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andrew-mc [135]
2 years ago
9

A point is plotted on the number line at 2 2/5 . A second point is plotted at −4 3/4 . What is the length of a line segment join

ing these points? Enter your answer as a simplified mixed number in the box.
Mathematics
2 answers:
Anastaziya [24]2 years ago
8 0

Answer:

  • 7 3/20

Step-by-step explanation:

<u>The distance is the absolute value of the difference of the coordinates:</u>

  • 2 2/5 - (-4 3/4) =
  • 2 2/5 + 4 3/4 =
  • 6 + 2/5 + 3/4 =
  • 6 + 8/20 + 15/20 =
  • 6 23/20 =
  • 7 3/20
Law Incorporation [45]2 years ago
5 0

Distance=

\\ \sf\longmapsto \left|2\dfrac{2}{5}-(-4\dfrac{3}{4})\right|

\\ \sf\longmapsto \left|2\dfrac{2}{5}+4\dfrac{3}{4}\right|

\\ \sf\longmapsto \left|\dfrac{12}{5}+\dfrac{19}{4}\right|

\\ \sf\longmapsto \left|\dfrac{48+95}{20}\right|

\\ \sf\longmapsto \left|\dfrac{143}{20}\right|

\\ \sf\longmapsto \left|7\dfrac{3}{20}\right|

\\ \sf\longmapsto 7\dfrac{3}{20}

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Vladimir [108]
I believe it’s 0.4cm ...
5 0
2 years ago
Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This month, he sold 444444 chickens and 3636
Nostrana [21]

Answer: the cost of one chicken is $8

The cost of one duck is $5

Step-by-step explanation:

Let x represent the cost of one chicken.

Let y represent the cost of one duck.

Last month, he sold 50 chickens and 30 ducks for $550. It means that

50x + 30y = 550- - - - - - - - - - - 1

This month, he sold 44 chickens and 36 ducks for $532. It means that

44x + 36y = 532- - - - - - - - - - - 2

Multiplying equation 1 by 44 and equation 2 by 50, it becomes

2200x + 1320y = 24200

2200x + 1800y = 26600

Subtracting, it becomes

- 480y = - 2400

y = - 2400/- 480

y = 5

Substituting y = 5 Intl equation 1, it becomes

50x + 30 × 5 = 550

50x + 150 = 550

50x = 550 - 150

50x = 400

x = 400/50

x = 8

3 0
3 years ago
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leaks can write a 500-work essay in a hour. if she writes a essay in 10 minutes, how many words will it contain?
gavmur [86]

Answer:

about 83 words

Step-by-step explanation:

60/6=10

500/6 about 83

7 0
3 years ago
[09.02]
VLD [36.1K]

Answer:

4

Step-by-step explanation:

i took the test and got it right

7 0
3 years ago
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Drag each tile to the correct box. Vector t, with a magnitude of 4 meters/second and a direction angle of 60°, represents a swim
astraxan [27]

Answer:

From top to bottom, the boxes shown are number 3, 5, 6, 2, 4, 1 when put in ascending order.

Step-by-step explanation:

It is convenient to let a calculator or spreadsheet tell you the magnitude of the sum. For a problem such as this, it is even more convenient to let the calculator give you all the answers at once.

The TI-84 image shows the calculation for a list of vectors being added to 4∠60°. The magnitudes of the sums (rounded to 2 decimal places—enough accuracy to put them in order) are ...

... ║4∠60° + 3∠120°║≈6.08

... ║4∠60° + 4.5∠135°║≈6.75

... ║4∠60° + 4∠45°║≈7.93

... ║4∠60° + 6∠210°║≈3.23

... ║4∠60° + 5∠330°║≈6.40

... ║4∠60° + 7∠240°║≈ 3

_____

In the calculator working, the variable D has the value π/180. It converts degrees to radians so the calculation will work properly. The abs( ) function gives the magnitude of a complex number.

On this calculator, it is convenient to treat vectors as complex numbers. Other calculators can deal with vectors directly

_____

<em>Doing it by hand</em>

Perhaps the most straigtforward way to add vectors is to convert them to a representation in rectangular coordinates. For some magnitude M and angle A, the rectangular coordinates are (M·cos(A), M·sin(A)). For this problem, you would convert each of the vectors in the boxes to rectangular coordinates, and add the rectangular coordinates of vector t.

For example, the first vector would be ...

3∠120° ⇒(3·cos(120°), 3·sin(120°)) ≈ (-1.500, 2.598)

Adding this to 4∠60° ⇒ (4·cos(60°), 4°sin(60°)) ≈ (2.000, 3.464) gives

... 3∠120° + 4∠60° ≈ (0.5, 6.062)

The magnitude of this is given by the Pythagorean theorem:

... M = √(0.5² +6.062²) ≈ 6.08

___

<em>Using the law of cosines</em>

The law of cosines can also be used to find the magnitude of the sum. When using this method, it is often helpful to draw a diagram to help you find the angle between the vectors.

When 3∠120° is added to the end of 4∠60°, the angle between them is 120°. Then the law of cosines tells you the magnitude of the sum is ...

... M² = 4² + 3² -2·4·3·cos(120°) = 25-24·cos(120°) = 37

... M = √37 ≈ 6.08 . . . . as in the other calculations.

4 0
2 years ago
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