F (x) = 1/3 x for x=4

VashaNatasha [74]

{5+(10+11)/7}x6

(5+21/7)x6

(5+3)x6

8x6

48

The answer is 48

8 0

3 years ago

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

3 years ago

It is given that AB is parallel to CD and points E, G, H, and F are collinear. The measure of ZEGF is 180°, by the definition of

alex41 [277]

The completed statement filled in with the correct option is presented as follows;

It is given that AB is parallel to CD and points, E, G, H, and F are collinear. The measure of ‹EGF is 180° by the definition of a straight angle. ‹AGE and ‹AGF are adjacent, so the measure of ‹AGE plus the measure of ‹AGF equals the measure of angle ‹EGF. It can be said that the measure of ‹AGE plus the measure of ‹AGF equals 180°. ‹CHE and ‹AGF are same side interior angles, so the measure of angle ‹CHE plus the measure of angle ‹AGF equals 180°.

Substituting once again means that the measure of ‹AGE plus the measure of angle ‹AGF equals the measure of angle ‹CHE plus the measure of ‹AGF. The measure of angle ‹AGE is equal to the measure of ‹CHE using the Subtraction Property of Equality. Finally, by the definition of congruency, ‹AGE is congruent to ‹CHE

The correct option is therefore;

‹CHE and ‹AGE are same side interior angles; using the Subtraction Property of Equality

<h3>What relationships between angles formed by parallel lines can be used to complete the paragraph?</h3>

Angles, ‹CHE and ‹AGF are angles formed on the same side of the common transversal, EF, and are formed on the interior part of AB and CD.

Given that ‹CHE and ‹AGF are both on the line FGHE, and together with ‹CHF and ‹AGE form two linear pair angles, ‹CHE and ‹AGF are supplementary angles and add up to 180°.

According to the substitution property of equality, both sides of an equation remain equal following the subtraction of the same quantity from both sides.

Given that we have:

‹AGE + ‹AGF = ‹CHE + ‹AGF

Subtracting ‹AGF from both sides gives;

‹AGE = ‹CHE (subtraction property of equality)

Learn more about the angles formed by parallel lines here:

brainly.com/question/17430387

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3 0

1 year ago

A 35 foot wire is secured from the top of a flagpole to a stake in the ground. If the stake is 14 feet from the base of the flag

cupoosta [38]

the answer is 21ft because the total is 35feet so 35 - 14 = 21

6 0

3 years ago

Read 2 more answers

Which two numbers below have a least common multiple of 48?

gladu [14]

Answer:

D) 3 and 16

Step-by-step explanation:

A common multiple is the result of multiplicacion of two numbers

3x16= 48

3 0

3 years ago