Brandon sights a helicopter above a building that is 200 feet away at an angle of elevation of 30 degrees. To the nearest foot, How high above the ground the is the helicopter

The linear equation is defined as the equation, which can be represented in the form of y=mx+b.

The cost of one pizza is $ 8.99.

Given that,

Now, using the linear equation formula:

Total cost = Cost of three pizzas + Cost of Salad

Substituting the values, the equation becomes:

$ 38.95 = 3x + $ 11.98

$ 38.95 - $ 11.98 = 3x

$ 26.97 = 3x

x = [tex]\dfrac{26.97}{3}[/tex]

x = $8.99

Therefore, the value of each pizza is $8.99.

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Answer:

1. x² + 2x + 2

2. x² + 4

3. x² - 4x + 8

Step-by-step explanation:

(1) ( x+1+i ) ( x+1-i )

= ( x+1 )²- i²  [ Since ( a+b ) ( a-b ) = a² - b² ]

= x² + 1 + 2x - ( √-1 )²

= x² + 1 + 2x + 1

= x² + 2x + 2

(2) ( x+2i ) ( x - 2i )

= x² - (2i)² [ ( a+b ) ( a-b ) = a² b²

= x² - 4i²

= x² - 4 (-1) [Since i² = -1 ]

= x² + 4

(3) ( x - 2i - 2 ) (x + 2i - 2 )

= ( x-2 )² - ( 2i )² [ ( a+b ) ( a-b ) = a² - b² ]

= x² + 4 - 4x - 4 ( i )²

= x² + 4 - 4x - 4 ( -1 )²

= x² - 4x + 4 + 4

= x² - 4x + 8

Answer:

P(A*B) = 0.18

Step-by-step explanation:

Given : We are given that a and b are independent events .

            P(A) = 0.4

            P(B) = 0.45

Solution :

Since , A and B are independent events so by

[tex]P(A*B) = P(A\cap B)=P(A)\ast P(B)[/tex]

⇒[tex]P(A*B) = 0.4\times 0.45[/tex]

[tex]P(A*B) = 0.18[/tex]

Thus,  [tex]P(A*B) = 0.18[/tex]

In addition to linear, quadratic, rational, and radical functions, there are exponential functions. Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1. Just as in any exponential expression, b is called the base and x is called the exponent.

An example of an exponential function is the growth of bacteria. Some bacteria double every hour. If you start with 1 bacterium and it doubles every hour, you will have 2x bacteria after x hours. This can be written as f(x) = 2x.

Before you start,   f(0) = 20 = 1

After 1 hour           f(1) = 21 = 2

In 2 hours              f(2) = 22 = 4

In 3 hours              f(3) = 23 = 8

and so on.

With the definition f(x) = bx and the restrictions that b > 0 and that b ≠ 1, the domain of an exponential function is the set of all real numbers. The range is the set of all positive real numbers. The following graph shows f(x) = 2x.

Answer:

The amount before the tip  is $50.

Step-by-step explanation:

Given : Matt paid $55 at a restaurant. That amount included a 10% tip.

To find : What was the check amount before the tip?

Solution : We have given

Matt paid  = $55 .

amount included a 10% tip.

Let the amount before the tip = x.

Tip amount = 10% of x is

[tex]\frac{10 x}{100}[/tex] = 0.1 x .

Tip amount = 0. 1 x

Total amount = x + 0.1x = 55 .

1.1 x = 55.

On dividing both sides by 1.1

x = 50.

So, the amount before the tip  is $50.

Therefore, The amount before the tip  is $50.

If the resort makes snow while it is snowing naturally then for 9 hours it will take until the run can open.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The pace at which a resort creates snow is t/12,

the rate at which snow falls naturally is t/36.

(1/12) + (1/36) = (1/t)

Take LCM,

(3/36) + (1/36) = (1/t)

1/t = 4/36

4t = 36

t = 9 hours.

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Erika has three pieces of ribbon, each of 25 yards' length.

Then in total she has 3·25=75 yards of ribbon.

Since 1 yd = 36 in, then 75 yd = 75·36=2700 in.

Now she needs to cut pieces that are 22 inches long, thus

[tex]2700:22=122\dfrac{16}{22}[/tex] pieces.

Answer: she can cut from the three pieces of ribbon 122 pieces that are 22 inches long.

Answer:

(r-7)(r+7)

hope this helps! :)

Answer:

1.  the width of the carpet in the living room

Ans. The monomial, x, a factor of the expression x2 + 9x

2  the length of the carpet in the living room

Ans . the binomial, (x + 9), a factor of the expression x2 + 9x

3  the area of the carpet in the bedroom

Ans. the second-degree term of the expression x2 + 9x

4.  the increase in the area of carpet needed for the living room

Ans. the first-degree term of the expression x2 + 9x

Step-by-step explanation:

Jennifer has carpet in her square bedroom.

Formula of area of square = [tex]a^2[/tex]

Where a is the side length

Side length of her bedroom is x

Area of the bedroom is [tex]x^2[/tex]

So, area of carpet for bedroom is [tex]x^2[/tex]

She decides to also purchase carpet for her living room which is rectangular in shape and 9 feet longer than her bedroom. (no change in width)

So, length of living room = 9+x

Width = x

Area of living room = [tex]x*(9+x)[/tex]

                                 [tex]=x^{2} +9x[/tex]

So, increase in area of carpet for living room in comparison to the area of carpet for bedroom is 9x

1.  the width of the carpet in the living room

Ans. The monomial, x, a factor of the expression x2 + 9x

2  the length of the carpet in the living room

Ans . the binomial, (x + 9), a factor of the expression x2 + 9x

3  the area of the carpet in the bedroom

Ans. the second-degree term of the expression x2 + 9x

4.  the increase in the area of carpet needed for the living room

Ans. the first-degree term of the expression x2 + 9x

The expression represents the number of cards remaining in the deck will be 52 - 3p. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A deck of cards has 52 cards. If p is the number of players and each player receives 3 cards. Then the expression is given as,

⇒ 52 - 3p

The expression represents the number of cards remaining in the deck will be 52 - 3p. Then the correct option is C.

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The total area of the figure, which includes a rectangle and a semicircle, is 29.00ft². This is achieved by calculating the individual areas of the rectangle and semicircle, and then adding them together.

The figure in question is composed of a rectangle and a semicircle. The area of a rectangle is found by multiplying its length by its width, so the area of the rectangle part is 7.2ft * 3.4ft = 24.48ft². The area of a semicircle is found using the formula ½πr², where r is the radius of the circle. In this case, the diameter of the semicircle is the same as the width of the rectangle (3.4ft), so the radius will be half of that (1.7ft). Therefore, the area of the semicircle is ½π(1.7ft)² = 4.52ft² (rounded to the nearest hundredth). So, the total area of the figure is the sum of the rectangle and the semicircle area, which equals to 24.48ft² + 4.52ft² = 29.00ft².

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The area of the figure which is composed of a semi-circle and a rectangle is approximately 23.24 ft².

The figure in the image is composed of a semi-circle and a rectangle.

The area of a semicircle is expressed as;

A = 1/2 × πr²

The area of a rectangle is expressed as;

Area = length × width

From the diagram;

Diameter = 3.4 ft

Radius r = 1.7 ft

Width of the rectangle = 3.4ft

Length = 7.2ft - 1.7ft = 5.5ft

Now, to determine the area of the figure, we sum the area of the semi-circle and the area of the rectangle.

Area =  ( 1/2 × πr² ) + ( length × width )

Plug in the values:

Area =  ( 1/2 × 3.14 × 1.7² ) + ( 5.5 × 3.4 )

Area =  ( 1/2 × 3.14 × 2.89 ) + ( 5.5 × 3.4 )

Area =  4.5373 + 18.7

Area = 23.24 ft²

Therefore,  the total area has a measure of 23.24 ft².

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Answer:

Step-by-step explanation:

Alright, lets get started.

Once the triangle has all angles less than 90 degree, is called Acute triangle.

Once the triangle has one angle more than 90 degree, is called Obtuse triangle.

Once the triangle has one angle equal to 90 degree, is called Right triangle.

So, the given triangle has its angle 55, 55, 70.

Each angle is acute angle, so the triangle is Acute triangle.  :   Answer

Hope it will help :)

Required math argument to justify the conjecture that trip,

11 x 5 + 4 x 10 = 95

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Trip has 15 coins worth 95 cents. four of the coin are each worth twice as much as the rest.

So, we get,

Required math argument to justify the conjecture that trip,

11 x 5 + 4 x 10 = 95

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Perimeter of a polygon is equal to sum of all sides of the polygon

Sides of the polygons are 11 ft, 7 ft, 18 ft, 22 ft, 14 ft and 23.5 ft

Sum of all sides of the polygon is given by = 11 ft + 7 ft + 18 ft + 22 ft + 14 ft + 23.5 ft

= 95.5 ft

Perimeter of a polygon = 95.5 ft

Hope this helps..!!

Thank you :)

The membership will last for about 1 year.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Let's start by subtracting the initiation fee from the total amount Cleo paid:

$174.99 - $24.99 = $150

This represents the total amount Cleo will pay for the monthly membership fees.

To find out the number of months of membership this represents, we divide by the monthly fee:

$150 ÷ $12.50 = 12

Therefore, Cleo's membership will last for 12 months.

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The algebraic expression that is equivalent to the given rational expression is (x-11), but when we substitute x=11 into the expression, we receive 0. However, this leads to an indeterminate form in the original rational expression.

The rational expression given in the question is x^2-121/x+11. If we factorize x^2-121, we'll get (x-11)(x+11), because x^2-121 is a difference of squares. Now, the expression becomes: (x-11)(x+11)/(x+11). We see that (x+11) on numerator and denominator will cancel out each other. This leaves us with (x-11).

Now, let's substitute x=11 in (x-11). We obtain 11-11 which equals 0. So the correct answer is (x-11), but we get 0 when we substitute x=11 into the expression. This actually results in an indeterminate form because the original rational expression becomes a 0/0 form, which points to a situation of undefined or indeterminate form.

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Answer:

The number in decimal expression is:

3.1

Step-by-step explanation:

We have to write the given number in a decimal expression.

The information about the number is given as:

three and ten hundredths.

Hence, in decimals the number is written as:

3.1

( since , three is to be written before the decimal point

as 3 is 3.0

and the number 10 is to be written after the decimal .

since, 10/100=0.1)

Hence, the number in decimal expression is:

3.1

The decimal equivalent to three and ten hundredths is 3.1

1 hundredth = 1/100 = 0.01

10 hundredth = 10/100 = 0.1

Therefore,

three and ten hundredths

= 3 + 0.1

= 3.1

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The distance between the point P( 8 , 0 , -6 ) to the plane x + y + z = 6 is

d = ( 4 / √3 )

What is the distance between a point and a plane?

The distance between a point and a plane is the smallest perpendicular distance between the point and the plane in question. In other words, the length of the perpendicular parallel to the normal vector dropped from the given location to the provided plane is the shortest distance between two points.

Let the point be P( x₀ , y₀ , z₀ )

Let the plane be Ax + By + Cz + D = 0

The distance between point P and plane is

d = | Ax₀ + By₀ + Cz₀ + D | / √ ( A² + B² + C² )

Given data ,

Let the point be P( x₀ , y₀ , z₀ ) = P ( 8 , 0 , -6 )

Let the equation of plane be x + y + z = 6

A = 1

B = 1

C = 1

D = -6

Now , the distance between the point and the plane is given by ,

d = | Ax₀ + By₀ + Cz₀ + D | / √ ( A² + B² + C² )

Substituting the values in the equation , we get

d = | 8 + 0 + ( -6 ) + ( -6 ) | / √ ( 1 + 1 + 1 )

d = | 8 - 6 - 6 | / √3

d = | -4 | / √3

d = 4 / √3

Therefore , the value of d = 4 / √3

Hence , The distance between the point P( 8 , 0 , -6 ) to the plane
x + y + z = 6 is d = ( 4 / √3 )

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