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zloy xaker [14]
3 years ago
9

Use the picture below to answer questions 14a and 14b

Mathematics
1 answer:
Colt1911 [192]3 years ago
7 0

Answer:

x = 35, ∠ BDE = 130°

Step-by-step explanation:

(4x - 10) and (x + 95) are corresponding angles and are congruent, then

4x - 10 = x + 95 ( subtract x from both sides )

3x - 10 = 95 ( add 10 to both sides )

3x = 105 ( divide both sides by 3 )

x = 35

Thus

∠ BDE = 4x - 10 = 4(35) - 10 = 140 - 10 = 130°

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Equilateral triangle ABC has an area of \sqrt{3}√ ​3 ​ ​​ . If the shaded region has an area of \piπK − \sqrt{3}√ ​3 ​ ​​ , what
Liono4ka [1.6K]

Answer:

The value of k = 4/3

Step-by-step explanation:

* Lets explain how to solve the problem

- An equilateral triangle ABC is inscribed in a circle N

- The area of the triangle is √3

- The shaded area is the difference between the area of the circle

  and the area of the equilateral triangle ABC

- The shaded are = k π - √3

- We need to find the value of k

* <u><em>At first lets find the length of the side of the Δ ABC</em></u>

∵ Δ ABC is an equilateral triangle

∴ Its area = √3/4 s² , where s is the length of its sides

∵ The area of the triangle = √3

∴ √3/4 s² = √3

- divide both sides by √3

∴ 1/4 s² = 1

- Multiply both sides by 4

∴ s² = 4 ⇒ take √ for both sides

∴ s = 2

∴ The length of the side of the equilateral triangle is 2

* <u><em>Now lets find the radius of the circle</em></u>

- In the triangle whose vertices are A , B and N the center of the circle

∵ AN and BN are radii

∴ AN = BN = r , where r is the radius of the circle

∵ The sides of the equilateral angles divides the circle into 3 equal

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∵ The measure of the central angle in a circle equal the measure

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∵ ∠ANB is an central angle subtended by arc AB

∵ The measure of arc AB is 120°

∴ m∠ANB = 120°

- By using the cosine rule in Δ ANB

∵ AB = 2 , AN = BN = r , m∠ANB = 120°

∴ (2)^{2}=r^{2}+r^{2}-2(r)(r)cos(120)

∴ 4=r^{2}+r^{2}-2(r)(r)(-0.5)

∴ 4=r^{2}+r^{2}-(-r^{2})

∴ 4=r^{2}+r^{2}+r^{2}

∴ 4=3r^{2}

- Divide both sides by 3

∴ r^{2}=\frac{4}{3}

- Take square root for both sides

∴ r = 2/√3

* <u><em>Lets find the value of k</em></u>

∵ Area circle = πr²

∵ r = 2/√3

∴ Area circle = π(2/√3)² = (4/3)π

∵ Area shaded = area circle - area triangle

∵ Area triangle = √3

∴ Area shaded = (4/3) π - √3

∵ Area of the shaded part is π k - √3

- Equate the two expressions

∴ π k - √3 = (4/3) π - √3

∴ k = 4/3

* The value of k = 4/3

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How many subsets can be made from a set of six elements, including the null set and the set itself?
BlackZzzverrR [31]

Answer:

B) 64

Step-by-step explanation:

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3 years ago
Arianys wants to ride her bicycle 55.5 miles this week. She has already ridden 19 miles. If she rides for 5 more days, which equ
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The equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5

<h3>Writing equation</h3>

From the question, we are to determine the equation that could be used to determine, m, the average number of miles she would have to ride to meet her goal

From the given information,

"<em>Arianys wants to ride her bicycle 55.5 miles</em>"

and

"<em>She has already ridden 19 miles</em>"

Thus,

The number of miles she needs to ride more is

55.5 miles - 19 miles

= 36.5 miles

If m is the average number of miles she would have to ride for 5 more days to complete her goal,

Then, we can write that  

m = 36.5/5

OR

m = (55.5 - 19)/5

Hence, the equation that could be used to determine, m, is 5m = 55.5 - 19. The correct option is C. m = (55.5 - 19)/5

Learn more on Writing equation here: brainly.com/question/28351087

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Answer:

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When we match this triangle with another right triangle to make  the rectangle is another right triangle with sides 6 yards and 3 1/3 yards.

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