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Fudgin [204]
3 years ago
10

Prove that the figure is a parallelogram. If so, classify the parallelogram. Be specific and justify your answer.

Mathematics
1 answer:
sesenic [268]3 years ago
8 0

Answer:

Step-by-step explanation:

If it is a parallelogram the opposite sides will a have the same slope.

Using the diagram  we see from the coordinates of A and B:

Slope of AB = (5 - -1)/(-1 - -5)

= 6/4

= 3/2.

In the same way

slope of CD = (2 - -4) / (1 - -3)

= 3/2.

So AB and  CD can be shown to be parallel.

Similarly the lines BC and AD are parallel.

So the figure is a parallelogram

Finding the perimeter (counting the units between the points):

Perimeter = 2AB + 2BC

By Pythagoras:

AB =   sqrt (6^2 + 4^2) = sqrt 52

BC = sqrt (3^2 + 2^2) = sqrt 13

So Perimeter = 2sqrt52 + 2sqrt13

= 4sqrt13 + 2 sqrt13

= 6sqrt13

or 21.63 unit^2 to 2 decimal places.

Area = sqrt52 * perpendicular distance between the lines AB and CD.

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The perimeter of a square garage door is 16 yards. How long is each side of the garage door?
Andre45 [30]

Answer:

each side will be 4

Step-by-step explanation:

since a square has 4 sides the equation will be 16÷4

8 0
3 years ago
Read 2 more answers
A bag contains 20 slips of paper Individually numbered. If a slip of paper and a letter in the word PENNSYLVANIA is chosen at ra
Soloha48 [4]

Answer:

P(M4\ n\ V) = 2.083\%

Step-by-step explanation:

Given

Paper = 20 slips

Word: PENNSYLVANIA

Required

Determine P(Multiple of 4 and V)

The sample size of the 20 slips is:

n(S) = 20

The outcomes of multiples of 4 is:

M4= \{4,8,12,16,20\}

n(M4) = 5

So, the probability of multiples of 4 is:

Pr(M4) = \frac{5}{20}

Pr(M4) = \frac{1}{4}

The sample size of PENNSYLVANIA is:

n(S) = 12

The outcome of V is:

n(V) = 1

So, the probability of V is:

P(V) = \frac{1}{12}

So, the required probability is: P(Multiple of 4 and V)

P(M4\ n\ V) = P(M4) * P(V)

P(M4\ n\ V) = \frac{1}{4} * \frac{1}{12}

P(M4\ n\ V) = \frac{1}{48}

P(M4\ n\ V) = 0.02083

Express as percentage

P(M4\ n\ V) = 0.02083 * 100\%

P(M4\ n\ V) = 2.083\%

4 0
3 years ago
The perimeter of a rectangle garden is 364 feet. If the width of the garden is 85 feet, what is it length?
kherson [118]

P=2(L+W)

P=364

L=99

sub and find W

364=2(99+W)

divide both sides by 2

182=99+w

subtract 99 from both sides

83=W

w=83ft

6 0
2 years ago
NEED HELP URGENT!! How do I solve this on number 30?(please go through the steps)
tatiyna

x^2+6x-5=0

x^2=2x

2x+6x-5=0

2x+6x=8x

8x-5=0

+5 +5

(if you don’t know what I’m doing here is that I’m removing the negative 5 by putting a positive 5 since both of them make 0. Also the “x” always stay alone and the unit stays as the unit)

(I putted the positive under the 0 because what u do to the unit you need to do the same thing with the other.)

8x/8=5/8

(If ur lost here it means dividing.)

The answer

X=0.625

(btw I’m not really sure if this is right so um don’t really trust me in this lol)

3 0
3 years ago
Explain your answer !! <br> Have a nice day <br><br> Will give braisnlt
lora16 [44]

Answer:

The equations are:

4H + 3P = 13.75

2H + 5P = 11.25

Hotdog = 2.50

Pretzel = 1.25

Step-by-step explanation:

Let:

H = hot\ dog

P =Pretzel

For Tina:

4H + 3P = 13.75

For Doug:

2H + 5P = 11.25

Solving for the price of both items:

We have:

4H + 3P = 13.75 --- (1)

2H + 5P = 11.25 --- (2)

Multiply (2) by 2

2 * (2H + 5P = 11.25)

-------------------

4H + 10P = 22.50 --- (3)

Subtract (3) from (1)

4H + 3P = 13.75

4H + 10P = 22.50

----------------------

4H - 4H + 3P - 10P = 13.75 - 22.50

3P - 10P = 13.75 - 22.50

-7P = -8.75

Solve for P

P = \frac{-8.75}{-7}

P = 1.25

Substitute 1.25 for P in (2)

2H + 5P = 11.25

2H + 5 * 1.25 = 11.25

2H + 6.25 = 11.25

Collect Like Terms

2H = 11.25-6.25

2H = 5

Solve for H

H = \frac{5}{2}

H = 2.50

3 0
3 years ago
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