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kobusy [5.1K]
3 years ago
8

In the figure shown DE = 7x-13 and DF =3x+3 what is the length of DF?

Mathematics
1 answer:
Phoenix [80]3 years ago
7 0

Answer:

The length of DF is 15

Step-by-step explanation:

Since the two lines are equal, which is given by the markings on the triangle, then you can set the two lengths equal and find x.

7x - 13 = 3x + 3

4x - 13 = 3

4x = 16

x = 4

Now that we know x = 4, we can plug into the DF length to find its amount.

DF = 7x - 13

DF = 7(4) - 13

DF = 28 - 13

DF = 15

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A rectangular box is designed to have a square base and an open top. The volume is to be 500in.3 What is the minimum surface are
mr_godi [17]

The minimum surface area that such a box can have is 380 square

<h3>How to determine the minimum surface area such a box can have?</h3>

Represent the base length with x and the bwith h.

So, the volume is

V = x^2h

This gives

x^2h = 500

Make h the subject

h = 500/x^2

The surface area is

S = 2(x^2 + 2xh)

Expand

S = 2x^2 + 4xh

Substitute h = 500/x^2

S = 2x^2 + 4x * 500/x^2

Evaluate

S = 2x^2 + 2000/x

Differentiate

S' = 4x - 2000/x^2

Set the equation to 0

4x - 2000/x^2 = 0

Multiply through by x^2

4x^3 - 2000 = 0

This gives

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Take the cube root

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Substitute x = 7.94 in S = 2x^2 + 2000/x

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Evaluate

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Hence, the minimum surface area that such a box can have is 380 square

Read more about surface area at

brainly.com/question/76387

#SPJ1

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