a stainless patio heater is a square pyramid. the lenght of one side of the base is 21.6 in. the slant height of the pyramid is 91.3 in. what is the height of the pyramid

Answer:

x = 33°

Step-by-step explanation:

         Vertically opposite angles are congruent.

          ∠AOB = ∠DOC

       4x - 6     = 2x + 60

Add 6 to both sides,

               4x  = 2x + 60 + 6

               4x = 2x + 66

Subtract 2x from both sides,

          4x - 2x = 66

                 2x = 66

Divide both sides by 2

                    x = 66 ÷ 2

                    [tex]\boxed{x = 33}[/tex]

∠AOB = 4x - 6

          = 4*33 -6

          = 132 -  6

∠AOB = 126°

∠DOC = 126°

The total amount of that Harry will need for the project is nineteen and seven twentieth feet. option A

Addition of Fraction

Wood 1:

Length of each = 2 5/8 feet

Number of pieces = 6

Total = Length of each × Number of pieces

= 2 5/8 × 6

= 21/8 × 6

= 126 / 8

= 15 3/4 meters

Wood 2:

Length of each = 1 1/5 feet

Number of pieces = 3

Total = Length of each × Number of pieces

= 1 1/5 × 3

= 6/5 × 3

= 18/5

= 3 3/5 meters

Total amount of wood needed for the project = 15 3/4 meters + 3 3/5 meters

= 126/8 + 18/5

= (630+144) / 40

= 774/40

= 19 14/40

= 19 7/20 meters

Therefore, the total amount of wood that Harry will need for the project is nineteen and seven twentieths feet. option A

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Answer:

your welcome

Step-by-step explanation:

A. she scored 89 %

B. 89 points

Answer: Let's call the total number of coins Karen and Bill have "t".

We can start by writing an expression for the number of coins Bill has:

2x - 9 = 9 + 2x

So the total number of coins Karen and Bill have is:

t = x + (2x - 9)

Simplifying the expression for t:

t = 3x - 9

So the total number of coins Karen and Bill have is equal to 3 times the number of coins Karen has minus 9.

Step-by-step explanation:

As per the concept of polygon,

a) The sum of the interior angles is 10,440° then the number of sides is 58

b) The value of each interior angle is 171°, then the number of sides is 36

A polygon is a two-dimensional geometric shape made up of straight lines and angles. The number of sides a polygon has is directly related to the sum of its interior angles.

a), we can use the formula for the sum of the interior angles of a polygon, which is (n-2) times 180 degrees, where n is the number of sides. To find n, we can rearrange the formula to

=> n = (sum of interior angles / 180) + 2.

Plugging in the value of 10,440 degrees for the sum of interior angles, we get

=> n = (10440 / 180) + 2 = 58.

Therefore, the polygon in item a) has 58 sides.

For item b), we can use the formula for the value of each interior angle of a regular polygon, we get

=> n = (180(n-2)) / 171 = (180n - 360) / 171.

Solving for n, we find that the polygon in item b) has 36 sides.

In conclusion, polygons with the angle values shown in items a) and b) have 58 and 36 sides respectively. These formulas can be applied to any polygon to find the number of sides based on its interior angle values.

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Answer:

Circumference = 12.56 yd

Area = 12.56 yd²

Step-by-step explanation:

Equations we need to know:

Circumference of circle - 2πr

Area of circle - πr²

1) Circumference

2 x 3.14 x 2 = 12.56

2) Area

3.14 x 2² = 12.56

We have to make sure the we are using the radius and not the diameter otherwise our answer would be wrong

Hope this helps, have a lovely day! :)

Answer:

Area=12.56yd^2, Circumfrence=12.56yd

Step-by-step explanation:

the formula for the area of a circle is pi*r^2 and since pi is 3.14 and r is 2 so r^2 is 4 and 4*3.14 is 12.56 (r is the radius)

the formula for the circumference of a circle os 2*pi*r and r is 2 so its 2*3.14*2 multiplying all these terms again gives us 12.56 but be careful with the units as with the area comes yd^2 and with the circumference comes yd only

Which question are you seeking the answer to?

The average speed that Patrick used to run from his home to a shop and walk back to his home is 1.33 m per second.

The average speed is the total distance divided by the total time.

The average or mean is the quotient of the total value and the total time or number of items in a data set.

The distance from Patrick's home to a shop = 400 m

Running speed from home to the shop = 2 m per second

The total time used in running to the shop = 200 seconds (400/2)

The distance from the shop to Patrick's home = 400 m

Walking speed from shop to the home = 1 m per second

The total time used in walking back to the home = 400 seconds (400/1)

The total distance to and from shop = 800 m (400 x 2)

The total time used to run to and walk from the shop = 600 seconds (200 + 400)

The average speed for the whole journey = Total Distance/Total Time

= 800/600 = 1.33 m per second

Thus, for covering a total distance of 800 m in 600 seconds, Patrick's average speed was 1.33 m per second.

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Answer:

4

Step-by-step explanation:

We know

f = 52

What is the value of f divided by 13

52 divided by 13 = 4

So, the value of f divided by 13 is 4.

The connection string for SQL Server using Windows Authentication is as follows:

Server=myServerAddress;Database=myDataBase;Trusted_Connection=True;

Specify the server address in the format "Server=myServerAddress". Replace "myServerAddress" with the name or IP address of the SQL Server instance you want to connect to.

Specify the name of the database you want to connect to in the format "Database=myDataBase". Replace "myDataBase" with the name of the database.

Use Windows Authentication by setting "Trusted_Connection=True". This means that the user running the application is authenticated using their Windows credentials, rather than a SQL Server login.

Use semicolons (;) to separate the different parts of the connection string.

Using Windows Authentication is a more secure and convenient way to connect to a SQL Server database, as it eliminates the need to store and manage login credentials in the application.

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Answer:

Step-by-step explanation:

Just divide the amount of the giftcard between the unit cost of the books.

[tex]\frac{gift-card-amount}{cost-of-books}=\frac{27}{3}=9[/tex]

Brad can buy 9 books with his gift card

Answer:

D. 27 units.

Step-by-step explanation:

See my attachments.

The length of the diagonal of the print would be = 36.7 in . That is option A (to the nearest tenth).

The print has the shape of a rectangle which is a type of a quadrilateral that has four sides with two sides parallel to each other.

The diagonal length of the print can be calculated by the use of the Pythagorean formula;

That is c² = a² + b²

C = hypothenuse = ?

a = 22 - 4 = 18in

b = 36 - 4 = 32 in

c² = 18² + 32²

c² = 324 + 1024

c² = 1348

C= √1348

C = 36.7 in ( nearest tenth)

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Answer:

[tex]\frac{2}{11}[/tex]

Step-by-step explanation:

[tex]\frac{6}{11} * \frac{1}{3}[/tex]

since 6 and 3 are opposite of each other in this multiplication problem, you can divide them by 3 since they are both divisible by 3

[tex]\frac{2}{11} * \frac{1}{1} = \frac{2}{11}[/tex]

The triangle on the left is a 45 45 90 triangle and the triangle on the right is a 30 60 90 triangle.

In a 45 45 90 triangle, the length of the hypotenuse is equal to the length of either one of the legs times the square root of 2. So that means that a and c are both 18.

In a 30 60 90 triangle, the length of the hypotenuse is twice that of the leg opposite the 30 degree angle. So that means that b is 36. The length of the leg opposite the 60 degree angle is the length of the other leg times the sq root of 3. So that would give you d = 18 sq root 3.

Answer: 37164

Step-by-step explanation:

14% of 32,600 is 4564

-To find the new value of the car, you must add the 14% of the original value and the original value together

-4,564 + 32,600 = 37164

The equation of line is y = 30x + 75 , where the slope is m = 30 and the y intercept is 75

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 1 , 105 )

Let the second point be Q ( 3 , 165 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 165 - 105 ) / ( 3 - 1 )

Slope m = ( 60 / 2 )

Slope m = 30

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 105 = 30 ( x - 1 )

On simplifying the equation , we get

y - 105 = 30x - 30

Adding 105 on both sides of the equation , we get

y = 30x + 75

Hence , the equation of line is y = 30x + 75

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The remaining number of windows is given by the equation A = 11 windows

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of windows that needs to be washed = 30 windows

The number of windows that was washed before lunch = ( 2/5 ) of the total

Substituting the values in the equation , we get

The number of windows that was washed before lunch = ( 2/5 ) x 30

The number of windows that was washed before lunch = 2 x 6

The number of windows that was washed before lunch = 12 windows

So , the remaining number of windows = 30 - 12 = 18 windows

And ,

The number of windows that was washed after lunch = 7 windows

So , the remaining number of windows that needs to be washed A = remaining number of windows - number of windows that was washed after lunch

On simplifying the equation , we get

The remaining number of windows that needs to be washed A = 18 - 7

The remaining number of windows that needs to be washed A = 11 windows

Hence , the equation is A = 11 windows

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Thus, a line graph would be more appropriate for this particular data set to observe the changes in the miles driven over a certain number of days.

Data refers to any collection of facts, figures, or information that can be processed, analyzed, and interpreted to gain insights and knowledge. It can be in various forms such as text, images, audio, video, or numerical values, and can be collected from various sources such as surveys, sensors, social media, or transactions.

Given by the question: -

The most appropriate graph to construct for the given data is a line graph because it would show how the miles driven change over time between each individual data point. A line graph is useful for showing trends or changes over time, and it allows us to see the progression of the miles driven during the trip. This graph would have days on the x-axis and miles driven on the y-axis, with a line connecting the data points. This would help to visualize any patterns or trends in how the miles driven change over time during the trip.

On the other hand, a scatter plot would show the relationship between the two variables, but it would not show the changes over time. While scatter plots are useful for showing relationships between variables, they do not show the order or progression of the data points over time.

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Answer:

Step-by-step explanation:

So here is what I did. If the picture is square then you would multiply Length times the Width to get 49 square inches. But if it’s not a square then you would still multiply Length by Width.

If functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.

A relation is a function if it has only One y-value for each x-value.

The given functions are f(x)=x² +16x-24 and g(x)=x²-5x-17.

We need to find  (ƒ + g)(x).

From properties we have (ƒ + g)(x)=f(x)+g(x)

(ƒ + g)(x)=x² +16x-24+x²-5x-17.

Add the like terms

(f+g)(x)=2x² +11x-41

Hence, if functions f(x)=x² +16x-24 and g(x)=x²-5x-17 then (f+g)(x) is 2x² +11x-41.

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Based on the information in the graph, the angles of the parallelogram would be 68° and 112°, while the length of its sides would be 15 and 8.

To identify the length and angles of this figure we must carefully look at the lengths shown and the angles shown. Taking into account the shape of the parallelogram, we can infer that the values that correctly complete the dimensions of the figure are:

This is because the parallelogram has two equal sides and equal bases, so if the upper one measures 15, the lower one must measure the same. Additionally, if the side measures 8 the other side must measure 8. In the case of the angles it would be the same.

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A. 327 and C.751 have a remainder of 1 when divided by 2

Even Numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. They are  numbers that are a multiple of 2. Examples are: 2, 4, 6, 8, 10, and so on are even numbers.

How to determine this,

By dividing each words by 2

327 divided by 2 = 163 remainder 1

So, this is not an even number when divided by 2

400 divided by 2 = 200 remainder 0

This is an even number

751 divided by 2 = 375 remainder 1

This is not an even number

148 divided by 2 = 74 remainder 0

This is an even number

1356 divided by 2 = 678 remainder 0

So, this is an even number

Therefore, only 327 and 751 have a remainder of 1 when  divisible by 2.

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The false statement regarding the trigonometric ratios is given as follows:

In △ABE, the sin(A) is the same as the tan(F) in △ACF because the triangles are 45-45-90 triangles and therefore similar.

The three trigonometric ratios are defined as follows:

For similar triangles, the ratios are equal, as the side lengths are proportional.

In a 45-45-90 triangle, the sine is equals to the cosine.

However, similar triangles have different values of sine and tangent, hence the first statement is false.

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The farmer will make 14 baskets containing each of 5 apples and 7 peaches.

In mathematics, the greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest common divisor of x and y is denoted {\displaystyle \gcd}.

here, we have,

How many baskets can be made which contain both apples and peaches and each basket should contain the same combinations of fruits?

Given:

A farmer harvests 70 apples and 98 peaches.

They want to make baskets that have both apples and peaches to sell at the market.

Each basket should contain the same combinations of fruit.

They want to sell all the apples and peaches and as many baskets as possible.

Find:

How many baskets can the farm make having x apples and y peaches in the baskets?

Solution:

So, for solving this kind of question first we have to find the greatest common factor, we get;

70 = 2*5*7

98 = 2*7*7

the common factor are 2 and 7

the greatest common factor is 2*7=14

70 apples = 14*5

98 peaches = 14*7

So, the farmer will make 14 baskets each of 5 apples and 7 peaches.

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The probability that a student will enter a building that is not a multiple of 12 is 0.914

We can find the probability by finding the number of buildings that are not a multiple of 12 and dividing it by the total number of buildings (70).

The buildings that are multiples of 12 are:

12, 24, 36, 48, 60, and 70

So there are 6 buildings thar are multiple of 12.

So, the number of buildings that are not a multiple of 12 is

70 - 6 = 64

Therefore, the probability that a student will enter a building that is not a multiple of 12 is

= 64/70

= 0.914

= 91.4 %

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Answer:

[tex]y = 1[/tex]

Step-by-step explanation:

Rearranging the equation:

[tex]y = -8[/tex]

Three points to be considered:

1. Above is a horizontal line cutting through the y-axis at y value of [tex]-8[/tex].
2. A horizontal line has a slope (or gradient) of 0.
3. Parallel lines have the same slope (or gradient)

∴The straight line passing through (2, 1) will also have a zero slope. In addition, this is a horizontal line, which cuts the y-axis at y value of 1.
The equation of straight line:

y = 1

According to the information, the surface area of the pyramids is as follows: 1.377 inches², 2.208 inches², 3.160 inches².

To find the surface area of the pyramids we must perform the following mathematical operations.

A. Find the surface area of the base:

B. We must find the surface area of the faces:

1.

2.

3.

To find the total area of the total surface of the figures we must perform the following procedure:

C. Add the area of the base to the area of the faces:

1.

2.

3.

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The area of the rectangular lawn Rachel mows is 100 square yards

The formula for calculating the area of a rectangle is expressed with the formula;

Area = lw

Where;

Now, substitute the values as given,

length = 12 yards

Width = 8 1/3 = 25/3 yards

Then,

Area = 12 × 25/3

Divide the factors

Area = 4(25)

Multiply the values

Area = 100 square yards

Hence, the value is 100 square yards

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