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murzikaleks [220]
3 years ago
5

Factor 6(×)^3+43(×)^2+79(×)+12

Mathematics
1 answer:
Marysya12 [62]3 years ago
3 0
The answer is (6x+1)•(x+4)•(x+3)
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The perimeter of a rectangle is 30.8 km and it’s diagonal length is 11 km. Find it’s length and width
blsea [12.9K]

Answer:

Length of the rectangle is 15.0325 km and width is 0.3765 km.

Explanation:

Given:

Perimeter of a rectangle = 30.8 km

Length of diagonal of rectangle = 11 km

To find:

The length and width of rectangle=?

Solution:

Lets assume length of the rectangle = x km

And assume width of the rectangle = y km

Lets first create equation using given  perimeter

perimeter of rectangle = 2 ( length +  width )

=> 30.8 km = 2 ( x + y )  

=>x + y = \frac{30.8}{2}

=> y = 15.4 – x             ------(1)

As diagonal and two sides of rectangle forms right angle triangle whose hypoteneus is diagonal ,  

=> length^2 + width^2 = diagonal^2

=> x^2 + y^2 = 11^2

=> x^2 + y^2 = 121

On substituting value of y from (1) in above equation we get

=> x^2 + (15.4-x)^2 = 121

=>x^2 + (15.4)^2 + x^2 – 2 x 15.4 \times x   = 121

=> 2x^2-30.8x + 237.16 -121  = 0

=> 2x^2-30.8x + 116.16 = 0

Solving above quadratic equation using quadratic formula

General form of quadratic equation is  

ax^2 +bx +c = 0

And quadratic formula for getting roots of quadratic equation is  

x= \frac{ -b\pm\sqrt{(b^2-4ac)}}{2a}

As equation is 2x^2-30.8x + 116.16 = 0, in our case

a = 2 ,  b = -30.8 and c = 116.16

Calculating roots of the equation we get

x=\frac{ -(-30.8)\pm\sqrt{(-30.8)^2-4(2)( 11)} } {(2\times2)}

x=\frac{30.8\pm\sqrt{(948.64-88)}}{4}

x=\frac{30.8\pm\sqrt{860.64}}{4}

x=\frac{30.8\pm\sqrt{860.64}}{4}

x=\frac{(30.8\pm29.33)}4

x=\frac{(30.8+29.33)}{4}

x=\frac{(30.8-29.33)}{4}

=> x = 15.0325 or x = 0.3675

As generally length is longer one ,  

So x = 1.0325

From equation (1) y = 15.4 – x = 0.3765

Hence length of the rectangle is 15.0325 km and width is 0.3765 km.

6 0
3 years ago
Sue has 18 sweets.
Norma-Jean [14]
Easy:

((18-x) -5) + ((18+x)➗2)
7 0
3 years ago
An account earns simple interest. Find the principal.
Alexandra [31]

Answer:

$ 900

Step-by-step explanation:

Simple interest = Principle * Time * Rate / 100

Now by substituting :

27 = Principle * 2 * 1.5 / 100

Principle = 27 * 100 / 2 * 1.5

Principle = 2700 / 3

So Principle = $ 900

Hope it helps

5 0
3 years ago
It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for
frosja888 [35]
Last one 7 and 3
9(7)+20(3)>120
63+ 60
123>120
Says 123 minutes is longer than 120 that's why it is that answer
7 0
3 years ago
Read 2 more answers
Need help (midpoints)
Zinaida [17]

Answer:

5

Step-by-step explanation:

i know it

5 0
2 years ago
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