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3 years ago

If the volume of an object is 100cm3 and the density is 4g/cm3. What is the mass of the object in g?

Mathematics

1 answer:

3241004551 [841]3 years ago

7 0

Answer:

400g

Step-by-step explanation:

mass= density × volume

Substitute the given value of density and volume.

Mass of the object

= 4(100)

= 400g

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3 years ago

Use the Distance Formula and the Pythagorean Theorem to find the distance between each pair of points. M (10, −4) and N (2, −7)

xenn [34]

Answer:

$d=\sqrt{73}\approx8.54$

Step-by-step explanation:

So we have the two points (10,-4) and (2,-7).

And we want to find the distance between them using the Distance Formula and the Pythagorean Theorem. Let's do each one individually.

1) Distance Formula.

The distance formula is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Let's let (10,-4) be (x₁, y₁) and let's let (2,-7) be (x₂, y₂). So:

$d=\sqrt{((2)-(10))+((-7)-(-4))^2$

Simplify:

$d=\sqrt{(2-10)^2+(-7+4)^2$

Subtract:

$d=\sqrt{(-8)^2+(-3)^2$

Square:

$d=\sqrt{64+9}$

Add:

$d=\sqrt{73}$

Approximate:

$d\approx8.54$

So, the distance between (10,-4) and (2,-7) is approximately 8.54 units.

2) Pythagorean Theorem

Please refer to the graph.

So, we want to find the distance. This will be the length of the red line, or the hypotenuse.

First, let's find the length of the two legs.

The longer leg will be the difference between the two x-coordinates. So, the length of the longer leg is:

$(10-2)=8$

Note: It doesn't matter if we do 2-10, which gives -8, since we are going to square anyways. Also, distance is always positive, so 8 would be our answer.

And the shorter leg is the difference between the two y-coordinates. Namely:

$(-7-(-4))=-3=3$

So, the shorter leg is 3 units.

So now, we can use the Pythagorean Theorem, which is:

$a^2+b^2=c^2$

Substitute 8 for a and 3 for b. So:

$(8)^2+(3)^2=c^2$

Square:

$64+9=c^2$

Add:

$c^2=73$

Take the square root:

$c=\sqrt{73}\approx8.54$

This is the same as our previous answer, so we can confirm that it's correct.

So, using both the distance formula and the Pythagorean Theorem, the distance between the two points is approximately 8.54.

And we're done!

5 0

3 years ago

Read 2 more answers

Factor 3y^(2) + 13y + 4

Elena-2011 [213]

Answer:

(3y + 1)(y + 4)

Step-by-step explanation:

3y^(2) + 13y + 4 = 3y^(2) + 12y + y + 4 = 3y(y + 4) + 1(y + 4) = (3y + 1)(y + 4)

6 0

3 years ago

The histogram shows the ages of cars sold at a car auction. what percent of the cars was less than 20 years old or more than 40

Alexus [3.1K]

The histogram is attached. Every column shows on the bottom the range of age and on the left the number of cars of that particular age.

In order to find the percentage of cars with less than 20 years or more than 40 years, you have to sum up the numbers of cars in the first two columns from left (age 0-9 and 10-19) and the last two (age 40-49 and 50-59).
The number of cars of requested age is: 3 + 2 + 0 + 3 = 8

Now, you need to calculate the total number of cars (sum the cars of every column): 3 + 2 + 8 + 4 + 0 + 3 = 20

Lastly, you need to calculate the ration between the cars of requested age and the total number of cars, and transform it into a percentage:
8 ÷ 20 = 0.40 = 40%

Therefore, your answer is 40%.