What is the relationship between an angle of elevation and an angle of depression in a right triangle?

Answer:

Step-by-step explanation:

let the number=x

2x-5=3

2x=3+5

2x=8

x=8/2=4

Given the 22 m. horizontal distance and the angles of elevation of 26°

and 31° gives the height of the building as approximately 2.49 meters.

Horizontal distance from the building = 22 m

Angle of elevation to the top of the roof = 26°

Angle of elevation to the top of the antenna = 31°

Height of his eyes from the ground = 1.53 m

Required:

The height of the antenna.

Solution:

In a right triangle, we have relative to an angle of the triangle, we have;

Opposite side = Adjacent side

Height of the building + Height of antenna = [tex]1.53 + 22 \times tan \left(31^{\circ} \right)[/tex] ≈ 14.75

Which gives;

Height of the building = [tex]1.53 + 22 \times tan \left(26^{\circ} \right)[/tex] ≈ 12.26

Therefore;

Height of the antenna ≈ 14.75 - 12.26 ≈ 2.49

Learn more about trigonometric tangent ratio here:

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Answer:

520

Step-by-step explanation:

100% - 15% = 85%

85% of the original price is  442 dollars

100% = x

solve for x:

x * 0.85 = 442

x= 520 dollars

regular price is 520 dollars.

Answer:

Not possible.

Step-by-step explanation:

The sum of all 3 angles in a triangle is 180°. With the 80° and 105°, those add up to a total of 185°. This is bigger than can be with a given triangle. Therefore, a triangle with an 80° angle and a 105° angle is not possible.

Answer:

No it isn't possible

Step-by-step explanation:

sum of three angles of any triangle is 180 degrees.

so, as per Given question sum of only two angles exceeds 180 degrees which is " 80+105= 185" so it's not possible.. Hope this answer helps you

Answer:

si

Step-by-step explanation:

si  :v

Answer:

yes

Step-by-step explanation:

y = x + 89

-5 = -94 + 89

-5 = -5

Answer:

$60 per ticket

Step-by-step explanation:

$215 is what it costs after the discount, so add the amount taken off, back on.

215+25

 240

Then, divide by 4 to find the cost of each individual ticket.

240/4

60

Hope it helps!

Step-by-step explanation:

let wrong answers be y

let right answer be x

3x-1y=79

find another equation

Answer:

2

Step-by-step explanation:

1+1 = 2

So the answer is 2

hope this helps

Answer:

check footprints and then check finger print the finger print pour powder on it and Trace

Answer:

15, 21, 35, 105

Step-by-step explanation:

A composite number is a positive integer that has more than two different factors. For example, composite number include 4, 6, 8, 9, 10, 12, 14, 15, 16, 18...etc.

So, if we multiply 3x5x7=105  

All the factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. So we just need to figure out the factors that are composite which are

15, 21, 35, 105

The list all the composite factors of K : 15, 21, 35, 105

"It is an integer that has only two different factors 1 and that integer itself."

"It is a method to find the prime factors of a given number."

"It is an integer that has more than two different factors. "

For given question,

The prime factorization of K is:

K = 3 × 5 × 7

This means the number K is, 3 × 5 × 7 = 105

The factors of 105 are: 1, 3, 5, 7, 15, 21, 35, 105.

We need to list all the composite factors of K.

From above factors of 105 we can observe that,

15 has factors 1, 3, 5, 15;

21 has factors 1, 3, 7, 21;

35 has factors 1, 5, 7, 35;

and 105 has more than two factors factors as mentioned above.

This means, the numbers 15, 21, 35 and 105 are composite numbers.

Therefore, the list all the composite factors of K : 15, 21, 35, 105

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Answer:

[tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

let x=2.16666...

10 x=21.666...(1)

100 x=216.666...(2)

(2)-(1) gives

90x=195

6x=13

x=13/6

x=2 1/6

Answer:

1 hour

Step-by-step explanation:

hope it helps ....

Answer:

3/10 of a cup

Step-by-step explanation:

Find how many cups of strawberries each student got by dividing 6 by 20:

= 6/20

Simplify this by dividing each number by 2:

= 3/10

So, each student got 3/10 of a cup of strawberries

Answer:

2nd option

Step-by-step explanation:

f(x) + g(x)

= 4x - 5 + 3x + 7 ← collect like terms

= 7x + 2

domain is all real numbers

Answer:

11 feet

Step-by-step explanation:

Given,

Area of square ( a^2 ) = 121 ft

To find : Length of each side ( a ) = ?

Formula : -

Area of square = a^2

a^2 = 121

a = √121

a = 11 feet

Answer:

11 ft = side length

Step-by-step explanation:

The area of a square is found by

A = s^2

121 = s^2

Taking the square root of each side

sqrt(121) = sqrt(s^2)

11 = s

Answer:

13.7 units

Step-by-step explanation:

Hi there!

The dotted lines and the hypotenuse of the green triangle create a new right triangle, with one of its acute angles measuring 17 degrees and its hypotenuse measuring 47 units.

Given this information and that we must solve for the side opposite the given angle, we can use the sine ratio:

[tex]sin\theta=\frac{opposite}{hypotenuse}[/tex]

Plug in known information

[tex]sin17=\frac{x}{47}\\47*sin17=x\\13.7=x[/tex]

Therefore, the value of x when rounded to the nearest tenth is 13.7 units.

I hope this helps!

Answer:

see explanation

Step-by-step explanation:

Angles on the circumference subtended on the same arc are equal

Angle at the centre is twice the angle at the circumference subtended on the same arc.

Then

∠ BAC = ∠ BDC = 29°

∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°

Answer:

A) 0.019

B) 0.563

Step-by-step explanation:

a) We will use Poisson distribution formula to solve this;

The formula is given as;

P(X = x) = ((e^-λ) × (λˣ))/x!

Mean is 1. Thus;

λ = 1 aircraft/hour.

Thus, the probability that more than three aircrafts will arrive within an hour is written as; P(X > 3)

Thus;

P(X > 3) = 1 - P(X ≤ 3)

Thus;

1 - P(X ≤ 3) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]

Solving through online calculator, we have;

P(X > 3) = 1 - 0.98101

P(X > 3) = 0.01899

To 3 decimal places, we have; P(X > 3)= 0.019

b) Probability of one 1-hour interval not containing more than 3 arrivals is, let's first find;

P(X ≤ 3) = 1 - P(X > 3)

P(X ≤ 3) = 1 - 0.01899

P(X ≤ 3) = 0.98101

Since there are 30 one-hour intervals, then we have;

Probability that none of the thirty 1-hour intervals will contain more than 3 arrivals;

(P ≤ 3) = (0.98101)³⁰

(P ≤ 3) = 0.5626

Approximating to 3 decimal places, we have;

(P ≤ 3) = 0.563

Answer:

4x² - 24x + 20 = 0

Step-by-step explanation:

a(1)² + b(1) + 20 = 0

a(5)² + b(5) + 20 = 0

a + b = - 20 ⇒ b = - a - 20 ...... (1)

25a + 5b = - 20 .......... (2)

(1) -----> (2)

25a + 5( - a - 20) = - 20

20a - 100 = - 20 ⇒ a = 4

4 + b = - 20 ⇒ b = - 24

4x² - 24x + 20 = 0

Answer:

-3

Step-by-step explanation:

Step 1: Solve (-2+(-1))^2/3 3

           1. -2+(-1) = -3

           2. (-3)^2 = 9

           3. 9/3 = 3

Step 2: Solve (-4)^2-17 -1

           1. 3/-1

Step 3: Simplify 3/-1 = -3. I hope this helped and please don't hesitate to reach out with more questions!

Answer:

[tex]{ \tt{ = \frac{7}{9} \div \frac{1 }{3} }} \\ = { \bf{ \frac{7}{9} \times \frac{3}{1} }} \\ = \frac{7}{3} [/tex]

Answer:

yeah it is

y is directly proportional to x

proportionality constant is 9

Answer:

(0, 9)

Step-by-step explanation:

The y-intercept is the point when x = 0. By looking at the graph, when x = 0, y = 9. Therefore, the y-intercept of the line is (0, 9).

Answer:

71.51

Step-by-step explanation:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=3·3+7·3+7·3+1

2·﹣34+2·(3·7)2+2·(3·7)2﹣74+2·(7·7)2﹣74=71.51219

Answer: I believe but not 100% sure

1) C

2) B

Step-by-step explanation:

The pH value of the apple juice is 3.5, option C) is the correct answer.

The pH value of the ammonia is 8.9, option D) is the correct answer.

The pH of a solution is defined as the logarithm of the reciprocal of the hydrogen ion concentration  [H+] of the given solution.

From the formular;

pH = -log[ H⁺ ]

Given the data in the question.

For the Apple juice;

pH = -log[ H⁺ ]

pH = -log[ 0.0003 ]

pH = 3.5

The pH value of the apple juice is 3.5

Option C) is the correct answer.

For the ammonia;

pH = -log[ H⁺ ]

pH = -log[ 1.3 × 10⁻⁹]

pH = 8.9

The pH value of the ammonia is 8.9

Option D) is the correct answer.

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Answer: a Line going up and down

Step-by-step explanation:

Answer:

See explanation below

Step-by-step explanation:

The line x = 5 would be vertical and lies on x = 5 within the x-axis.

Figura 1 = ⅓

Figura 2 = ½

Figura 3 = 4/7

Figura 4 = 4/9

↦ Count all the shaded regions (for numerator) & all the parts of the figure (for denominator).

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐

Answer:

isoceles

Step-by-step explanation:

The vertices are not equal