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Daniel [21]
3 years ago
6

The length of a rectangle is five times its width. The perimeter of the rectangle is at most 96 cm. Which inequality models the

relationship between the width and the perimeter of the rectangle?
2w+2⋅(5w)>96
2w+2⋅(5w)<96
2w+2⋅(5w)≤96
2w+2⋅(5w)≥96
Mathematics
2 answers:
aivan3 [116]3 years ago
7 0

Let

L--------> the length of the rectangle

W-------> the width of the rectangle

we know that

the perimeter of the rectangle is equal to

P=2L+2W

P\leq 96\ cm

so

(2L+2W)\leq 96 ---------> equation 1

L=5W ---------> equation 2

Substitute equation 2 in equation 1

2*(5W)+2W\leq 96

therefore

<u>the answer is the option</u>

2w+2⋅(5w)≤96


Komok [63]3 years ago
3 0

Answer:

2w+2⋅(5w)≤96

Step-by-step explanation:

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a) The <em>perimeter</em> function of the rectangle is p = 18\cdot x -2\cdot x^{3}.

b) The domain of the <em>perimeter </em>function is x \in [-3, 3].

<h3>How to analysis the perimeter formula of a rectangle inside a parabola</h3>

a) The perimeter of a rectangle (p) is the sum of the lengths of its four sides:

p = AB\cdot AC (1)

If we know that AB = 2\cdot x and AC = 9-x^{2}, then the perimeter of the rectangle is represented by the following formula:

p = 2\cdot x \cdot (9-x^{2})

p = 18\cdot x -2\cdot x^{3}

The <em>perimeter</em> function of the rectangle is p = 18\cdot x -2\cdot x^{3}. \blacksquare

b) The domain of the function is the set of values of x associated to the function. After a quick inspection, we find that the domain of the <em>perimeter </em>function is x \in [-3, 3]. \blacksquare

<h3>Remark</h3>

The statement is incomplete and poorly formatted. The correct form is described below:

<em>As shown at the right, rectangle ABCD has vertices C and D on the x-axis and vertices A and B on the part of the parabola </em>y = 9-x^{2}<em> that is above the x-axis. a) Express the perimeter </em>p<em> of the rectangle as a function of the x-coordinate of A. b) What is the domain of the perimeter function?</em>

To learn more on rectangles, we kindly invite to check this verified question: brainly.com/question/10046743

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