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kykrilka [37]
3 years ago
9

A piece of copper wire which is 56cm long is bent to form a rectangle of area 171cm².find the length and the width of this recta

ngle.​
Mathematics
1 answer:
devlian [24]3 years ago
3 0

Answer:

Length= 19cm

Width= 9cm

Step-by-step explanation:

let the length of the rectangle be L cm and its width be W cm.

Perimeter of rectangle= 56cm

2L +2W= 56

L +W= 56 ÷2

L +W= 28

L= 28 -W -----(1)

Area of rectangle= length ×width

LW= 171 -----(2)

Susbt. (1) into (2):

W(28 -W)= 171

28W -W²= 171 <em>(</em><em>expand</em><em>)</em>

W² -28W +171= 0 <em>(</em><em>bring</em><em> </em><em>everything</em><em> </em><em>to</em><em> </em><em>one</em><em> </em><em>side</em><em>)</em>

(W -19)(W-9)= 0 <em>(</em><em>factorise</em><em>)</em>

W-19=0 or W-9=0

W= 19 or W= 9

Subst into (1):

L=28 -19 or L= 28 -9

L=9 or L= 19

Since we usually take the longer side of the rectangle to be its length, L= 19 and hence W=9.

Therefore its length is 19cm and its width is 9cm.

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<u>A .</u>Length = x+5\\breadth = x-2<u></u>

<u>B. </u>domain of f(x)= x^2+3x-10 here is all values of x > 2 .

<u>Step-by-step explanation:</u>

Correct question is : the function f(x)= x^2+3x-10models the area of a rectangle. a: describe the length and width of the rectangle in terms of x b: what is a domain for above function in relation to rectangle . Let's solve:

a: describe the length and width of the rectangle in terms of x

Let's factorise f(x)= x^2+3x-10 :

⇒ f(x)= x^2+5x-2x-10

⇒ f(x)= x(x+5)-2(x+5)

⇒ f(x)= (x+5)(x-2)

Since , ⇒ f(x)=length(breadth) So

Length = x+5\\breadth = x-2 .

b: what is a domain for above function in relation to rectangle

Since area is always > 0 , and (length , breadth)>0 So,

⇒ f(x)= (x+5)(x-2)>0\\x>0 \\x>2 Therefore, domain of f(x)= x^2+3x-10 here is all values of x > 2 .

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3 years ago
Michelle has an area in her garden for some plants and she wants to plant both tomatoes and bell peppers she can purchase tomato
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Answer:

The number of tomato plants are <u>70</u> and the number of bell pepper plants are <u>60</u>.

Step-by-step explanation:

Given:

Michelle has an area in her garden for some plants and she wants to plant both tomatoes and bell peppers she can purchase tomato plants for $1.50 and she can purchase bell pepper plants were $2.00.

Michelle is counted up enough space in her garden for a total of 130 plans she has $225 to spend.

Now, to find the number of plants she can purchased for her garden.

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And let the number of bell pepper plants be y.

<em>So, the total number of plants :</em>

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<em>Now, the total money she has to spend:</em>

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<em>The number of bell pepper plants = 60.</em>

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