Find the greatest common factor of 48^a 38a

What is an exaple of linear

Viefleur [7K]

Answer:

a line

Step-by-step explanation:

6 0

2 years ago

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Regular hexagon ABCDEF is inscribed in circle X and has an apothem that is 6√3 inches long. Use the length of the apothem to cal

Phantasy [73]

Answer:

Part A

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the given values we get;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

R = 12 inches

The radius of the circumscribing circle is 12 inches

Part B

The length of each side of the hexagon, 's', is;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

s = 12 inches

The perimeter, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon is 72 inches

Step-by-step explanation:

The given parameters of the regular hexagon are;

The length of the apothem of the regular hexagon, a = 6·√3 inches

The relationship between the apothem, 'a', and the circumradius, 'R', is given as follows;

$a = R \cdot cos \left(\dfrac{\pi}{n} \right)$

Where;

n = The number of sides of the regular polygon = 6 for a hexagon

'a = 6·√3 inches', and 'R' are the apothem and the circumradius respectively;

Part A

Therefore, we have;

$The \ circumradius, \ R = \dfrac{a}{cos \left(\dfrac{\pi}{n} \right)}$

Plugging in the values gives;

$The \ circumradius, \ R = \dfrac{6 \cdot \sqrt{3} }{cos \left(\dfrac{\pi}{6} \right)} = \dfrac{6 \cdot \sqrt{3} }{\left(\dfrac{\sqrt{3} }{2} \right)} = 6 \cdot \sqrt{3} \times \dfrac{2}{\sqrt{3} } = 12$

The circumradius, R = 12 inches

Part B

The length of each side of the hexagon, 's', is given as follows;

$s = a \times 2 \times tan \left(\dfrac{\pi}{n} \right)$

Therefore, we get;

$s = 6 \cdot \sqrt{3} \times 2 \times tan \left(\dfrac{\pi}{6} \right) = 6 \cdot \sqrt{3} \times 2 \times \left(\dfrac{1}{\sqrt{3} } \right) = 12$

The length of each side of the hexagon, s = 12 inches

The perimeter of the hexagon, P = n × s = 6 × 12 = 72 inches

The perimeter of the hexagon = 72 inches

5 0

2 years ago

Determine the width of the pond.

Delicious77 [7]

Answer:

180 ft.

Step-by-step explanation:

$\frac{90}{135} = \frac{120}{x}$

$90x = 16200$

4 0

2 years ago

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Which expressions show the prime factorization of 90?

Andreas93 [3]

Prime factorization means that we divide 90 by prime numbers only.

90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5

2 x 3 x 3 x 5 = 90

2 x 3² x 5 = 90
or 2,3,3,or 5

7 0

3 years ago

Mark reduce the size of a photo to a height of 4 inches. What is the new width if it was originally 16 inches tall and 8 inches

uranmaximum [27]

Answer:

Step-by-step explanation:

new height is ¼ of original height

new width = ¼×8 = 2 inches

4 0

2 years ago

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