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musickatia [10]
2 years ago
15

Find the midpoint of the line segment whose endpoints are (3, 10) and (7, 8).

Mathematics
2 answers:
Debora [2.8K]2 years ago
8 0

Answer:

The midpoint of line segment is (5,9).

Step-by-step explanation:

Given : Line segment whose endpoints are (3, 10) and (7, 8).

To find : Find the midpoint of the line segment .

Solution : We have given that endpoints  (3, 10) and (7, 8).

By the midpoint segment formula :

     Midpoint :

(\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2}).

Here, the coordinate of x_{1} = 3 ,   x_{2} = 7 ,

                                      y_{1} = 10 ,      y_{2} = 8 ,

Plugging values in formula ,

Midpoint =(\frac{3+7}{2} , \frac{10+8}{2}).

Midpoint =(\frac{10}{2} , \frac{18}{2}).

Midpoint = (5 , 9).

Therefore, the midpoint of line segment is (5,9).

Stels [109]2 years ago
6 0

Answer:

Option 2 is correct.

Step-by-step explanation:

Given the coordinates of lines segment (3, 10) and (7, 8). we have to find the mid-point of given line segment.

Mid-point formula states that if (x_1,y_1) and (x_2,y_2) are the coordinates of end points of line segment then the coordinates of mid-point are

(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

∴ Coordinates of mid-point of line segment joining the points          (3, 10) and (7, 8) are

(\frac{3+7}{2},\frac{10+8}{2})=(\frac{10}{2},\frac{18}{2})=(5,9)

Hence, option 2 is correct.

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The ratio of the number of dogs the number of cats is 4:5. There are 270 animals on the rescue Farm. The number of dogs is 4/5.
mafiozo [28]

Answer:

<em>Here is the complete question:</em>

The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:

a. The number of dogs is 4/5 the number of cats.

b. 4/5 of the pets at the farm are dogs.

c. There are exactly 30 more cats than dogs.

d. There are exactly 30 dogs at the farm.

e. 5/9 of the pets at the farm are cats.

a,c and e are true statements.

Step-by-step explanation:

Let the number of dogs be "d' and number of cats be "c".

According to the question:

⇒ c+d=270   ...equation (i)

Arranging the ratio:

⇒ \frac{4}{5} = \frac{d}{c}

⇒ 4c=5d

⇒ c=(\frac{5}{4})d    ...equation (ii)

Plugging (ii) in equation (i).

⇒ c+d=270

⇒ \frac{5}{4} d+d=270

⇒ \frac{5d+4d}{4} =270

⇒ 9d=270\times 4

⇒ d=\frac{270\times 4}{9}

⇒ d=120

Number of dogs "d" = 120

Number of cats "c" = (270-120) = 150

Lets check each statement:

a.

The number of dogs is 4/5 the number of cats.

⇒ \frac{4}{5} \times 150

⇒ \frac{4\times 150}{5}

⇒ 120

Statement is true.

b.

4/5 of the pets at the farm are dogs.

⇒ \frac{4}{5} \times 270

⇒ 216

Number of dogs = 120

So the above statement is false.

c.

There are exactly 30 more cats than dogs.

⇒ c-d =30

⇒ 150-120=30

Statement is true.

d.

There are exactly 30 dogs at the farm.

False, as there are 120 dogs

e.

5/9 of the pets at the farm are cats.

⇒ \frac{5}{9} \times 270

⇒ 150

Statement is true.

So,

Statement  a,c and e are true as we could observe in the explanation.

8 0
2 years ago
How would you find the vertices of an image of a figure was rotated 270 degrees clockwise? 15 POINTS! DESPERATE
boyakko [2]

Rotation Coordinate Notation About the Origin:

90–degree counterclockwise: (x, y) → (-y, x)

180–degree counterclockwise: (x, y) → (-x, -y)

270–degree counterclockwise: (x, y) → (y, -x)

Use this to help you..

Example -

The vertices of a triangle are

( 1 , 3 ) ( 3 , -4 ) , ( - 6 , -8 )

270 degrees , clockwise , rotated from origin ( x , y ) - ( y , -x )

The first vertice = ( 1 , 3 )

after rotation - ( 3 , - 1 )

The second vertice = ( 3 , -4 )

After rotation - ( -4 , -3 )

The third vertice = ( -6 , - 8 )

After rotation - ( -8 , 6 )

Hope my answer helps!

5 0
3 years ago
Read 2 more answers
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