The length of a rectangle plus its width is 36 cm. The area is 323 square cm. What are the length and width of the rectangle?

Mama L [17]

HL (hypotenuse leg)
Hope this helps

3 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

Factorise using suitable identities (0.1x-0.2y)^2

Sav [38]

Answer:

Step-by-step explanation:

(a - b)² = a² - 2ab + b²

a = 0.1x

b = 0.2y

(0.1x - 0.2y)²= (0.1x)² - 2*0.1x*0.2y + (0.2y)²

= (0.1)²x² - 0.04xy + (0.2)²y²

= 0.01x² - 0.04xy + 0.04y²

3 0

3 years ago

Which is equivalent to 3sqrt8^x ?

creativ13 [48]

The correct answer is A.

7 0

3 years ago

The graph represents the cost y (in dollars) to open an online gaming account and buy x games. Write an equation in slope-interc

Luba_88 [7]

Answer:

y = 10x + 15

Step-by-step explanation:

you pick two points on the line

I picked (3,45) and (6,75)

you subtract the two x’s and y’s

75 - 45 = 30 (30 is the rise) you go up from 45 to 75

6 - 3 = 3 (you move 3 times to the right to get to the 6) so 3 is the run

slope = rise/run so 30/3 = 10

The y-intercept is the place you start on the graph so that is 15

8 0

3 years ago

Read 2 more answers