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Lubov Fominskaja [6]
3 years ago
11

The area of a rectangle is 259 cm2 and its lenght is 18.5 cm find

Mathematics
1 answer:
crimeas [40]3 years ago
7 0

The breadth of rectangle is 14 cm

The perimeter of rectangle is 65 cm

<em><u>Solution:</u></em>

Given that,

Area of rectangle = 259 square centimeter

Length of rectangle = 18.5 cm

<em><u>The area of rectangle is given by formula:</u></em>

Area\ of\ rectangle = length \times breadth

<h3><u>Find the breadth:</u></h3>

Substitute the given values in above formula:

259 = 18.5 \times breadth\\\\breadth = \frac{259}{18.5}\\\\breadth = 14

Thus breadth is 14 cm

<h3><u>Find the perimeter:</u></h3>

The perimeter of rectangle is given by formula:

Perimeter = 2(length + breadth)

Substitute the given values in above formula:

perimeter = 2(18.5+14)\\\\perimeter = 2(32.5)\\\\perimeter = 65

Thus perimeter of rectangle is 65 cm

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The fraction 60/100 is equal to 60÷100 and can also be expressed in decimal form as 0.6.

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Step-by-step explanation:

Convert metre to centimetre

Recall: 1m = 100cm

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3 years ago
The polynomial p(x)=3x^3-20x^2+37x-20 has a known factor of (x-4). Rewrite p(x) as a product of linear factors. p(x) =
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Answer:

p(x) = (3x^{2} - 8x + 5)(x - 4)

Step-by-step explanation:

p(x) has degree 3

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So

p(x) = (ax^{2} + bx + c)(x - 4)

To find a, b and c, we have to divide p(x) by x - 4.

So

Finding a:

Dividing the first term of p(x) by x - 4.

\frac{3x^{3}}{x - 4} = 3x^{2}

So a = 3.

Now multiplying 3x² by, x - 4, we have:

3x^{2}(x - 4) = 3x^{3} - 12x^{2}

Subtracting p(x) from this:

3x^{3} - 20x^{2} + 37x - 20 - (3x^{3} - 12x^{2}) = 3x^{3} - 20x^{2} + 37x - 20 - 3x^{3} + 12x^{2} = -8x^{2} + 37x - 20

Finding b:

Dividing the first term, after the subtraction, by x - 4.

\frac{-8x^{2}}{x - 4} = -8x

So b = -8.

Multiplying -8x by x - 4, we have:

-8x(x-4) = -8x^{2} + 32x

Then

-8x^{2} + 37x - 20 - (-8x^{2} + 32x) = -8x^{2} + 37x - 20 + 8x^{2} - 32x = 5x - 20

Finding c:

\frac{5x}{x - 4} = 5

So c = 5.

Just to verify if the remainder is 0.

5(x - 4) = 5x - 20

5x - 20 - (5x - 20) = 0

Ok

Then:

p(x) = (ax^{2} + bx + c)(x - 4)

p(x) = (3x^{2} - 8x + 5)(x - 4)

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Step-by-step explanation:

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