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Elis [28]
2 years ago
8

Two consecutive odd integers have a sum of 44. Find the integers.

Mathematics
1 answer:
ivanzaharov [21]2 years ago
7 0

Step-by-step explanation:

Answer

Let2odintegers

(2n+1),(2n+3)

→(2n+1)+(2n+3)=44

⇒4n+4=44

⇒4n=40

⇒n=10

then,integerare

2n+1=21

2n+3=23

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Charlie is watching hot air balloons. balloon a has risen at a 50° angle. balloon b has risen at a 78° angle. if the distance fr
AfilCa [17]

The distance from Balloon A to Balloon B, d ≈ 1,052 feet

What is distance ?

  • Distance is defined to be the magnitude or size of displacement between two positions.
  • Note that the distance between two positions is not the same as the distance traveled between them.
  • Distance traveled is the total length of the path traveled between two positions. Distance traveled is not a vector.

The given parameters are;

The angle at which Balloon A rises, x° = 50° above horizontal

The angle at which Balloon B rises, y° = 78° above horizontal

The (vertical) distance of Balloon A to the ground, h = 1,000 ft.

The required parameter;

The distance from Balloon A to Balloon B, d

We find the distances of the balloons from Charlie and the angle between the balloon strings, θ, then apply cosine rule

Let,

The height of the balloon strings are equal

The distance of Balloon A to the ground, h₁ = The distance of Balloon B to the ground, h₂ = 1,000 ft.

The distance of the Balloon A  from Charlie, l₁, is given as follows;

l₁ × sin(x°) = h₁

∴ l₁ = h₁/(sin(x°))

Which gives;

l₁ = 1,000 ft./(sin(50°)) ≈ 1,305.41 ft.

l₁ ≈ 1,305.41 ft.

For Balloon B, we get;

h₁ = h₂ = 1,000 ft.

∴ l₂ = 1,000 ft./(sin(78°)) ≈ 1,022.34 ft.

l₂ ≈ 1,022.34 ft

The angle between the balloon strings, θ = 180° - (x° + y°)

∴ θ = 180° - (50° + 78°) = 52°

The angle between the balloon strings, θ = 52°

By cosine rule, we have;

d = √(l₁² + l₂² - 2 × l₁ × l₂ × cos(θ))

∴ d = √(1,305.41² + 1,022.34² - 2 × 1,305.41×1,022.34 × cos(52°)) ≈ 1,052 feet

Therefore, the distance from Balloon A to Balloon B, d ≈ 1,052 feet

Learn more about distance

brainly.com/question/15172156

#SPJ4

7 0
2 years ago
How many solutions does the system have?<br> y=-2x -4 <br> y=3x + 3
baherus [9]

Answer:

x=−7/5and y=−6/5

Step-by-step explanation:

Step: Substitute−2x−4foryiny=3x+3:

y=3x+3

−2x−4=3x+3

−2x−4+−3x=3x+3+−3x(Add -3x to both sides)

−5x−4=3

−5x−4+4=3+4(Add 4 to both sides)

−5x=7

−5x

−5

=

7

−5

(Divide both sides by -5)

x=−7/5

7 0
2 years ago
242 X 38 1 9 36 9,1 96 Which digits belong in the blue boxes shown on the multiplication problem?
babymother [125]

Answer:

C. 726

Step-by-step explanation:

9196-1936=7260 and take away the 0 so your answer will be 726

4 0
2 years ago
Read 2 more answers
Simplify: 3(a-2)+4(3-a)-10
Neporo4naja [7]

Answer:

-a - 4

Step-by-step explanation:

3(a-2)+4(3-a)-10

3a - 6 + 12 - 4a - 10

-a - 4

3 0
3 years ago
Algebra applications: find the value of x and y​
Inga [223]

Answer : The value of x and y is 8 and 10 respectively.

Step-by-step explanation :

As we known that if two parallel lines are cut by a transversal line then consecutive interior angles are supplementary.

From the given figure we conclude that:

5x-y+150=180       ...........(1)

5x-y=180-150

5x-y=30      ............(2)

5x+y+130=180       ...........(3)

5x+y=180-130

5x+y=50        ...........(4)

Now we adding equation 2 and 4, we get the value of x.

5x-y+5x+y=30+50

10x=80

x=8

Now we are putting the value of x in 4, we get the value of y.

5x+y=50

5(8)+y=50

y=50-40

y=10

Therefore, the value of x and y is 8 and 10 respectively.

3 0
3 years ago
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