What is the perimeter of the trapezoid

If two sides a and b and the included angle c are known in a triangle, then the area k is found using the formula k equals 1/2(ab sin c)

Draw a triangle ABC with side lengths a, b, and c, and height h from vertex C to side AB.

Use the definition of sine to write sin(c) as the ratio of the opposite side to the hypotenuse in the right triangle CHC': sin(c) = h / c.

Rearrange the above equation to get h = c sin(c).

The area of the triangle ABC can be calculated as half the product of the base and height, which is k = (1/2)ab sin(c).

Substituting h = c sin(c) in the above equation yields k = (1/2)ab sin(c), which is the formula for the area of a triangle when two sides and the included angle are known.

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Therefore, the sum of fraction 1/4 and 5 1/3 is 67/12.

To add the fractions 1/4 and 5 1/3, you need to find a common denominator for both fractions. First, convert the mixed fraction 5 1/3 into an improper fraction:

5 1/3 = (5 * 3 + 1) / 3 = 16/3

Now, let's find a common denominator. The denominators of the two fractions are 4 and 3. The least common multiple (LCM) of 4 and 3 is 12. Next, we'll convert both fractions to have a denominator of 12:

1/4 = (1 * 3) / (4 * 3)

= 3/12

16/3 = (16 * 4) / (3 * 4)

= 64/12

Now that both fractions have the same denominator, we can add them:

3/12 + 64/12 = (3 + 64) / 12

= 67/12

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Answer:

x = 14

Step-by-step explanation:

You can find the perimeter of a rectangle by adding up all the sides. Keep in mind that opposite sides in a rectangle are congruent, which means that the perimeter of a rectangle is essentially 2*length + 2*width. We know the perimeter is 70, the length is x+7, and the width is x, so we can set up the equation to solve for x:

2(x + 7) + 2x = 70

2x + 14 + 2x = 70

4x = 56

x = 14

True. Since the square matrix that represents the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same. This property is a fundamental characteristic of orthogonal matrices and holds true for all orthogonal matrices.

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False While it is true that the square matrix that represents the DCT coefficient is orthogonal, it does not mean that its inverse and transpose are the same.

the inverse of an orthogonal matrix is its transpose. However, the transpose of the matrix does not necessarily mean that it is the same as the inverse of the matrix. In the statement is false because the inverse and transpose of an orthogonal matrix are not always the same.


The Discrete Cosine Transform (DCT) coefficient matrix is an orthogonal matrix. In the case of orthogonal matrices, the inverse matrix is indeed equal to the transpose of the original matrix. This is because the product of an orthogonal matrix and its transpose results in the identity matrix.

Since the square matrix representing the DCT coefficient is an orthogonal matrix, its inverse and transpose are the same.

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Answer:

5 feet

Step-by-step explanation:

By triangle inequality, the sum of lengths of any two sides has to be strictly greater than the length of the third side.

Let x feet be the length of the third side.

We have 3+x>7, x+7>3 and 3+7>x.

Solving these, we get x > 4, x > -4 and x < 10.

The solution is therefore 4 < x < 10 and the smallest whole number which satisfies the inequality is 5.

Therefore the answer is 5 feet.

Answer:

each student gets 1 sheet. There are 73 sheets left.

Step-by-step explanation:

Each student only needs 1 sheet and so you just do 80-7 and you get 73

a) The divergence of f = \(e^{xy\) i - cosy j + sin z²k is y \(e^{xy\) + sin y + 2z cos z², and the curl is 0.

b) The divergence of f = xi + yj - zk is 1, and the curl is 0.

a) To find the divergence and curl of the vector field f = \(e^{xy\) i - cosy j + sin z²k:

Divergence:

The divergence of a vector field f = P i + Q j + R k is given by the formula:

div(f) = ∇ · f = ∂P/∂x + ∂Q/∂y + ∂R/∂z

Given f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the divergence as follows:

∂P/∂x = ∂/∂x(\(e^{xy\)) = y \(e^{xy\)

∂Q/∂y = ∂/∂y(-cosy) = sin y

∂R/∂z = ∂/∂z(sin z²) = 2z cos z²

Therefore, the divergence of f is:

div(f) = y \(e^{xy\) + sin y + 2z cos z²

Curl:

The curl of a vector field f = P i + Q j + R k is given by the formula:

curl(f) = ∇ × f = ( ∂R/∂y - ∂Q/∂z ) i + ( ∂P/∂z - ∂R/∂x ) j + ( ∂Q/∂x - ∂P/∂y ) k

Using the vector field f = \(e^{xy\) i - cosy j + sin z²k, we can calculate the curl as follows:

∂P/∂y = ∂/∂y(\(e^{xy\)) = x \(e^{xy\)

∂Q/∂z = ∂/∂z(-cosy) = 0

∂R/∂x = ∂/∂x(sin z²) = 0

∂R/∂y = ∂/∂y(sin z²) = 0

∂Q/∂x = ∂/∂x(-cosy) = 0

∂P/∂z = ∂/∂z(\(e^{xy\)) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

b) To find the divergence and curl of the vector field f = xi + yj - zk:

Divergence:

∂P/∂x = ∂/∂x(x) = 1

∂Q/∂y = ∂/∂y(y) = 1

∂R/∂z = ∂/∂z(-z) = -1

Therefore, the divergence of f function is:

div(f) = ∇ · f = 1 + 1 - 1 = 1

Curl:

∂P/∂y = ∂/∂y(x) = 0

∂Q/∂z = ∂/∂z(y) = 0

∂R/∂x = ∂/∂x(-z) = 0

∂R/∂y = ∂/∂y(-z) = 0

∂Q/∂x = ∂/∂x(y) = 0

∂P/∂z = ∂/∂z(x) = 0

Therefore, the curl of f is:

curl(f) = (0 - 0) i + (0 - 0) j + (0 - 0) k

curl(f) = 0 i + 0 j + 0 k

curl(f) = 0

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It is shown that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |1/f(x) - 1/f(y)| < ε/(2kM) for all x, y in a. This proves that 1/f is uniformly continuous on a.

What is uniformly continuous?

Uniform continuity is a property of a function in which for any given value ε > 0, there exists a corresponding value δ > 0 such that for all pairs of points in the function's domain whose distance is less than δ, the difference in the function's values at those points is less than ε. In other words, a function is uniformly continuous if its rate of change does not vary significantly over its entire domain, and small changes in its input result in correspondingly small changes in its output.

To show that 1/f is uniformly continuous on a, we need to prove that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |1/f(x) - 1/f(y)| < ε for all x, y in a.

Given that f is uniformly continuous on a, we know that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |f(x) - f(y)| < ε/k for all x, y in a.

We also know that |f(x)| > k for all x in a.

Using these facts, we can begin by manipulating the expression |1/f(x) - 1/f(y)|:

|1/f(x) - 1/f(y)| = |(f(y) - f(x))/(f(x)f(y))|

Since |f(y) - f(x)| < ε/k, we can substitute this into the above expression:

|1/f(x) - 1/f(y)| < |(ε/k)/(f(x)f(y))|

Now, we need to find a way to relate f(x)f(y) to |x - y|.

Since f is uniformly continuous, we know that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |f(x) - f(y)| < ε/k for all x, y in a.

This implies that |f(x)f(y)| < k(f(x) + f(y)) < 2kM, where M is the supremum of |f(x)| over a.

Thus, we have:

|1/f(x) - 1/f(y)| < ε/(2kM)

Therefore, we have shown that for any ε > 0, there exists a δ > 0 such that |x - y| < δ implies |1/f(x) - 1/f(y)| < ε/(2kM) for all x, y in a. This proves that 1/f is uniformly continuous on a.

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Answer:

Rate is 8.5%

Step-by-step explanation:

Step 1: Write the given terms

Principal (p)=Rs8800

Rate(r)=?

Time(t)=3.5 years

Interest=Rs2618

Step 2: Write the formula for calculating Simple interest

\(i = \frac{prt}{100} \)

Step 3: Make r the subject of the equation

\(by \: cross \: multiplication \\ 100i = prt \\ divide \: both \: sides \: by \: pt \\ r = \frac{100i}{pt} \)

Step 4: Find the value of r by substituting the values in step 1

\(r = \frac{100 \times 2618}{8800 \times 3.5} \\ r = \frac{261800}{30800} \\ r = 8.5\)

Hence, the rate is 8.5%

The least number of trips that Ava must make in order to deliver 250 cartons of books is 10 trips.

The least number of trips that Ava must make in order to deliver 250 cartons of books can be found by dividing the total number of cartons by the number of cartons that her car can hold per trip.

This can be written as:
Least number of trips = Total number of cartons / Number of cartons per trip

Substituting the given values into the equation, we get:
Least number of trips = 250 cartons / 26 cartons
Least number of trips = 9.62

Since Ava cannot make a fraction of a trip, we need to round up to the nearest whole number. Therefore, the least number of trips that Ava must make in order to deliver 250 cartons of books is 10.

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I think its B because it is always B

The mean of the following data 0,5,30,25,16,18,19,26,0,20,28 is 17.

Hence option D is the correct option.

Mean is the average value of a given set of data. It is calculated by the formula,

Mean =  {Summation of all the values in the data set} / {Number of observations is the data set}

That is, Mean = {Σ all values in the data set} / {number of observations}

The given data set is as follows,

0,5,30,25,16,18,19,26,0,20,28

The number of observations in the data set is 11.

The summation of all the values in the data set is = {0 + 5 + 30 + 25 +
16 + 18 + 19 +26 + 0 + 20 + 28} = 187

Therefore, by applying  the formula of Mean we get

Mean = 187/ 11 = 17

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When using the "rule of thirds" when examining an extremity, the bone is divided into thirds. Therefore, the correct option is option C.

First aid is the initial and urgent help provided to anyone who has a little or major disease or injury,[1] with the goal of preserving life, preventing the condition from getting worse, or promoting recovery until medical help arrives. First aid is typically administered by a person with only little medical training. The idea of first aid is expanded to include mental health in mental health first aid. When using the "rule of thirds" when examining an extremity, the bone is divided into thirds.

Therefore, the correct option is option C.

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Answer: The Lowest Common Denominator is 28

Step-by-step explanation:

Since we need to find the lowest common denominator for the equation (-5/7, -5/4) (Respond if I'm wrong)

Step 1. Find LCM. 7: 7, 14, 21, 28, 35, ... 4: 4, 8, 12, 16, 20, 24, 28, ...

Step 2. Match LCM. 7: 7, 14, 21, 28, 35, ... 4: 4, 8, 12, 16, 20, 24, 28, ...

Step 3. Match both number to their corresponding fractions. (-5/28, -5/28). Notice how the numerator stays the same? We leave them alone, since -5 = -5.

Step 4. Match the equation. -5/28 = -5/28

Answer:

c

Step-by-step explanation:

Interquartile range or IQR is the range of the "box" in the graph. So we have 54 and 36 so we subtract 54-36.

So we get 18.

The two functions, F(x) = x + 6x^2 + 9x + 18 and g(x) = x + 3, are not equal.

In F(x), the highest power of x is x^2, while in g(x), the highest power of x is x^1. This difference alone indicates that the functions are not equal since their terms involve different powers of x.

To further demonstrate this, let's simplify and compare the two functions. Expanding F(x), we have F(x) = 6x^2 + (1+9)x + 18 = 6x^2 + 10x + 18. On the other hand, g(x) remains unchanged as x + 3.

If the two functions were equal, their corresponding terms would have to be equal. However, looking at the simplified forms, we can see that the coefficients of the x^2 terms (6 in F(x)) are different from each other, and the constant terms (18 in F(x) and 3 in g(x)) are also different. Hence, the two functions are not equal.

In summary, the functions F(x) = x + 6x^2 + 9x + 18 and g(x) = x + 3 are not equal because their terms involve different powers of x and have different coefficients.

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Answer: Im pretty sure the answer is 4 and 3/8

Step-by-step explanation:

hope this helps!

Answer:

4 and 3/8

Step-by-step explanation:

Plz brainliest

Answer:

32,8+3,27=36,07

36,07-0,15=35.92

Step-by-step explanation:

The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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Subtraction Property of Equality and Addition Property of Equality are two different approaches to resolving a real-world problem that can be depicted by an equation.

When the identical quantity is added to the both sides of an equation, it generates an equivalent equation, according to the addition property of equality.

To maintain equality, if we deduct a number from one side of the equality, we must subtract the very same number from the opposite side of the equality.

Thus, Subtraction Property of Equality as well as Addition Property of Equality are two different ways of solving a real-world problem that may be represented by an equation.

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An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.

In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.

When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.

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Step-by-step explanation:

Looking closely,

when x1=0, y1= 3

Also, when x2= 3, y2= 1

The slope therefore is,

(y2-y1)/(x2-x1)

= 1-3/2-0

= -2/2

Slope = -1

Each twelve-inch square tile weighs approximately 27 ounces.

To calculate the weight of each tile in ounces, we need to convert the weight of the box from pounds to ounces and divide it by the number of tiles in the box. Since there are 16 ounces in a pound, the weight of each box is 36 pounds * 16 ounces/pound = 576 ounces.

If there are 20 tiles in each box, we divide the weight of the box (576 ounces) by the number of tiles (20) to get the weight of each tile: 576 ounces / 20 tiles = 28.8 ounces. Rounding to the nearest ounce, each twelve-inch square tile weighs approximately 27 ounces.


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Answer:

the slope is 1

Step-by-step explanation:

Answer:

slope = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 1, 4) and (x₂, y₂ ) = (4, 9)

m = \(\frac{9-4}{4-(-1)}\) = \(\frac{5}{4+1}\) = \(\frac{5}{5}\) = 1

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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Answer:

Step-by-step explanation:

We may not be able to fit 16 cases in the box because their combined volume will be greater than the box which will make it impossible.

The dimensions of the big box is given as:

Length= 26 cm

Breadth= 15 cm

Height= 20 cm

So its volume can be calculated by:

Volume= Length x Breadth x Height

Volume= 26 cm x 15 cm x 20 cm

Volume1= 7800 cm³

Now, the dimension of one disc case is given as:

Length= 1.6 cm

Breadth= 14.2 cm

Height= 19.3 cm

The volume of one disc case will be:

Volume= 1.6 cm x 14.2 cm x 19.3 cm

Volume= 438.496 cm³

So, volume of 16 disc cases= 16 X volume of one disc case

Volume2= 16 x 438.496 cm³

Volume2= 7015.936 cm³

Since Volume1 < Volume2

So, 16 disc cases cannot be fit into a box.

Answer:

It will be compressed vertically

Step-by-step explanation:

y = Cf(x) 0 < C < 1 compresses it in the y-direction

Since we are multiplying by 1/4 it will compress it by 1/4 in the y direction

Answer:

When you multiply the whole function by a constant, which can be identified as "C", you can have the following situations:

- If  the function is stretched.

- - If  the function is compressed.

You have that 0<1/4<1

Therefore, you can conclude that be compressed vertically.

Step-by-step explanation:

The given function is f (x) = x²

The new function is f 1 (x) = 1/4 x².

The general function of the form is f(x) = a · x²

i) If |a| < 1   the graph is compressed vertically by a factor of a.

ii)  If |a| > 1  the graph is stretched vertically by a factor of a.

Here:  a = 1/4 < 1

Answer:

80?

Step-by-step explanation:

correct me if I'm wrong...

Answer:

The answer is 80.

Step-by-step explanation:

Answer:

\(\boxed{\dfrac{ 5}{y}}\)

Step-by-step explanation:

Given expression:

Applying the exponent rule: x⁰ = 1

    \(\implies 5(x^0)y^{-1\)

    \(\implies 5(1)y^{-1\)

Applying the exponent rule: c⁻ⁿ = 1/cⁿ

    \(\implies 5(1)y^{-1\)

    \(\implies \dfrac{ 5(1)}{y}\)

Simplify the numerator:

    \(\implies \dfrac{ 5(1)}{y}\)

    \(\implies \boxed{\dfrac{ 5}{y}}\)

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Let x = weight and y = height. It is possible to have a certain weight correspond to multiple heights. This means the input x has multiple output y values. Therefore, we cannot have a function here. A function is only possible if for any x input, there is exactly one y output. The x value must be in the domain.