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emmasim [6.3K]
3 years ago
11

I need help with number 15. Could you also please explain how you got your answers too?

Mathematics
1 answer:
atroni [7]3 years ago
4 0

By definition, an angle bisector divides an angle into two equal parts. Thus, ∠AEB ≅ ∠BEC by definiton.

Because EA is perpendicular to ED, it makes a right angle at E. Thus the measure of ∠AED is 90°.

Using these two pieces of information - the definition of an angle bisector and the definition of perpendicular, we can find the measure of the pieces inside by angle addition.  

Now we take those two definitions and our given angles to find x. Thus,

m∠AEB + m∠BEC + m ∠CED = m∠AED by angle addition

m∠AEB + m∠BEC + m ∠CED = 90  by definition of perpendicular

m∠AEB + m∠AEB + m ∠CED = 90   by defintion of angle bisector for EA.

(4x + 1) + (4x +1) + m ∠CED = 90         because m∠AEB =4x + 1 is given

4x +1 + 4x +1 + 3x = 90                          because m∠CED =3x is given

11x + 2 = 90                                       by collecting like terms

11x = 88                                        by subtracting 2 on both sides

x = 8                                            by dividing both sides by 11.

Now we can substitute to find the angles.

Since m∠AEB is 4x + 1, then m∠AEB = 4(8) + 1 = 32 + 1 = 33°.  Since m∠CED is 3x, then m∠CED is 3(8) = 24 degrees. The remaining angle, ∠BEC, was equal to ∠AEB by definition of angle bisector. It too is 33 degrees.


Therefore, x = 8, m∠AEB = m∠BEC = 33° and m∠CED = 24°

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A swimming pool has a diameter of 24 feet. What is the minimum amount of fabric needed to cover the pool if the cover must hang
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Answer:

531.167 ft²

Step-by-step explanation:

Given data

Dimension of pool

Diameter =24ft

Radius =12ft

If the cover must hang by 1ft around, then the diameter is 26ft

Radius =13ft

Area of cover = πr²

Substitute

Area = 3.142*13²

Area =3.143*169

Area =531.167 ft²

Hence the minimum area is 531.167 ft²

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2 years ago
How do I find the displacement? Help frl
liubo4ka [24]

Answer:

  • distance traveled: 30 m
  • displacement: 21.4 m

Step-by-step explanation:

You want the distance traveled and the displacement after walking 17 m south and 13 m east.

<h3>Distance</h3>

The distance traveled is the sum of the lengths of each leg of the trip:

  17 m + 13 m = 30 m

You have traveled a distance of 30 m.

<h3>Displacement</h3>

The displacement is the distance from your final position to your starting position. If you draw a diagram of the journey, you see the displacement is the hypotenuse of a right triangle with legs 17 m and 13 m. The Pythagorean theorem can help you find this length:

  h = √(a² +b²)

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10. Two lighthouses are located on a north-south line.
Kamila [148]

The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)

The distance between both lighthouses is 5783.96 m

I've added an attachment that represents the scenario.

From the attachment, we have:

\mathbf{\angle A = 180^o - 120^o\ 43'}

Convert to degrees

\mathbf{\angle A = 180^o - (120^o +\frac{43}{60}^o)}

\mathbf{\angle A = 180^o - (120^o +0.717^o)}

\mathbf{\angle A = 180^o - (120.717^o)}

\mathbf{\angle A = 59.283^o}

\mathbf{\angle B = 39^o43'}

Convert to degrees

\mathbf{\angle B = 39^o + \frac{43}{60}^o}

\mathbf{\angle B = 39^o + 0.717^o}

\mathbf{\angle B = 39.717^o}

So, the measure of angle S is:

\mathbf{\angle S = 180 - \angle A - \angle B} ---- Sum of angles in a triangle

\mathbf{\angle S = 180 - 59.283 - 39.717}

\mathbf{\angle S = 81}

The required distance is distance AB

This is calculated using the following sine formula:

\mathbf{\frac{AB}{\sin(S)} = \frac{AS}{\sin(B)} }

Where:

\mathbf{AS = 3742}

So, we have:

\mathbf{\frac{AB}{\sin(81)} = \frac{3742}{\sin(39.717)}}

Make AB the subject

\mathbf{AB= \frac{3742}{\sin(39.717)} \times \sin(81)}

\mathbf{AB= 5783.96}

Hence, the distance between both lighthouses is 5783.96 m

Read more about bearing and distance at:

brainly.com/question/19017345

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5w^22

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