An aircraft hangar is semi-cylindrical with
diameter 40 m and length 50 m. A helicopter
places a cable across the top of the hangar, and
one end is pinned to the corner at A. The cable
is then pulled tight and pinned at the opposite
corner B. Determine the length of the cable.

Answer:

x = 102°

Reason

They're both Alternate Exterior angles

ALTERNATE EXTERIOR ANGLES ARE EQUAL.

Answer:

About 50.14 Centimeters

Step-by-step explanation:

The formula for the volume of a cylinder is:

[tex]\pi(r^2)h[/tex]

Now, let's plug in the values. (We'll use 3.14 for pi.)

[tex]3.14(r^2)76 = 600,000[/tex]

All we do now, is solve for r. Divide 76 on both sides...

[tex]3.14(r^2) = 7894.74[/tex]

Divide 3.14 on both sides...

[tex]r^2 = 2514.25[/tex]

Lastly, find the square root on both sides.

[tex]\sqrt{r^2} = \sqrt{2514.25}[/tex]

[tex]r = 50.14[/tex]

Therefore, the r, or the radius, is around 50.14 centimeters. Hope this helps!

Answer:

8 seats

Step-by-step explanation:

n = 8 ---booths

r = 1 --- hostess

Order is required

Important Order? We solve using permutation.

nPr = n!/(n - r)!

So we have:

8p1 = 8!/(8 - 1)!

IF we do the math correctly, we get this:

8p1 = 8/7!

Finally let's expand to come up with the solution.

8p1 = 8 x 7/7

8p1 = 8

So the answer is 8!

I hope this helps! Have a good day (PLS GIVE BRAINLIEST)

There are 8 types of different arrangements possible for the hostess to seat customers at the waiter’s booths if order is important.

What is Permutation and Combination ?

The various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

Total number of booths = 8

To determine we will use the generalized expression

How many ways can you arrange 'r' from a set of 'n' if the order matters

P(n,r) = n! / (n-r)!

P(8,1) = 8!/ (8-1)!

= 8!/7!

= 8

So there are 8 types of different arrangements possible for the hostess to seat customers at the waiter’s booths if order is important.

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Answer:

c. 9ft

Step-by-step explanation:

[tex]x^{2} + 12^{2} = 15^{2}[/tex]

[tex]x^{2}[/tex] + 144 = 225

[tex]x^{2}[/tex] = 81

x = 9

Multiplying the  second equation by -4 eliminates the x terms when adding the first equation.The second equation is 4x + 5y = -8

In order to eliminate the x terms when adding the first equation, you need to multiply the second equation by -4. The formula and calculation steps are as follows:

Formula:

Equation 1 + (-4 x Equation 2)

4x + 5y = -8

-4(4x + 5y) = -4(-8)

-16x -20y = 32

Adding the two equations together gives:

0x + 25y = 24

Therefore, multiplying the second equation by -4 eliminates the x terms when adding the first equation.

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Answer:

Step-by-step explanation:

Use the law of cosines to find the side AB:

Use the Heron's area formula next:

Now

Next

Substitute this into the first equation:

Answer:

AB = 7 cm

Step-by-step explanation:

Sine Rule for Area

[tex]\sf Area =\dfrac{1}{2}ab \sin C[/tex]

where:

Given:

Substitute the given values into the formula and solve for x:

[tex]\begin{aligned} \sf Area & = \dfrac{1}{2}ab \sin C \\\\\implies \sqrt{300} & = \dfrac{1}{2}(x+3)x \sin 60^{\circ}\\\\\sqrt{300} & = \dfrac{\sqrt{3}}{4}(x+3)x\\\\\dfrac{4\sqrt{300}}{\sqrt{3}} & = x^2+3x\\\\40 & = x^2+3x\\\\x^2+3x-40 & = 0\\\\ (x-5)(x+8)& = 0\\\\ \implies x & = 5, -8\end{aligned}[/tex]

As length is positive, x = 5 only.

Substitute the found value of x into the expressions for the side lengths:

Cosine rule

[tex]c^2=a^2+b^2-2ab \cos C[/tex]

(where a, b and c are the sides and C is the angle opposite side c)

Substitute the found values into the formula and solve for AB:

[tex]\begin{aligned}c^2 & =a^2+b^2-2ab \cos C\\\implies AB^2 & =8^2+5^2-2(8)(5) \cos 60^{\circ}\\AB^2 & =89-40\\AB^2 & =49\\AB & =\sqrt{49}\\AB & = \pm 7\end{aligned}[/tex]

As length is positive, AB = 7 cm.

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Answer:

Degree measure of each angle is 90⁰, 47⁰ and 43⁰

Step-by-step explanation:

since the triangle is right angled, we assume that Q and S are the other angles of this triangle R

Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰

5x - 13 + 4x - 5 = 90⁰

9x = 108

x = 12

We now replace x in Q and S to get the angles

Q = 5(12) -13

= 47⁰

S = 4(12) - 5

= 43⁰

Part A: Based on the text, an inference that can be made about laughter is that it can be a positive response to a situation or a way of expressing joy.

Inference is the process of drawing conclusions from given facts or evidence. It involves making a logical guess or assumption based on the available information. Inference requires the use of critical thinking to draw conclusions that are most likely to be accurate.

Part B:
Yes - Laughter is described as a response to a situation and can be a way of expressing joy.
No - There is no evidence that laughter is a negative response to a situation.

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Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 - ∅), and cos = AB/AC = sin(90 - ∅).

The right triangle's angle serves as the domain input value for the six basic trigonometric operations, which produce a range of numbers as their results.Understanding the trigonometric functions of the four quadrants' graphs, domains, differentiation, and integration will be achievable.

Here,

Sinx = perp./hypo.

Cosx equals base/hypo.

So,

Sin = B/C

A= cos(90 -∅ ) = BC/AC

So,

Cos(90 -∅ ) = Sin(BC/AC)

And,

cos = AC/AB

AB/AC = sin(90 -∅ )

So,

cos AB/AC = sin (90 -∅ )

Therefore , the solution ot the given problem of trigonometry comes out to be Option (A) and (F) are the correct answers since sin = BC/AC = cos(90 -∅ ), and cos = AB/AC = sin(90 - ∅).

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Answer:

x and y values are doubled; scale factor is 2

Step-by-step explanation:

(4,5) becomes (8,10)

(2,5) becomes (4,10)

(1,4) becomes (2,8)

Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.

A parallelogram has a unique variation known as a rhombus. A rhombus has opposing sides that are parallel and opposing angles that are equal. A rhombus also has equal-length sides and diagonals that are at right angles to one another. The term "rhombus" can also refer to a diamond or rhombus. A rhombus has equal opposite angles. At a 90° angle, the diagonals split in half. 180 degrees is the sum of adjacent angles.

given

There is a line that passes through the parallel line; the alternate interior angles are 3 and 39.

The alternative interior angles are similar, hence Angle 3 = 39.

Since the upper left triangle is a triangle, angles 3, 4, and the center angle all add up to 180 degrees. The angle in the middle is 90 degrees. hence, we may locate angle 4.

angle 4=51.

Since Angle 1 and Angle 4 are alternate internal angles, Angle 1 also equals 51.Angles 1 and 2 of the rhombus are bisector by 51 and 2, respectively.

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Answer:

12 + 3x + 2y

Step-by-step explanation:

14 + 8x + 2y -5x - 2

14 + -2 + 8x -5x + 2y

12 + 3x + 2y

Answer:

3x + 2y + 12

Step-by-step explanation:

In the photo.

Answer:

[tex]y = 2x + 3[/tex]

Step-by-step explanation:

We can find the slope.

[tex] \frac{ 5 + 1}{1 + 2 } = 2[/tex]

so m is 2

[tex]y = 2x + c[/tex]

Plug one the equations in to find c.

[tex] - 1 = 2( - 2) + c[/tex]

[tex] - 1 = - 4 + c[/tex]

[tex]3 = c[/tex]

so the equation is

[tex]y = 2x + 3[/tex]

Answer:

there's one solution bc the lines have one point in common

Answer:

[tex]\huge\boxed{\text{4.2 feet}}[/tex]

Step-by-step explanation:

In order to solve this problem, we can use the basic trigonometric functions.

Let's first start to break down the triangle scenario we're given.

Now we know the three angles of the triangle and one side.

We can find the other two sides (or just the base side, in our case), using trigonometric functions such as sin, cos, and tan. We can substitute in their formulas and find lengths based on angle measures.

We know using SOH CAH TOA the relationships between opposites, adjacents, and hypotenuses with these functions. SOH CAH TOA states that:

Using the triangle, we want to find a relationship that has the base we need as an opposite/adjacent that can use the hypotenuse (since it's the only side length we know.

Well, we can take the sin of the 25 degree angle - it's opposite is the base leg and the hypotenuse is 10.

We can then represent this using an equation:

Therefore, the length of the base leg is 4.2 feet

Hope this helped!

Answer:

4.2 feet

Step-by-step explanation:

.................

Answer:

x = 20

Length = 20ft

Width = 12ft

Step-by-step explanation:

A = 240

x^2 - 8x = 240

x^2 - 8x - 240 = 0

x^2 - 20x + 12x - 240 = 0

x(x-20) + 12(x-20) = 0

(x+12)(x-20) = 0

x = 20

x = -12 (which we discard since x is a length)

So the dimensions are 20ft and 20-8 = 12ft

Answer: 19

Step-by-step explanation:

56-13=43

43-24=19

Answer: 19

Step-by-step explanation: 13 + 24 = 37

so (56 - 37 = 19)

Answer:

the value of x is 40 degree and the value of (2x+11) is 91 degree.

Step-by-step explanation:

hope it helps you.

Answer:

7

Step-by-step explanation:

hope this helps:))))))

Isosceles Triangle has 50°, 65°, 65°

An isosceles triangle is a triangle that has two sides of equal length. The two equal sides are called the legs and the third side is called the base of the triangle.

Properties of Isosceles Triangle:

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Answer:

1.   f(x)=1-1/2

4.   y=10x

5.   yes

Step-by-step explanation:

1)
f(x) = 4(2 + 3x) + 3 is a linear function.

2)

The slope of the function is 6.

3)

The linear function is (1/2)x - 4.

4)

y = x² + 2 is not a linear function.

5)

No, it is not a linear function.

6)

Graph D does not represent a linear function.

7)

Graph B does not represent a linear function.

8)

Table D is a linear function.

9)

Table B is not a linear function.

10)

3x + 2y = 6 is a linear function.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

1)

f(x) = 4(2 + 3x) + 3

f(x) = (1/2)x² - 5

f(x)= 5 - x²

f(x) = 1 - 1/x

The graph of each function is given below.

The red line in the graph represents f(x) = 4(2 + 3x) + 3.

This is a straight line which means it is a linear function.

2)

f(x) = 2(3x - 7)

f(x) = 6x - 14

It is in the form of y = mx + c where m is the slope.

So,

m = 6

3)

f(x) = (1/2)x - 4

f(x) = x³ - 2

The graph is given below.

The red line represents f(x) = (1/2)x - 4.

This is a linear function.

4)

y = 3x + 12

y = x² + 2

y = 10x

y = 9

The graph is shown below.

The green curve is y = x² + 2.

This is not a linear function.

5)

y = 2x² - 6

This is not a linear function because we have x².

The graph is given below.

6)

Graph D represents a non-linear function.

7)

Graph B represents a non-linear function.

8)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table D has the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

= (4 - 7) / (-1 + 2)

= -3/1

= -3

Table D is a linear function.

9)

If the rate of change between two (x, y) from the graph is the same then it is a linear function.

Table B does not have the same rate of change.

Rate of change = (y(2) - y(1)) / (x(2) - x(1))

Table B is not a linear function.

10)

The green line on the graph represents a straight line.

The green line is a linear function.

The green line is 3x + 2y = 6.

Thus,

The answers are given above.

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Answer:

value of 10^-3= 0.001

hope it helps.

Answer:

Step-by-step explanation:

10^(-3) is equivalent to

   1

---------  which in turn is equivalent to 1/1000, or 0.001.

 10^3

On solving the provided question, we can say that - the answer of the following sequence 1.9, 3x , 8x will be 13.78x

A sequence is a collection of numerals (referred to as "terms"), for example, 2, 5, 8. A specific pattern that some sequences follow may be leveraged to make them infinitely long. To continue the series, add 3 and use the example of 2,5,8. Formulas that show where to look for words inside a sequence can be found there. Informally, a sequence in mathematics is a collection of items that are in some order (or events). It has components, much like a set (also called elements or terms). The length of the sequence refers to the total, potentially unlimited number of ordered items. arranging two or more objects in a logical sequence. Chronological.

sequence 1.9, 3x , 8x

answer is = 13.78x

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On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.

Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.

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In the above scenario, note that the total distance of the flight is given as: 48.4 miles (approximately). This is solved using the law of Sines to find x.

The connection between the sides and angles of non-right (oblique) triangles is defined by the Law of Sines. Simply put, it asserts that the ratio of the length of a triangle's side to the sine of the angle opposite that side is the same for all triangle sides and angles.

Thus, with regard to the problem modeled in the attached triangle, because two angles are given, the missing angle is 180° − (157° + 8°) or 15°. Use the Law of Sines to find x.

Using the law of ins we can state that:

Sin 8°/x = sin 15°/90

90 (Sin 8°) /x = Sin 15°

90 Sin 8° = x Sin 15°

90 Sin 8° / Sin 15° = x

90 (0.13917310096)/ 0.2588190451 = x

Thus,

x = 48.3951213156

x [tex]\approx[/tex] 48.4

Thus, the distance of the flight is approximately 48.4 miles.

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Assuming the bags are filled at a constant rate, the average time it takes to fill one bag of leaves is 5 minutes.

To calculate the average time it takes to fill one bag of leaves, we need to know the total amount of time spent filling bags and divide that by the number of bags filled.

First, we know that the staff works an average of six hours per day. Since mowing and raking typically take four hours, we can assume that the remaining two hours are spent filling bags.

To find out how long it takes to fill one bag, we divide the total time spent filling bags by the number of bags filled. In this case, it would be:

(2 hours) / (24 bags) = 0.083 hours (or 5 minutes)

So the average time it takes to fill one bag of leaves is 5 minutes.

It's important to note that this is an average time and may not reflect the exact time it takes for each bag to be filled. Factors such as the size of the bag, the type of leaves being filled, and the skill level of the staff could all affect the time it takes to fill a bag.

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Answer:

9/4 *(x-2)

Step-by-step explanation:

Replace xa and y in the given function then solve for y

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let’s find the area of the circle.

A = 3.14(7)^2 = 153.86

Now the area of the square:

14•14=196

Now we find the area of the shaded region:

196 - 153.86 = 42.14

the shaded region is 42.14 cm

Answer:

answer what

Step-by-step explanation: