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kompoz [17]
3 years ago
15

Determine whether each quadrilateral is a parallelogram. Justify your answer. Yes/No? Reason... opposite side congruent, opposit

e angles congruent, opposite sides parallel, diagonals bisect each other, one pair of parallel and congruent sides, not enough information? (look at the image)

Mathematics
1 answer:
suter [353]3 years ago
4 0

Answer:

yes it is a parallelogram because opposite sides parallel.

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Subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5
emmasim [6.3K]

- 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5. This can be obtained by finding sum separately and then subtracting them.

<h3>What is the required number:</h3>

Here in the question it is given that,

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

By separating them as two parts

  • sum of -5/6 and -1 3/5  
  • sum of 2 2/3 and -6 2/5

⇒ sum of -5/6 and -1 3/5  

- 5/6 + - 1 3/5 = - 5/6 + - 8/5  (∵ a b/c = (ac+b)/c(5+3)/5 = 8/5)

                      = (- 25 - 48)/30  (LCM = 30)

                      = - 73/30

⇒ sum of 2 2/3 and -6 2/5

2 2/3 + -6 2/5 = 8/3 + -32/5

                       = (40 - 96)/15  (LCM = 15)

                       = - 56/15

subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5

= (sum of 2 2/3 and -6 2/5) - (sum of -5/6 and -1 3/5)

= (- 56/15) - (- 73/30 )  

= - 56/15 + 73/30

= - 112/30 + 73/30   (LCM = 30)

= - 39/30

= - 13/10

= - 1.3

Hence - 1.3 is the number we get when we subtract the sum of -5/6 and -1 3/5 from the sum of 2 2/3 and -6 2/5.

Learn more about fractions here:

brainly.com/question/10354322

#SPJ1

6 0
2 years ago
A pet food company wants to know the number of pets owned by adults ages 21 to 70. The frequency table shows the data from a sim
Brut [27]
Thank you for posting your question here. I think the question is "
<span>What is the estimated mean for the population? Explain your answer and show your work."

Below is the solution. I hope it helps.

</span>µ= (1*248 +2*567 +3*1402 +4*728 +5*419 +6*456 +7*203)/(1 +2 +3 +4 +5 +6 +7) 
<span>=14752/28≈ 526.9</span>
6 0
3 years ago
3 over 2 divided by 8 over 3
Veseljchak [2.6K]

Answer:

Step-by-step explanation:

3/2/8/3

=9/16

3 0
3 years ago
Read 2 more answers
HELP ASAP 20 POINTS CAUSE IM DESPERATE ToT
Elenna [48]

1. By de Moivre's theorem,

\left(4\left(\cos\left(\dfrac{7\pi}9\right) + i \sin\left(\dfrac{7\pi}9\right)\right)\right)^3 = 4^3 \left(\cos\left(\dfrac{21\pi}9\right) + i \sin\left(\dfrac{21\pi}9\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac{7\pi}3\right) + i \sin\left(\dfrac{7\pi}3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\cos\left(\dfrac\pi3\right) + i \sin\left(\dfrac\pi3\right)\right) \\\\ ~~~~~~~~ = 64 \left(\dfrac12 + i\dfrac{\sqrt3}2\right) \\\\ ~~~~~~~~ = \boxed{32 + 32\sqrt3\,i}

2. First write the given number in exponential/trigonometric form.

z = 5-5\sqrt3\,i

has modulus

|z| = \sqrt{5^2 + \left(-5\sqrt3\right)^2} = \sqrt{100} = 10

and since it lies in the second quadrant of the complex plane, its argument is

\arg(z) = \pi + \tan^{-1}\left(-\dfrac{5\sqrt3}5\right) = \pi + \tan^{-1}\left(-\sqrt3\right) = \pi - \dfrac\pi3 = \dfrac{2\pi}3

So, we have

z = 5 - 5\sqrt3\,i = 10 e^{i2\pi/3} = 10 \left(\cos\left(\dfrac{2\pi}3\right) + i \sin\left(\dfrac{2\pi}3\right)\right)

Now we apply de Moivre's theorem again, and make sure to account for the multivalued-ness of the exponential function. For k\in\{0,1,2,3,4\}, the fifth roots of z are

z^{1/5} = 10^{1/5} e^{i(2\pi/3 + 2\pi k)/5}

k=0 \implies z^{1/5} = 10^{1/5} e^{i2\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{2\pi}{15}\right) + i \sin\left(\dfrac{2\pi}{15}\right)\right)}

k=1 \implies z^{1/5} = 10^{1/5} e^{i8\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{8\pi}{15}\right) + i \sin\left(\dfrac{8\pi}{15}\right)\right)}

k=2 \implies z^{1/5} = 10^{1/5} e^{i14\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{14\pi}{15}\right) + i \sin\left(\dfrac{14\pi}{15}\right)\right)}

k=3 \implies z^{1/5} = 10^{1/5} e^{i20\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{4\pi}3\right) + i \sin\left(\dfrac{4\pi}3\right)\right)} k=4 \implies z^{1/5} = 10^{1/5} e^{i26\pi/15} = \boxed{10^{1/5} \left(\cos\left(\dfrac{26\pi}{15}\right) + i \sin\left(\dfrac{26\pi}{15}\right)\right)}

6 0
2 years ago
Thirty bouquets contain 750 rose stems. How many rose stems will 9 such bouquets hold?
dangina [55]

Answer:

225 rose stems

Step-by-step explanation:

750 / 30 = 25 rose stems per bouquet

25(9) = 225 rose stems

7 0
3 years ago
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