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2 years ago

The diagram shows a rhombus inside a regular hexagon work out the angle x

Mathematics

1 answer:

steposvetlana [31]2 years ago

7 0

Answer:

Step-by-step explanation:

The rest of the question is the attached figure.

Given: A rhombus inside a regular hexagon, work out the angle x.

As shown

ABCDEF is a regular hexagon.

The regular hexagon have 6 congruent angles, and the sum of the interior angles is 720°

So, the measure of one angle of the regular hexagon = 720/6 = 120°

So, ∠F = ∠BAF = 120°

AFEG is a rhombus.

The rhombus have 2 obtuse angles and 2 acute angles.

∠F is one of the obtuse angles of the rhombus = 120°

∠F and ∠FA G are supplementary angles

So, ∠F + ∠FA G = 180°

∴ ∠FA G = 180° - ∠F = 180 - 120 = 60°

∴ x = ∠GAB = ∠BAF - ∠FA G = 120 - 60 = 60°

<u>So, the measure of the angle x = 60°</u>

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irga5000 [103]

Telephone computers tv microwave

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2 years ago

There are three choices of jellybeans - grape ,cherry and orange. if the probability of getting a grape is 3/10 and the probabil

muminat

When looking at probabilities, two ideas are always true.

1) Any probability is more than 0.

2) The sum of all the probabilites is 1.

Idea #2 works here. (For example, think of how a die has six things and the probability of each is 1/6. So 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1.) Let G = the probability of grape, C = probability of cherry and O = the probability of orange. From Idea #2, G + C + O = 1. Since we know G and C, then

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1 year ago

The dimensions of a rectangular bin are consecutive integers. If the volume of the bin is 4896 cubic inches, what are the dimens

Rom4ik [11]

cubed root of 4896 = 16.98

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17-1 = 16

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1 year ago

Read 2 more answers

Which number in the monomial 215x18y3z21 needs to be changed to make it a perfect cube?

Murljashka [212]

Remember
xyz=(x)(y)(z)
if x and y and z are all perfect cubes, xyz is also a perfect cube

remmeber
(x^n)^m=x^(mn)
so if it is perfect cube it can be factored into
(x^n)^3, such taht n is a whole number
basiclaly, see if the expoent is divisble by 3

all of them should be perfect cubes

215x^18y^3z^21

split them up to see which ones need changing

215=5*43, not a perfect cube
could be changed to 6^3, which is 216

x^18=(x^6)^3

y^3=y^3
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the 215 needs to be changed

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2 years ago

Read 2 more answers

Marginal cost At a certain factory the marginal cost is 3(q-4)^2 dollars per unit when the level of production is q units.

viktelen [127]

Answer:

a.) C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH b.) $170

Step-by-step explanation:

(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:

Marginal cost (MC) = change in total cost/change in quantity

Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:

Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k

where k is a constant.

The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k

C(q) = -(1/4)*(q^3 - 12q^2 + 48q - 64) + k = -(1/4)*q^3 + 3q^2 - 12q -16 + k

Thus:

C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH

(b) C(14) = -(1/4)*14^3 + 3*14^2 - 12*14 + 436 = -686 + 588 - 168 + 436 = $170

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1 year ago