medical terminology The term ____________________ describes an inflammation of the stomach and small intestine.

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

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What is the common difference in this sequence 4,13,22,31,40<br>A) 9<br>B) 1/9<br>C) 11<br>D) 10

tatiyna

Answer:

The common difference is (a.): 9, as you add 9 in order to get to the next number in the sequence each time.

+if this helped you, please consider marking it the Brainliest. thank you.

5 0

3 years ago

Mia has two cylindrical bird feeders. Her red bird feeder has a diameter of 10 inches and is 8.3 inches tall. What is the volume

Temka [501]

The volume of the red bird feeder will be equal to V=651.88 cubic inches

<h3>What is volume?</h3>

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length,width and height of the cube or Cuboid.

It is given that:-

Diameter = 10 inches

Height = 8.3 inches

Volume=?

Since the feeder is cylindrical so the volume will be calculated as:-

$\rm Volume=\dfrac{\pi }{4}d^2H\\\\\\Volume=\dfrac{\pi }{4}(10)^2(8.3)\\\\\$

V=651.88 cubic inches

Hence volume of the red bird feeder will be equal to V=651.88 cubic inches

To know more about Volume follow

brainly.com/question/1972490

#SPJ1

4 0

3 years ago

Which value of y makes the two rectangles similar? <br> 3<br> 8.2<br> 25.2 <br> 28.8

elena55 [62]

8.4/4.8=y/14.4
y=25.2
Here is the answer

5 0

3 years ago

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The volume of a sphere is 1928π m3 . What is the surface area of the sphere to the nearest tenth?

Rufina [12.5K]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad \begin{cases}
r=radius\\
------\\
V=1928\pi 
\end{cases}\implies 1928\pi =\cfrac{4}{3}\pi r^3
\\\\\\
1928\pi =\cfrac{4\pi r^3}{3}\implies \cfrac{3\cdot 1928\pi }{4\pi }
=r^3\implies 1446=r^3
\\\\\\
\sqrt[3]{1446}=r\\\\
-------------------------------\\\\
\textit{surface area of a sphere}\\\\
S=4\pi r^2\qquad r=\sqrt[3]{1446}\implies S=4\cdot \pi \cdot \sqrt[3]{1446^2}$

8 0

3 years ago

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