A woman looking out from the window of a height 30m, observed that the angle of depression of the top of a flagpole was 44°. if the foot of the pole is 25m from the foot of the building and on the same horizontal ground, find, correct to the nearest whole number, the angle of depression of the foot of the pole from the woman

Answer:

[tex]13^{\circ}[/tex]

Step-by-step explanation:

Consider the smaller of the two triangles with angle [tex]x[/tex].

Using vertically opposite angles, one of the angles of this triangle is [tex]85^{\circ}[/tex].

Using corresponding angles combined with angles on a straight line, one of the angles is [tex]82^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex], so [tex]x=13[/tex].

Answer:

I believe it would be x=-5

Step-by-step explanation:

..

The area of the circular base of the fountain is 179 square feet.

A circle's area is equal to its radius, r, squared, then multiplied by the mathematical constant pi: A = pi x r2.

A cylinder has two bases that are two congruent circles at the top and bottom. The radius r of a cylinder is only the radius of the circular bases, and the height h of a cylinder is the perpendicular distance between these bases.

Combined area of the walkway and fountain: (3.14)112=379.94 ft2.

Fountain area: (3.14)8*2=200.96 feet

Walkway area: 379.94-200.96=178.98 square feet, which is also rounded to 179 square feet.

The area of the circular base of the fountain is 179 square feet.

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The number of hours that the team trians per week is 17 hours.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the the swim tea spends 1/2h in the gym followed by 1 1/4 in the pool. On Saturday there is no gym work but double the swim team time. The number of hours will be:

( 1 1/4 + 1/2 + 2 1/2) × 4

= 4.25 × 4

= 17 hours.

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Answer: To solve this system of equations, you can use the substitution method.

First, you can solve one of the equations for one of the variables in terms of the other. For example, you can solve the first equation for y:

y = (-4x - 8)/4

Then, you can substitute this expression for y into the second equation to find the value of x:

-2x - 2((-4x - 8)/4) = 4

-2x + 4x + 8 = 4

2x = -4

x = -2

You can then substitute this value of x back into the first equation to find the value of y:

y = (-4(-2) - 8)/4 = (8 - 8)/4 = 0

Thus, the solution to the system of equations is x = -2 and y = 0.

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

4x + 3 = 11

(4x + 3) - 3 = 11 - 3

4x = 8

4x/4 = 8/4

x = 2

As you can see, to isolate x, we must do the opposite operations to both sides.

Three true statements about the angles of the given figure are,

1. angle 1 and the 55 degree angle are adjacent.

5. angle 1 = 180 degree - 55 degree

6. angle 2 = 180 degree - 55 degree - 45 degree.

Complementary angles are two angles whose measures add up to 90 degrees. For example, an angle of 45 degrees and an angle of 45 degrees are complementary. When two angles are complementary, they form a right angle. The symbol for complementary angles is ∠A + ∠B = 90°.

Acute angles are angles whose measure is less than 90 degrees. They are sharp angles that are less than a right angle. On the other hand, obtuse angles are angles whose measure is greater than 90 degrees. They are angles that are greater than a right angle and less than 180 degrees. In other words, obtuse angles are angles that are wider than a right angle but less than a straight angle.

Analysing all the statements given in the question,the corrrect options are

Option 1, since angle 1 and 55 degree share the same vertex.

Option 5, since the sum of angle 1 and 55 degree is 180 degrees being supplementary angles.

Option 6, since the sum of all the interior angles of a triangle is 180 degrees.

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Answer:

no sign (not positive or negative)

Step-by-step explanation:

The value of the expression

4.3 ⋅ (-3.2) ⋅ 0

is 0, as the value of any number multiplied by zero is 0.

The number zero is neither positive or negative; hence there is no sign.

Answer:

a：20 km

b：384

Step-by-step explanation:

a：

[tex] \frac{2.5}{ 8} = \frac{1}{x} [/tex]

[tex]x = 20[/tex]

b：

[tex] \frac{2.5}{8} = \frac{120}{y} [/tex]

[tex]y = 384[/tex]

Answer:

The cost for 1 pizza is $8.99

Step-by-step explanation:

We know

Natalia paid a total of 38.95 for 3 pizzas and a salad

A salad = $11.98

We first find the total cost of 3 pizzas by

38.95 - 11.98 = $26.97

$26.97 is the cost for 3 pizzas; to find the cost of 1 pizza, we take

26.97 divided by 3 = $8.99

So, the cost for 1 pizza is $8.99

Answer:

The cost of 1 pizza is $8.99.

Step-by-step explanation:

Let

[tex]t[/tex] = total price

[tex]p[/tex] = pizzas

[tex]s[/tex] = salads

Natalia bought 3 pizzas and 1 salad

[tex]38.95=3p+1s[/tex]

We are given the price of the salad.

[tex]38.95=3p+11.98[/tex]

Now we can find the cost of 1 pizza.

Lets solve for [tex]p[/tex].

Subtract 11.98 from both sides of the equation.

[tex]26.97=3p[/tex]

Divide both sides of the equation by 3.

[tex]p=\frac{26.97}{3}\\p=8.99[/tex]

A random selection of one of the families is made, and a computer is discovered there. P(computer AND TV) = 5/6.

We surveyed 400 households. 60% of people had computers, while 90% of them had TVs.

These were something that every family owned at least one of.

A random selection of one of the families is made, and a computer is discovered there.

Check to see if there is a TV there as well.

union: # with computer, # with TV, - # with both, # with both

400 = 360 + 240 - # with both # with both = 200 / 400 = 0.9 * 400 + 0.6 * 400

P(computer AND TV) = 200/400 = 1/2 ——-

P(TV | computer) + P(TV and computer) / P(computer) = 0.5/0.6 = 5/6

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Answer:

n = 5/8

Step-by-step explanation:

-2n = -1 1/4

-1 1/4 = -5/4

So, our equation is

-2n = -5/4

Divided both sides by -2

n = 5/8

So, the answer is

n = 5/8

The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)

Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.

The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.

That is, c² = a² + b²

Where, a = 16

b = 18

c² = 16²+18²

c² = 256 + 324

c² = 580

C =√580

C = 24.1

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The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached

The values of the constants in the sinusoidal function, h = a + b·(c·t) are;

a = 30

b = -20

c = π/1.5

A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.

The diameter of the Ferris wheel = 40 m

The location of the axle above the ground = 30 m

The time it takes to make a complete a rotation = 3 minutes

The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;

h = a + b·cos(c·t)

The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.

Therefore;

At t = 0, h = 30 - 40/2 = 10

h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b

a + b = 10

Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;

a = 30

a + b = 10, therefore;

b = 10 - a

b = 10 - 30 = -20

b = -20

At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50

50 = a + b·cos(1.5·c)

50 = 30 - 20 × cos(1.5·c)

20 × cos(1.5·c) = 30 - 50 = -20

cos(1.5·c) = -1

cos(π) = -1

Therefore; 1.5·c = π

c = π/1.5

The equation is therefore;

h = 30 - 20·cos((π/1.5)·t)

a = 30, b = -20, c = π/1.5

Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel

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The solution for x in the equation given as x² = 1/4 is (b) x = ±1/2

From the question, we have the following parameters that can be used in our computation:

An equation

The equation as poorly stated in the question is represented as

x2=14

When written properly

We have the following representation

x² = 1/4

Solving further, we need to take the square root of both sides of the equation

So, we have the following representation

√x² = ±√1/4

Evaluate the exponents on the left-hand side

So, we have the following representation

x = ±√1/4

Evaluate the exponents on the right-hand side

So, we have the following representation

x = ±1/2

Hence, the solution is (b) x = ±1/2

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Answer:

720,000,000,000,000 or 720 trillion picoseconds.

Step-by-step explanation:

1 picosecond = 1 trillionth of a second. Therefore 1 second has 1 trillion picoseconds:

0.000 000 000 001 seconds = 1 picosecond

0.000 000 000 001 * 1,000,000,000,000 seconds = 1 * 1,000,000,000,000 picosecond

1 second = 1,000,000,000,000 picoseconds

Now, one minute is the same as 60 seconds so we multiply the equation by 60:

1 minute = 60 seconds = 60,000,000,000,000 picoseconds

Finally, we need 12 minutes to be converted to picoseconds.

12 minutes = 720 seconds = 720,000,000,000,000 picoseconds.

So therefore, 12 minutes is equal to 720,000,000,000,000 picoseconds or 720 trillion picoseconds.

Hope this helps!!!

Across the y-axis, translated 2 units to the right and four units to the left, the new function is now h(x) = -(x + 2)3 - 4

Step (i): The type of transformation change of the function

a) The translated left "c" units are x - c;

b) The translated right "c" units are x + c

Step (ii) The given function is translated "2" units right side, then the new function is

followed by the translated "4" units left sides and reflected across the y-axis.

Now the new function is h(x).

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Answer:

0.25 in/h

Step-by-step explanation:

1. change 2 3/4 t0 2.75

2. 2.75/11= 0.25

The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

To determine this:

Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.

Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.

We know the total number of farm animal legs is 40 legs.

So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.

Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

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The place with the highest temperature is Oslo.

The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .

The new temperature in Moscow is 11 degrees Celsius .

When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.

The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:

= - 4 . 3 - ( - 9 . 5 )

= - 4.3 + 9 .5

= 5. 2 degrees Celsius

The new temperature in Moscow is:

= - 7.9 - 3.1

= 11 degrees Celsius

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x=5 is the value of the x that is the solution of the given inequality.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

>,< and not equal to are types of inequality.

x=5 is the value of the x that is the solution of the given inequality.

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Answer:

X = 1 and below

Step-by-step explanation:

since X is less than 2.

the value of X will be 1 and below.

Yes , you can join Wikipedia as a creator who can help maintain the platform and update the content from time to time. There are also different types of job roles which you can find for Wikipedia .

You can also simply just create an account and start contributing as a member of Wikipedia.

For this the first step would be to select an appropriate username, which will be unique , as this will be used to identify and differentiate you from others. Then you can start contributing to Wikipedia and other Wikimedia projects.

Communicate with other editors via your own talk page. You can also opt in to exchanging emails with other users and thus increase your community.

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The number of real solution varies according to the degree of the equation and the nature of the equation, The answer is dependent on degree and nature.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

example:

A linear equation (degree 1) has one real solution.

A quadratic equation (degree 2) can have either two real solutions, one real solution or no real solutions, as it depends on the discriminant of the equation, as I explained in my previous answer.

A cubic equation (degree 3) can have one to three real solutions, depending on the coefficients of the equation.

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A unit rate I found at the grocery store was 10 bananas/ $5 this describe the price for 10 bananas but can also be used to identify the price for 1 banana.

In mathematics, a unit rate can be defined as a mathematical expression that includes two units to show the rate of a specific activity. For example, the expression 50 kilometers/2 hours shows a car covers a distance of 50 kilometers in two hours, which can be simplied as 25 kilometers per hour.

A unit rate I could observe last weekend while buying fruits and vegetables was 10 bananas/ $5. This unit rate is mainly used to inform buyers about the price of 10 bananas. However, this can also be simplified as $0.5 per banana and this would inform the buyers about the price per unit.

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Answer:

6n-5

Step-by-step explanation:

let 'n' equal 'a number'

the equation above means you are multiplying 6 and that number, then reducing it by 5

The ratio of spice A to spice B is : 49/87

Here, 2 1/3 grams of spice A was mixed with 4 1/7 grams of spice B.

First we convert the improper fraction into a proper fraction.

For improper fraction2 1/3,

2 1/3

= (2 × 3)/3 + 1/3

= 6/3 + 1/3

= (6 + 1)/3

= 7/3 which is a proper fraction.

and for 4 1/7

= (4 × 7)/7 + 1/7

= 28/7 + 1/7

= (28 + 1)/7

= 29/7

The ratio of spice A to spice B would be,

(2 1/3) / (4 1/7 )

= (7/3) / (29/7)

= (7/3) × (7/29)

= (7 × 7)/(3 × 29)

= 49/87

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The solution to w in the equation 9(w - 4) - 7w = 5(3w - 2) is w = -2.

Now, According to the question:

The given Equation:

9(w-4)-7w=5(3w-2)

To solve for w we first need to simplify our equation, removing any brackets and adding together similar terms. This gives us:

9(w-4)-7w=5(3w-2)

9w - 36 -7w = 15w - 10

2w - 36 = 15w - 10

Next, we subtract 2w from both sides to have all the variables on one side of our equation, then we add 10 to both sides to move the numerical values to one side.

2w - 36 = 15w - 10

2w -2w - 36 = 15w - 2w - 10

-36 = 13w - 10

-36 + 10 = 13w - 10 + 10

-26 = 13w

Finally, we divide both sides by 13 to find the value of w.

w = -2

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The complete question is this :

What is the solution to the equation of 9(w - 4) - 7w = 5(3w - 2).

Answer:

  -4/17

Step-by-step explanation:

You want the slope of the line described by the equation 20x +85y = 120.

Putting the equation in slope-intercept form by solving for y gives ...

  20x +85y = 120

  85y = -20x +120

  y = -20/85x +120/85

  y = -4/17x +24/17

The slope is the coefficient of x: -4/17.

The rate of change is -4/17.