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butalik [34]
2 years ago
10

In the diagram, GB = 2x + 3.. What is GB?

Mathematics
1 answer:
tia_tia [17]2 years ago
6 0

Answer:

GB = 15

Step-by-step explanation:

DC, EB and FA are the medians of the triangle.

The point G where the medians intersect is the centroid.

On each median the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint, hence

FG = 2GA, that is

5x = 2(x + 9)

5x = 2x + 18 ( subtract 2x from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

Hence

GB = 2x + 3 = (2 × 6) + 3 = 12 + 3 = 15

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Answer:

height = 14.5 ft

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Step-by-step explanation:

Let the side of the square base is a and the height of the box is h.

The material required to make the box is equal to the total surface area of the box.

Area of base = a²

Cost of square base is $ 2 per ft²

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Cost of making walls and the top is $ 1 per ft²

So, the cost of making walls and the top = 1 x ( 3a² + 2ah)

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According to the question

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h = \frac{144-5a^{2}}{2a}     .... (1)

The volume of the box is V = length x width x height

V = a x a x h

V = 72 a - 2.5 a³     from equation (1)

Differentiate both sides with respect to a.

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Put, it equal to zero for maxima and minima

7.5 a² = 72

a = 3.2 ft

Put in equation (1)

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h = 14.5 ft

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height = 14.5 ft

width = length = 3.2 ft

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Answer:

A

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