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3 years ago

Can you help me solve for x?

Mathematics

1 answer:

sergiy2304 [10]3 years ago

3 0

Answer:

x = 12

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

10x-10 = 60 +4x+2

Combine like terms

10x-10 = 62+4x

Subtract 4x from each side

10x-4x -10 = 62 +4x-4x

6x -10 = 62

Add 10 to each side

6x-10+10 = 62+10

6x= 72

Divide by 6

6x/6 = 72/6

x = 12

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Answer:

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Step-by-step explanation:

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3 years ago

What is the equation, in slope-intercept form, of the line that is perpendicular to the line

wolverine [178]

Answer:

y=3/2x+1

Step-by-step explanation:

y-4= -⅔(x-6)

y-4=-⅔x+4

y=-⅔x+4+4

(equation of line 1) y= -⅔x+8 gradient= -⅔

(line 2)gradient=3/2

note* the gradients of perpendicular lines multiplied result to -1

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3 =y+2

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multiply both sides by 2(x+2)to remove the denominators

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8 0

3 years ago

Find the dimensions of an open rectangular box with a square base that holds 2000 cubic cm and is constructed with the least bui

Vesnalui [34]

<h3>The dimensions of the given rectangular box are:</h3><h3>L = 15.874 cm , B = 15.874 cm , H = 7.8937 cm</h3>

Step-by-step explanation:

Let us assume that the dimension of the square base = S x S

Let us assume the height of the rectangular base = H

So, the total area of the open rectangular box

= Area of the base + 4 x ( Area of the adjacent faces)

= S x S + 4 ( S x H) = S² + 4 SH ..... (1)

Also, Area of the box = S x S x H = S²H

⇒ S²H = 2000

$\implies H = \frac{2000}{S^2}$

Substituting the value of H in (1), we get:

$A = S^2 + 4 SH = S^2 + 4 S(\frac{2000}{S^2}) = S^2 + (\frac{8000}{S})\\\implies A = S^2 + (\frac{8000}{S})$

Now, to minimize the area put :

$(\frac{dA}{dS} ) = 0 \implies 2S - \frac{8000}{S^2} = 0\\\implies S^3 = 4000\\\implies S = 15.874 \approx 16 cm$

Putting the value of S = 15.874 cm in the value of H , we get:

$\implies H = \frac{2000}{S^2} = \frac{2000}{(15.874)^2} = 7.8937 cm$

Hence, the dimensions of the given rectangular box are:

L = 15.874 cm

B = 15.874 cm

H = 7.8937 cm

3 0

4 years ago

Svetlanka [38]

Answer:

area of rectangle=l×b=2.4×5.8=13.92cm²

6 0

3 years ago

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