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2 years ago

The length of the rectangle is three times its width.The perimeter of the rectangle is at most 112 cm .

Mathematics

1 answer:

Slav-nsk [51]2 years ago

5 0

Option D is the correct answer

$2w+2.(3w)\leq 112$

Further explanation:

Let

$l\ be\ the\ length\ of\ rectangle\\and\\w\ be\ the\ width\ of\ rectangle$

The perimeter of a rectangle is given by:

$P=2w+2l$

It is also given that:

$P\leq 112$

So we can write as

$2l+2w\leq 112$

We also know that The length of the rectangle is three times its width

$l=3w$

Putting the value of l in the inequality

$2.(3w)+2w\leq 112$

Rearranging the terms

$2w+2.(3w)\leq 112$

Hence, option D is the correct answer.

Keywords: Inequalities, Perimeter

Learn more about inequalities at:

#LearnwithBrainly

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8 Leandra's fastest time for the 400 m is 70 seconds. In his next race he improves by

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8) a) The new fastest time is 56.7 seconds, b) The <em>overall percentage</em> improvement is 19 %.

9) The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

<h3>How to apply percentages in real life applications</h3>

In this problem we have two examples from real life, in which percentages are used. The first is the distance traveled by a runner in a given time and the second is the growth of a person in time. Change in variables based on percentages are described by the following formula:

C' = C · (1 + r / 100) (1)

Where:

C - Initial value
C' - Final value
r - Percentage of change.

Now we proceed to resolve on each case. 8) a) Please notice that the runner must cover the trail in less time and percentage time must be negative. If we know that C = 70 and r = - 10, then his new fastest time is:

C' = 70 · (1 - 10 / 100)

C' = 70 · 0.90

C' = 63

And again: (C' = 63, r = - 10)

C'' = 63 · (1 - 10 / 100)

C'' = 63 · 0.90

C'' = 56.7

The new fastest time is 56.7 seconds.

b) And the overall percentage improvement is:

r = (|C'' - C| / C) × 100 %

r = (|56.7 - 70| / 70) × 100 %

r = 19 %

The <em>overall percentage</em> improvement is 19 %.

9) If we know that C = 1.25 and r = 10, then the height next year is:

C' = 1.25 · (1 + 10 / 100)

C' = 1.375

And again: (C' = 1.375, r = 12)

C'' = 1.375 · (1 + 12 / 100)

C'' = 1.54

The height after the first increase is 1.375 meters and after the second increase is 1.54 meters.

To learn more on percentages: brainly.com/question/13450942

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2 years ago

At the grocery store, you can purchase lemons at 2 for $0.99. you can also buy a bag of 6 lemons for $2.50. Which is the better

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6 lemons is the better buy

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2 years ago

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Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. W

lesya692 [45]

Answer:

A)segment A"B"= AB / 2

Step-by-step explanation:

Triangle A″B″C″ is formed using the translation (x + 2, y + 0) and the dilation by a scale factor of one half from the origin. Which equation explains the relationship between segment AB and segment A"B"?

coordinate plane with triangle ABC at A(-3, 3), B(1, -3), and C(-3, -3)

A)segment A"B"= AB / 2

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C)segment AB / segment A"B"= 1/2

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Because

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2. Dilation causes the new segment to be transformed to a new length according to the old length * the scale factor of (1/2).

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3 years ago

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