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sdas [7]
3 years ago
13

Parallelogram ABCD has vertices: A(-3, 1), B(3, 3), C(4, 0), and D(-2, -2). In two or more complete sentences, explain how you c

an use the coordinates of the vertices to prove that parallelogram ABCD is a rectangle.

Mathematics
2 answers:
mina [271]3 years ago
4 0
You have to shoe that the angles between adjacent sides = 90 degrees. You do do this by showing the adjacent sides are perpendicular  by comparing their slopes. 
raketka [301]3 years ago
3 0

Answer:

Step-by-step explanation:

Remember, the slope of parallel lines is the same, while the slope of perpendicular lines is the negative reciprocal of each other.

We are given that points a(-3,1), b(3,3), c(4,0) and d(-2,-2). Let’s first identify the relationships between the lines that form the sides of rectangle ABCD.

Lines AD and BC are parallel

Lines AB and DC are parallel

Lines AB and AD are perpendicular

Lines BC and DC are perpendicular

Lines AD and BC are parallel, since the two lines share a slope of -3.

Lines AB and DC are parallel, since they both share a slope of 1/3.

Lines CD and BC are perpendicular, since they are the opposite reciprocal of each other. CD has a slope of 1/3. BC has a slope of -3.

Lines DC and AD are perpendicular as well. DC has a slope of 1/3. AD has a slope of -3.

Using this information, we can arrive at the conclusion that parallel lines DC and AB intersect with parallel lines BC and AD. The intersection of these pairs of parallel lines make up the sides of rectangle ABCD, which proves that the vertices of the parallelogram forms a rectangle.

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choli [55]

Answer:

y = x - 2

General Formulas and Concepts:

<u>Algebra I</u>

Slope-Intercept Form: y = mx + b

  • m - slope
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Step-by-step explanation:

<u>Step 1: Define</u>

Slope <em>m</em> = 1

y-intercept <em>b</em> = -2

<u>Step 2: Write linear function</u>

y = x - 2

8 0
3 years ago
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HELP ME PLEASE !!!!!!
koban [17]

Answer:

13.08

Step-by-step explanation:

Step 1: find the sum of all numbers

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Step 2: divide by how many values there are

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Step 3: solve

104.65 ÷ 8 = 13.08125....

Step 4: round to the hundredths place

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How much difference do a couple of weeks make for birth weight? Late-preterm babies are born with 34 to 36 completed weeks of ge
stiks02 [169]

Answer:

a) 0.3277

b) 0.0128

Step-by-step explanation:

We are given the following information in the question:

N(2750, 560).

Mean, μ = 2750

Standard Deviation, σ = 560

We are given that the distribution of distribution of birth weights is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P (less than 2500 grams)

P(x < 2500)

P( x < 2500) = P( z < \displaystyle\frac{2500 - 2750}{560}) = P(z < -0.4464)

Calculation the value from standard normal z table, we have,  

P(x < 2500) = P(z < -0.4464) = 0.3277 = 32.77\%

b) P ((less than 1500 grams)

P(x < 1500)

P( x < 1500) = P( z < \displaystyle\frac{1500 - 2750}{560}) = P(z < -2.2321)

Calculation the value from standard normal z table, we have,  

P(x < 1500) = P(z < -2.2321) = 0.0128 = 1.28\%

3 0
2 years ago
B. Lance is 39 years old. Ted is 22 years old.
Rudiy27

Answer:

28 years

Step-by-step explanation:

Sum of the years of Lance , Ted, Rosalinda = 39 + 22 +45 = 106 year

Sum of the years of Lance , Ted, Rosalinda & Erik = 33.5*4 = 134.0 year

Age of Erik = 134 - 106 = 28 years

8 0
3 years ago
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Answer:

20x

Step-by-step explanation:

\frac{80}{4}=\frac{20}{1}=20

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