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Marina CMI [18]
3 years ago
10

The kinetic energy (in joules ) of a moving object can be calculated from the expression 1/2mv to the second power, where m is t

he mass of the object in kilograms and v is it’s speed in meters per second. Find the kinetic energy of a 0.145-kg baseball that is thrown at a speed of 40 meters per second. E = ______ joules

Mathematics
1 answer:
yulyashka [42]3 years ago
7 0

E = 1/2 m v^2

E = 1/2 (0.145) (40)^2

E = 0.0725 x 1600

E = 116 kg m^2/s^2

1 joule = 1 kg m^2/s^2

so here E in joules is 116 joules

so E = 116 joules

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Hats and mittens are on sale at the store! One woman was able to buy 5 hats and 4 pairs of mittens for $30.
aalyn [17]

The price of one hat is $2 and one pair of mittens is $5

Step-by-step explanation:

Hats and mittens are on sale at the store!

  • One woman was able to buy 5 hats and 4 pairs of mittens for $30
  • Another woman purchased 3 pairs of mittens and 2 hats for $19
  • The price of one hat is x
  • The price of one pair of mittens is y

We need to find x and y

∵ One woman was able to buy 5 hats and 4 pairs of mittens for $30

∵ The price of one hat is x

∵ The price of one pair of  mittens is y

- Multiply 5 hats by x and 4 pairs of mittens by y and equate

  their sum by 30

∴ 5x + 4y = 30 ⇒ (1)

∵ Another woman purchased 3 pairs of mittens and 2 hats for $19

- Multiply 2 hats by x and 3 pairs of mittens by y and equate

  their sum by 19

∴ 2x + 3y = 19 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -2 and equation (2) by 5 to eliminate x

∵ -10x - 8y = -60 ⇒ (3)

∵ 10x + 15y = 95 ⇒ (4)

- Add equations (3) and (4)

∴ 7y = 35

- Divide both sides by 7

∴ y = 5

Substitute the value of y in equation (1) or (2) to find x

∵ 2x + 3(5) = 19

∴ 2x + 15 = 19

- Subtract 15 from both sides

∴ 2x = 4

- Divide both sides by 2

∴ x = 2

The price of one hat is $2 and one pair of mittens is $5

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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The length of a rectangle is three times its width. The perimeter of the rectangle is 100 inches. What are the dimensions of the
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Then 4w + 2w = 100 inches;

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w = 16.6;

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Step-by-step explanation:


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Answer:

More than half the students scored 81 or better on the test

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