves its a square.

If we do these problems enough we learn:  There's no point taking the square root.  In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides:  (-1, -6) (-6, 1) (1, 6) (6,-1)

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The answer is 6
See attached.

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Given the following sequence, find the 14th term: 3, 1, –1, –3, –5, . . .
AVprozaik [17]
3, 1, -1, -3, -5
 -2  -2  -2  -2

a(n) = a₁ + d(n - 1)
a(n) = 3 - 2(n - 1)
a(n) = 3 - 2(n) + 2(1)
a(n) = 3 - 2n + 2
a(n) = -2n + 3 + 2
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Read 2 more answers
13,000 inches equals how many miles
Nataly [62]

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0.205177 mi

Step-by-step explanation:

Step 1: Find conversions

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5280 ft = 1 mi

Step 2: Use Dimensional Analysis

13000 \hspace{2} in(\frac{1 \hspace{2} ft}{12 \hspace{2} in} )(\frac{1 \hspace{2} mi}{5280 \hspace{2} ft} )

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Find the length of each arc. Round your answer to the nearest tenth.
Ede4ka [16]

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6 0
3 years ago
4. The data shows the number of siblings each student in a 9th-grade class has.
antiseptic1488 [7]

Answer:

The correct option is Mean and standard deviation.

Step-by-step explanation:

The data set provided, arranged in ascending order is:

S = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 4}

Now, it is provided that Macy was absent when the data was collected and the class guessed she had 4 siblings. When  she returned, they found out she actually has 9 siblings.

So, the new data set is:

X = {0 , 0 , 0 , 1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 4 , 9}

The mean of a data set is the average value representing the entire data.

\bar X=\frac{1}{n}\sum X_{i}

The median is the middle value of the data set.

The inter-quartile range is the difference between the first and the third quartile.

The standard deviation is the value that represents how dispersed the data values are.

SD=\sqrt{\frac{1}{n}\sum (X_{i}-\bar X)^{2}}

From all the above statistic, the mean and standard deviation are the only ones that uses all the observations in the data set to compute their value.

So, on changing one of the 4s by a 9, the set of measures that will be affected are the mean and standard deviation.

Thus, the correct option is Mean and standard deviation.

3 0
3 years ago
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