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Sindrei [870]
2 years ago
12

Which figures can be circumscribed by a circle? Select all that apply.

Mathematics
2 answers:
Darina [25.2K]2 years ago
7 0

Answer:

A, B, C, D

Step-by-step explanation:

They All add up to 360

White raven [17]2 years ago
6 0

Answer:

B and D

Step-by-step explanation:

figures which can be circumscribed by a circle are called cyclic quadrilaterals.

the opposite angles of a cyclic quadrilateral sum to 180°

A

∠ B + ∠ D = 82° + 56° = 138° ≠ 180° ← not cyclic

B

∠ B + ∠ D = 103° + 77° = 180° and ∠ A + ∠ C = 90° + 90° = 180° ← cyclic

C

∠ B + ∠ D = 112° + 90° = 202° ≠ 180° ← not cyclic

D

∠ B + ∠ D = 90° + 90° = 180° and ∠ A + ∠ C = 90° + 90° = 180°← cyclic

Then B and D can be circumscribed by a circle

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Answer: 15.7 (1 decimal place)

Step-by-step explanation:

The formula for the circumference of a circle is d(diameter) x π(pi).

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a gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sel
adell [148]

Answer:

The price per wind chime that will maximize revenue = $ 315

Step-by-step explanation:

Given - A gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sell 5 fewer wind chimes per month.

To find - Find the price per wind chime that will maximize revenue.

Proof -

Given that,

Total Wind chimes selling = 160

Price of each Wind chime = $150

Now,

Given that, for each $15 increase in price, they will sell 5 fewer wind chimes per month.

So,

Let the price = 150 + 15x

So,

Number of wind Chimes sold per month = 160 - 5x

So,

Total Revenue, R = (150 + 15x)(160 - 5x)

                             = 24000 - 750x + 2400x - 75x²

                             = 24000 + 1650x - 75x²

⇒R(x) = 24000 + 1650x - 75x²

Differentiate R with respect to x , we get

R'(x) = 1650 - 150x

Now,

For Maximize Revenue, Put R'(x) = 0

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⇒150x = 1650

⇒x = 1650/150

⇒x = 11

∴ we get

Price per Wind chime = $ 150 + 15(11)

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                                    = $ 315

So,

The price per wind chime that will maximize revenue = $ 315

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