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Licemer1 [7]
3 years ago
5

The diagram shows a hexagon-shaped tile used for flooring. Each hexagon tile has an area of 18/3 in 2 Find x.​

Mathematics
2 answers:
mylen [45]3 years ago
7 0

Answer:

x = 12

Step-by-step explanation:

The hexagonal tile given here is made up of 6 triangles with equal bases and heights.

So, area of hexagonal tile will be equal to 6 times the area of one triangle.

Therefore,

18 \sqrt{3}  = 6 \times  \frac{1}{2}  \times 2 {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{x}{6} }  \\  \\ 18 \sqrt{3}  = 6  {( \sqrt{3)} }^{ \frac{x}{12} } . {( \sqrt{3)} }^{ \frac{2x}{12} }  \\  \\  \frac{18 \sqrt{3}  }{6}  = {( \sqrt{3)} }^{ \frac{x}{12}  +  \frac{2x}{12} }  \\  \\ 3 \sqrt{3}  =  {( \sqrt{3)} }^{ \frac{3x}{12} } \\  \\ 3. {3}^{ \frac{1}{2} }  =  {3}^{ \frac{3x}{24} }  \\  \\  {3}^{1 +  \frac{1}{2} }  =  {3}^{ \frac{x}{8} }  \\  \\ {3}^{ \frac{3}{2} }  =  {3}^{ \frac{x}{8} }  \\ (bases \: are \: equal \: so \: exponents \:  \\ will \: also \: be \: equal) \\ \implies  \frac{3}{2}  =  \frac{x}{8}  \\  \\ x =  \frac{3 \times 8}{2}  \\  \\ x = 3 \times 4 \\  \\ x = 12

alexira [117]3 years ago
7 0

Answer: x=12

Step-by-step explanation:

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The length of a rectangle is four feet longer than the width. the area is 21. find the dimension
MakcuM [25]
The length is 7 and the width is 3
7 0
3 years ago
Which expression is equivalent to −1/ 12x−1 /3?
alexandr402 [8]

Answer:

\frac{1}{12} (-x-4)

Step-by-step explanation:

the expression we have is:

-\frac{1}{12} x-\frac{1}{3}

To find an equivalent expression, it would be helpful to express 1/3 so that it has a 12 in the denominator:

\frac{1}{3}=\frac{4}{12}

so we substitute this:

-\frac{1}{12} x-\frac{4}{12}

and now we have 1/12 in both terms :

-\frac{1}{12}x-\frac{1*4}{12}

so we can factor it (we take it out of each term: in the first we are left with -x and in the second with -4):

\frac{1}{12} (-x-4)

the equivalent expression is: \frac{1}{12} (-x-4)

5 0
3 years ago
Find area and perimeter of shaded regions below
aleksandrvk [35]

Answer:

Step-by-step explanation:

ABCD is a square.

side = 24 cm

Area of square = side  * side = 24 * 24 = 576 cm²

Semicircle:

d = 24 cm

r = 24/2 = 12 cm

Area of semi circle =πr²

                               = 3.14 * 12 * 12

                               = 452.16 cm²

Area of shaded region = area of square - area of semicircle  + area of semicircle

  = 576  - 452.16 + 452.16

  = 576 cm²

Perimeter:

Circumference of semicircle = 2πr

               = 2 * 3.14 * 12

               = 75.36

Perimeter = 2* circumference of semicircle + 24 + 24

                = 2 * 75.36 + 24 + 24

                = 150.72 + 24 + 24

                 = 198.72 cm

6 0
3 years ago
Ahh I need help with this
sergiy2304 [10]

Answer:

i thinkbit is C but im in 6th grade and at may 5 i. not there yet

4 0
3 years ago
Read 2 more answers
X + 2y = 5<br>3x + 5y = 14<br>Solve the system of equations.<br>(3.1)<br>(7.-1)<br>(2.3/2)​
son4ous [18]

Answer:

(3,1) because x is 3 and y is 1.

Step-by-step explanation:

x+2y=5

3x+5y=14

Multiply first equation by 3:

3x+6y=15

3x+5y=14

Subtract 3x:

1y=1

Therefore, y = 1

Plug it back into 1st equation:

x+2(1)=5

x+2=5

Therefore, x = 3

Judging from your answers, it looks like (3,1) because x is 3 and y is 1.

I hope this helped!

5 0
3 years ago
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