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musickatia [10]
3 years ago
8

What is the value of x in the rhombus below?

Mathematics
2 answers:
GuDViN [60]3 years ago
7 0

Answer:

Option C

21\°

Step-by-step explanation:

we know that

The two diagonals of a rhombus are perpendicular

so

Let

O------> the center of the rhombus

m∠AOB=90\°

Remember that

The sum of the internal angles of a triangle is equal to 180\°

therefore

in the triangle AOB

m∠AOB+m∠OAB+m∠OBA=180\°

substitute the values

90\°+(2x+1)\°+(2x+5)\°=180\°

solve for x

(4x+6)\°=90\°

4x=90\°-6\°

x=21\°

Maurinko [17]3 years ago
5 0
Look into my attachment

in rhombus ABCD, ∠AOB = 90°

Look at ΔAOB
the sum of inner angles = 180°
∠BAO + ∠AOB + ∠ABO = 180°
2x + 1 + 90 + 2x + 5 = 180°
4x + 96 = 180
4x = 84
x = 21

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A minimum temperature of -4.44°C was recorded at a lake. A minimum temprature of 23.3°C was recorded later on the same day. Dete
GuDViN [60]

Answer:

27.74 is the difference

Step-by-step explanation:

23.3° C - (-4.44° C)

23.3 + 4.44

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5 0
2 years ago
OM , ON and OP are the angle bisectors of ∠AOB, ∠BOC, and ∠COD respectively. ∠AOD and ∠BOE are straight angles.
Orlov [11]

Find m∠BOC, if m∠MOP = 110°.

Answer:

m∠BOC= 40 degrees

Step-by-step explanation:

A diagram has been drawn and attached below.

  • OM bisects AOB into angles x and x respectively
  • ON bisects ∠BOC into angles y and y respectively
  • OP bisects ∠COD into angles z and z respectively.

Since ∠AOD is a straight line

x+x+y+y+z+z=180 degrees

2x+2y+2z=180^\circ

We are given that:

m∠MOP = 110°.

From the diagram

∠MOP=x+2y+z

Therefore:

x+2y+z=110°.

Solving simultaneously by subtraction

2x+2y+2z=180^\circ

x+2y+z=110°.

We obtain:

x+z=70°

Since we are required to find ∠BOC

∠BOC=2y

Therefore from x+2y+z=110° (since x+z=70°)

70+2y=110

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Therefore:

m∠BOC= 40 degrees

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Answer:

a) The interval for those who want to go out earlier is between 43.008 and 46.592

b) The interval for those who want to go out later is between 47.9232 and 51.9168

Step-by-step explanation:

Given that:

Sample size (n) =128,

Margin of error (e) = ±4% =

a) The probability of those who wanted to get out earlier (p) = 35% = 0.35

The mean of the distribution (μ) = np = 128 * 0.35 = 44.8

The margin of error = ± 4% of 448 = 0.04 × 44.8 =  ± 1.792

The interval = μ ± e = 44.8 ± 1.792 = (43.008, 46.592)

b) The probability of those who wanted to start school get out later (p) = 39% = 0.39

The mean of the distribution (μ) = np = 128 * 0.39 = 49.92

The margin of error = ± 4% of 448 = 0.04 × 49.92 =  ± 1.9968

The interval = μ ± e = 44.8 ± 1.792 = (47.9232, 51.9168)

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