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butalik [34]
3 years ago
6

What are the coordinates of the centroid of a triangle with vertices D(0,1),E(2,6), and F(7,2) enter your answer in the boxes

Mathematics
1 answer:
Daniel [21]3 years ago
7 0

The coordinates of centroid of given triangle are: (3,3)

Step-by-step explanation:

Given

D(0,1) = (x1,y1)

E(2,6) = (x2,y2)

F(7,2) = (x3,y3)

The centroid of a triangle when the vertices are known is given by:

C = (\frac{x_1+x_2+x_3}{3} , \frac{y_1+y_2+y_3}{3})

Putting the values

C = (\frac{0+2+7}{3} , \frac{1+6+2}{3})\\C = (\frac{9}{3} , \frac{9}{3})\\= (3,3)

Hence,

The coordinates of centroid of given triangle are: (3,3)

Keywords: Triangle, centroid

Learn more about triangles at:

  • brainly.com/question/10717746
  • brainly.com/question/10736268

#LearnwithBrainly

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Something on sale for $725. The original price was $1299. To the nearest tenth of a percent, what was the rate of discount?
ElenaW [278]

Answer:

44.2%

Step-by-step explanation:

Rate of discount = (difference in prices / original price) x 100

Difference in price = $1299 - $725 = $574

Original price = $1299

($574 / $1299) x 100 = 44.187837%

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

the hundredth figure is 8, which is greater than 5. 1 would be added to the tenth figure.

So it becomes 44.2%

4 0
2 years ago
How many ft are in 2mi
Harman [31]

Answer:

10560 ft

Step-by-step explanation:

1 mi = 5280 ft

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7 0
3 years ago
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Explain why -4 is not a real number but -8 is two equations below of what they look like
Margarita [4]

-4 isn't a real number because there is no square root of -4. However, there is a cube root of -8, because -2 * -2 * -2 = -8.

7 0
3 years ago
A company is manufacturing an open-top rectangular box. They have 30 cm by 16 cm sheets of material. The bins are made by cuttin
Natalija [7]

Answer:

a. (30 - 2x)(16 - 2x)x. b. length 21.2 cm , width = 7.2 cm and height x = 4.4 cm

Step-by-step explanation:

a. Let x be the side of the squares to be cut from each corner. Since we have two corners on each side, the length of the resulting box from the 30 cm by 16 cm sheet is L = 30 - 2x. Its breadth is B = 16 - 2x. The height of the resulting box is x. So its volume V = LBx = (30 - 2x)(16 - 2x)x.

b. To find the maximum value of V, we differentiate V with respect to x and equate it to zero.

So, dV/dx = 0

d(30 - 2x)(16 - 2x)x/dx = 0

-2(16 - 2x)x + (-2)(30 - 2x)x + (30 - 2x)(16 - 2x) = 0

32x + 4x² - 60x - 4x² + 480 - 60x - 32x + 4x² = 0

4x²- 120x + 450 = 0

x²- 30x + 112.5 = 0

Using the quadratic formula, we find x. So, with a = 1, b = - 15 and c = 112.5,

x = \frac{-(-30)+/-\sqrt{(-30)^{2} - 4 X 1 X 112.5} }{2 X 1} \\= \frac{30+/-\sqrt{900 - 450} }{2}\\ = \frac{30+/-\sqrt{450} }{2}\\ = \frac{30+/-21.21 }{2}\\\\ = \frac{30+21.21 }{2}   or  \frac{30-21.21 }{2}\\ = \frac{51.21 }{2}   or  \frac{8.79}{2}\\ = 25.605 or 4.395

x ≅ 25.61 or 4.4

V = (30 - 2x)(16 - 2x)x

Substituting the values of x into L and B, we have )x

L = (30 - 2x) = (30 - 2(25.61)) = 30 - 51.22 = -21.22

B = (16 - 2x) = (16 - 2(25.61)) = 16 - 51.22 = -35.22

Since L and B cannot be negative, we use the other value for x = 4.4, So

L = (30 - 2x) = (30 - 2(4.4)) = 30 - 8.8 = 21.2

B = (16 - 2x) = (16 - 2(4.4)) = 16 - 8.8 = 7.2

So V = LBx = 21.2 × 7.2 × 4.4 = 671.62 cm³

3 0
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Can someone please HELP! FOR BRAINLIEST!
RoseWind [281]

Answer:

1st pic:

step 2.

2nd pic:

Rene should add, not multiply 2 volumes.

The correct answer is 48+216 =264

3rd pic:

a, for blue prism: V = Area of base x Height = 48 x a =720

=> a = 720/48 = 15

b,  for orange prism: V = Area of base x Height = (12xb)/2 x 15 =720

=> b =(720x2)/(15x12)= 8

8 0
3 years ago
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