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3 years ago

Solve this system of linear equation the x- and y-value with a comma. 18x+13y=60 6x+2y=6

Mathematics

2 answers:

OLEGan [10]3 years ago

8 0

Answer:

18x + 13y = 60

6x + 2y = 6 ---> 6x = -2y +6 ---> 18x = -6y+18

Substitution

(-6y +18)+13y =60

-18 -18

--------------------------

7y = 42 so y=6

Then, 6x + 2(6) =6, which you will get x = -1

(-1, 6)

notka56 [123]3 years ago

8 0

Answer:

The solution is (-1, 6).

Step-by-step explanation:

Rewrite 18x+13y=60 6x+2y=6 as

18x+13y=60

6x+2y=6

and then mult. the 2nd equation by -3:

18x+13y=60

-18x - 6y= -18

Sum up the two equations:

18x+13y=60

-18x - 6y= -18

------------------

7y = 42, so y = 6.

Subbing 6 for y in the first equation results in:

18x + 13(6) = 60, which can be reduced to 3x + 13 = 10

Then 3x = -3, and x = -1.

The solution is (-1, 6).

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6-3x=5x-10x+8

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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

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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 = 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

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