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fiasKO [112]
3 years ago
6

A triangle with vertices D, E, and F are plotted on the coordinate plane at (0, 5). (2, 0), and (-4, 2), respectively. When cons

tructed,
medians DG and EH intersect at the point with which coordinates? Round each coordinate to the nearest tenth if necessary.


A. (-0.7, 2.5)

B. (-1, 1)

C. (-0.7, 2.3)

D. (-2, 3.5)
Mathematics
1 answer:
rodikova [14]3 years ago
4 0

Given:

Vertices of a triangle are D(0,5), E(2,0) and F(-4,2).

To find:

The intersection point of medians DG and EH.

Solution:

We know that, intersection point of all the medians of a triangle is called centroid.

The formula of centroid is

Centroid=\left(\dfrac{x_1+x_2+x_3}{3},\dfrac{y_1+y_2+y_3}{3}\right)

Vertices of a triangle are D(0,5), E(2,0) and F(-4,2). So, the centroid of the triangle is

Centroid=\left(\dfrac{0+2+(-4)}{3},\dfrac{5+0+2}{3}\right)

Centroid=\left(\dfrac{-2}{3},\dfrac{7}{3}\right)

Centroid=\left(-0.666...,2.333\right)

Round each coordinate to the nearest tenth.

Centroid=\left(-0.7,2.3\right)

Therefore, the correct option is C.

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Your sister is 14 yrs old. Your brother is 10 yrs less than twice your sisters age. Your cousin is half ur brothers age. Write a
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Pleaseeee help meenpleaseeee!!!!!!!!
Iteru [2.4K]

Answer:

-5/4

Step-by-step explanation:

4x-5y=10

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3 0
2 years ago
A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. mater
BartSMP [9]
Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x²        (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
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C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
C = 20(1.651)² + 180/1.651 = $163.54

Answer: $163.54

7 0
3 years ago
In 12 games last season the school baseball team scored 5, 11, 2, 0, 4, 8, 9, 6, 7, 4, 1, and 2 runs. What is the average number
Mashcka [7]

Hello there!

First, we need to put our data set into proper numerical order (least to greatest).

Set: , 1,2,2,4,4,5,6,7,8,9,11

Now, to find the mean, we need to add them all up.

1 + 2 + 2 + 4 + 4 + 5 + 6 + 7 + 8 + 9 + 11 = 59

Then, divide it by how many numbers there are : 12

59 divided by 12 = 4.9166667

Round it to the nearest tenth.

4.9166667 = 4.9

This means the average number of runs scored per game is 4.9 runs.

7 0
3 years ago
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