Find the value of x and explain how you got your answer ​

Here, we are to find the length and the , breadth of the rectangle

The length of the rectangle = 7 units and Breadth of the rectangle = 3 units

Let

length = l units

Breadth = b units

Perimeter of the rectangle = 20 units

length is the distance measured along the longest dimension of an object

width is the wideness of an object

perimeter refers to the total measurements of an objects

The breadth of a rectangle is 4 units less than its length

If,

Length = l

Then,

b = l - 4

Perimeter of a rectangle = 2(length + breadth)

20 = 2{l + (l - 4)

20 = 2(l + l - 4)

20 = 2(2l - 4)

20 = 4l - 8

20 + 8 = 4l

28 = 4l

l = 28/4

l = 7

b = l - 4

b = 7 - 4

b = 3 units

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The Pythagorean theorem states that the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse, which can be represented by the formula a^2 + b^2 = c^2.

In this formula, 'a' and 'b' represent the lengths of the two legs of the right triangle, while 'c' represents the length of the hypotenuse. By squaring each leg and adding them together, we obtain the square of the hypotenuse.

This theorem is a fundamental concept in geometry and has various applications in mathematics, physics, and engineering. It allows us to calculate unknown side lengths or determine if a triangle is a right triangle based on its side lengths. By using the Pythagorean theorem, we can establish a relationship between the different sides of a right triangle and apply it to solve a wide range of geometric problems.

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Answer:

X=10

Step-by-step explanation:

Using exponential smoothing with alpha (α) = 0.15, the forecast for period 6 is 284.61, calculated by recursively updating the forecast based on previous actual and forecast values.



To calculate the exponential smoothing forecast for period 6 using alpha (α) = 0.15, we can use the following formula:

Forecast(t) = Forecast(t-1) + α * (Actual(t-1) - Forecast(t-1))

Given the historical sales data provided, we can start by calculating the forecast for period 2 using the formula:

Forecast(2) = Forecast(1) + α * (Actual(1) - Forecast(1))

          = 300 + 0.15 * (326 - 300)

          = 300 + 0.15 * 26

          = 300 + 3.9

          = 303.9

Next, we can calculate the forecast for period 3:

Forecast(3) = Forecast(2) + α * (Actual(2) - Forecast(2))

          = 303.9 + 0.15 * (287 - 303.9)

          = 303.9 + 0.15 * (-16.9)

          = 303.9 - 2.535

          = 301.365

Similarly, we can calculate the forecast for period 4:

Forecast(4) = Forecast(3) + α * (Actual(3) - Forecast(3))

          = 301.365 + 0.15 * (232 - 301.365)

          = 301.365 + 0.15 * (-69.365)

          = 301.365 - 10.40475

          = 290.96025

Next, we can calculate the forecast for period 5:

Forecast(5) = Forecast(4) + α * (Actual(4) - Forecast(4))

          = 290.96025 + 0.15 * (255 - 290.96025)

          = 290.96025 + 0.15 * (-35.04025)

          = 290.96025 - 5.2560375

          = 285.7042125

Finally, we can calculate the forecast for period 6:

Forecast(6) = Forecast(5) + α * (Actual(5) - Forecast(5))

          = 285.7042125 + 0.15 * (278 - 285.7042125)

          = 285.7042125 + 0.15 * (-7.2957875)

          = 285.7042125 - 1.094368125

          = 284.609844375

Therefore, Using exponential smoothing with alpha (α) = 0.15, the forecast for period 6 is 284.61, calculated by recursively updating the forecast based on previous actual and forecast values.

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The given exponential function represents a decay function and as such the equation of the asymptote is; decay; y = 0

An exponential equation is defined as an equation with exponents whereby the exponents or even a part of the exponent is deemed a variable. For example, 2ˣ = 32

The standard form of exponential equation is written as; y= abˣ

Now, exponential equation can either be growth or decay depending on the rate constant value.

If the value of b < 1, it is a decay while if the value of b > 1, then it is growth.

We are given the exponential equation as;

y = 12(1/3)ˣ

We see that b = 1/3 which is less than 1, and as such it is a decay function.

The equation of the asymptote will be decay; y = 0

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Answer: decay y=0

Step-by-step explanation: it is what it is honestly

When two players A and B alternately flip a fair coin, the probability  E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.

Two players, A and B, turn a fair coin in succession (A tosses the coin first, then B tosses the coin, then A, then B and so on). The order of the heads and tails is noted. If there is a head followed by a tail, the game is done, and the person who throws the tail wins (HT sub-sequence).

We must ascertain the game's estimated duration. Allow T coin tosses for the game to proceed. Find E (T).

\(E(T) = first instance of HT in seriesE(T) =0.5×(1+2)+0.5×(1+E(T))\\0.5×E(T)=0.5×4\\E(T) =4\)

As a result, when two players A and B alternately flip a fair coin, The E(T) is 4. (A tosses the coin first, then B tosses the coin, then A, then B and so on).

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Answer:

3 hours

Step-by-step explanation:

divide the time value by 60

Answer:

Leslie worked for 3 hours

Step-by-step explanation:

There are 60 minutes in an hour, so simply divide 180 by 60, and you will get your answer, which is 3

Hope that helps

(the answer is) = 6466602

Step-by-step explanation:

here

AAA postulate can prove that the triangle BAC is congurant to triangle DEF

The function which describes the amount in dollars Emile has saved after t weeks is given by, A(t) = 30 + 15(t - 1).

Hence the correct option is (B).

The variable which represents the number of weeks is 't' and the amount saved after t weeks represented by 'A'.

Since from the table we can see that for every extra 1 unit of 't' there is an increase of $15 in 'A' in same rate.

From the table we can conclude that the relation between A and t is Linear.

So the function rule which describes the relation between them better, let that be, A = p*t + q, where p and q are arbitrary constants.

From the table we can see that, when t = 1 then A = 30. So,

30 = p*1 + q

p + q = 30 ................ (i)

Again when t = 6 then A = 105, so

6p + q = 105 ................... (ii)

Subtracting equation (i) from equation (ii) we get,

6p + q - p - q = 105 - 30

5p = 75

p = 75/5

p = 15

Substituting p = 15 in equation (i) we get,

15 + q = 30

q = 30 - 15 = 15

So the function which describes the amount saved A after t weeks is given by,

A(t) = 15t + 15

A(t) = 15t + 30 - 15

A(t) = 30 + 15(t - 1)

Hence the correct option is (B).

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The question is incomplete. The complete question will be -

\({ \green{ \tt{the \: origin}}}\)

The name given to the ordered pair (0,0) is the origin.

Answer:

a) The orgin

Step-by-step explanation:

Now we have to,

→ find the name of the ordered pair.

The coordinates are,

→ (0,0)

{It is the origin, where both axis collides}

Hence, the option (a) is correct.

Answer:

which one and I will help

Answer:

2miles

Step-by-step explanation:

Answer:

I think...I repeat I am not sure. The answer is C.

Answer:

Step-by-step explanation:

The square root of numbers refers to a value that when multiplied by itself, the answer is the original number. However, most numbers are non-perfect square, meaning their square roots are decimal numbers.

For non-perfect square numbers, the easiest way to get their square root is by the use of a calculator. But if there is no available calculator, there is also a way to find in which two consecutive integers their square root lies.

Find the nearest lower perfect square number.

Give the square root of the nearest lower perfect square number.

The two integers are the square root of it and the next number to it.

Let us now answer the given above by following these steps.

√120 - 10 and 11

The nearest lower perfect square number is 100.

√100 = 10

10 and 11

If A ⊆ C and B ⊆ C then A ∪ B ⊆ C [proved]

In set theory, the union of two sets A and B is the set of all elements that belong to A, or B, or both. Union is denoted by the symbol ∪. A ⊆ C indicates that set A is a subset of set C. It means that all elements of set A are also elements of set C. Similarly, B ⊆ C implies that every element in B is also in C. The proof for the given statement can be written as follows: Given: A, B, C are three finite sets. A ⊆ C, B ⊆ C. To Prove: A ∪ B ⊆ C.

Proof: Let x be an arbitrary element of A ∪ B. This means that x ∈ A or x ∈ B or both.

Case 1: If x ∈ A, then since A ⊆ C, it implies x ∈ C. Therefore, A ∪ B ⊆ C.

Case 2: If x ∈ B, then since B ⊆ C, it implies x ∈ C. Therefore, A ∪ B ⊆ C.

Case 3: If x ∈ A and x ∈ B, then x ∈ A ∪ B. Therefore, x ∈ C as A ⊆ C and B ⊆ C. Hence, A ∪ B ⊆ C.

Therefore, if A ⊆ C and B ⊆ C, then A ∪ B ⊆ C is true.

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Answer:

Commutative Property

Step-by-step explanation:

The property of multiplication that is being demonstrated is known as Commutative Property. This property basically shows that when multiplying two numbers the actual order in which they are multiplied does not matter and does not affect the result at all. For example, the in this scenario to get the total number of oranges we have to multiply the number of bags by the number of oranges in each bag, but whatever way we do this they equal the same

2 bags * 3 oranges per bag = 6 oranges

3 bags * 2 oranges per bag = 6 oranges

Therefore,

2 * 3 = 3 * 2

When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing with an alpha value of 0.01.

If you are testing the null hypothesis with an alpha value of 0.05, the critical value will be smaller than if you were testing the alpha value of 0.01. This is because a smaller alpha value means a more stringent test of significance, which requires stronger evidence to reject the null hypothesis.

Therefore, the critical value is larger for a smaller alpha value to reflect the higher level of evidence required for rejection. Conversely, a larger alpha value allows for a less stringent test of significance, requiring weaker evidence to reject the null hypothesis, which results in a smaller critical value.

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False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.

A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.

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Answer:

Step-by-step explanation:

The slope of the line is m = -5

4 is your x1

-3 is your y1

Plug into the equation y - y1 = m(x - x1)

y + 3 = -5(x - 4)

y + 3 = -5x + 20

   -3             -3

y = -5x + 17

Answer:

Step-by-step explanation:

−4  +  9  −   2x  −9x

−4  +   9  +  −  2x  +  −9x

−4  +  9  +  −2x  +−  9x

(   −2x+−9x   )+(   −4+9   )

−11x    +    5

Significant figures with representation of x are a) 14.8 m = 14.x m. b) $10.25 = 10.2x. c) 0.05 L = 0.0x L. d) 1.000 g/mL = 1.00x g/mL. e)  6200cm = 6200x cm. f)  403 kg = 40x kg.

a) 14.8m has 3 significant figures. Representation with x in place of estimated digit: 14.x m. b) $10.25 has 4 significant figures. Representation with x in place of estimated digit: 10.2x. c) 0.05 L has 1 significant figure. Representation with x in place of estimated digit: 0.0x L. d) 1.000 g/mL has 4 significant figures. Representation with x in place of estimated digit: 1.00x g/mL. e) 6200cm has 2 significant figures. Representation with x in place of estimated digit: 6200x cm. f) 403 kg has 3 significant figures. Representation with x in place of estimated digit: 40x kg. Significant figures are the digits in a measurement that are reliable and accurate. They provide an indication of the precision of a measurement, and allow us to communicate the level of certainty we have in a particular value. When determining the number of significant figures in a measurement, we typically follow a set of rules. Non-zero digits are always significant, zeros between non-zero digits are significant, and trailing zeros to the right of the decimal point are significant. Zeros at the beginning of a number or to the left of a non-zero digit are not significant. The use of significant figures is important in science and engineering to ensure accurate and reliable measurements. When performing calculations with measurements, the result should be reported with the same number of significant figures as the least precise measurement used in the calculation. In addition, when rounding a number, the last digit should be rounded to the nearest value consistent with the number of significant figures being used. Understanding significant figures is an important part of scientific and mathematical communication, and can help to ensure accuracy and consistency in the reporting of data and calculations.

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To find the surface area of the figure, we need to consider the individual surfaces and add them together.

First, let's identify the surfaces of the figure:

The lateral surface area of the larger prism (excluding the base)

The two bases of the larger prism

The lateral surface area of the smaller prism (excluding the base)

The two bases of the smaller prism

The lateral surface area of a prism is given by the formula: perimeter of the base multiplied by the height.

The bases of the prisms are rectangles, so their areas can be calculated by multiplying the length by the width.

To find the missing prism's surface area, we need to consider that it is a smaller prism nested inside the larger prism. The lateral surface area and bases of the missing prism should also be included.

Once we have calculated the individual surface areas, we add them together to find the total surface area of the figure.

Without specific measurements or dimensions of the figure, it is not possible to provide a numerical answer. Please provide the necessary measurements or dimensions to calculate the surface area.

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Answer:

oh.. maybe you can install photomath

Answer:

y=(x+4)^2

Step-by-step explanation:

A trick I use is if it is a plus sign then it goes left, if it is a minus sign then it goes right.

Angles congruent to ∠1= ∠4,∠8,∠5

Angles congruent to ∠2= ∠3,∠7,∠6

Angles congruent to ∠6= ∠3,∠7,∠2

Angles congruent to ∠7= ∠3,∠6,∠2

The opposing angles created by the connection of two straight lines are known as vertical angles or vertically opposed angles.

(Vertically opposite angle ∠1=∠4

Vertically opposite angle ∠8=∠5

consecutive exterior angle ∠4=∠8)

Angles congruent to ∠2= ∠3,∠7,∠6

Hence, Angles congruent to ∠1= ∠4,∠8,∠5

(Vertically opposite angle ∠2=∠3

Vertically opposite angle ∠7=∠6

consecutive exterior angle ∠3=∠7)

Angles congruent to ∠7= ∠3,∠6,∠2

(Vertically opposite angle ∠7=∠6

Vertically opposite angle ∠2=∠3

consecutive exterior angle ∠6=∠2)

Hence, Angles congruent to ∠6= ∠3,∠7,∠2

(Vertically opposite angle ∠6=∠7

Vertically opposite angle ∠3=∠2

consecutive exterior angle ∠7=∠3)

Hence, Angles congruent to ∠2= ∠3,∠7,∠6

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Answer:

A = 2.42 sq. meters

Step-by-step explanation:

13 feet = 13 × 0.305 = 3.965 meter

2 feet = 2 × 0.305 = 0.61 meter

A = lw

A = (3.965) × (0.61)

A = 2.41865 sq. meters

A = 2.42 sq. meters

(-5y³ + 3y³ - 3y³) + (5x³ + x³) + ( -2y² + 3y²)  is the combined terms of the given expression.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given terms are

⇒  -5y³ + 3y³ + 5x³ - 3y³ + x³ -2y²  + 3y²

Combine all y³ terms

-(5y³ + 3y³ -  3y³)

Combine all  x³ terms

(5x³ + x³)

Combine all y² terms

( -2y² + 3y²)

Add all together (-5y³ + 3y³ - 3y³) + (5x³ + x³) + ( -2y² + 3y²)  is the combined likely terms.

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The center of the circle x² + y² = 25 is (0, 0) and the radius is 5 units

Given that

x squared + y squared =25

Express properly

x² + y² = 25

The above equation is in its standard form

If not we would have to complete the square

To complete the square, we need to add and subtract a constant to both sides of the equation such that the left side becomes a perfect square trinomial.

So, we have

x² + y² = 25

The equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

center = (a, b)

radius = r

So the center of the circle is (0, 0) and the radius is √(25) = 5.

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To find the area of the region formed by revolving the curves x = e^t - t and y = 4e^(t/2) about the x-axis, we can use the method of cylindrical shells.

V = ∫[a,b] 2πx(y^2/16 - x) dx.  Integrating with respect to x from the lower limit a to the upper limit b will give us the volume of the region formed by revolving the curves about the x-axis.

The formula for the volume of a cylindrical shell is V = 2πrhΔx, where r is the radius, h is the height, and Δx is the width of the shell. First, let's express the equations in terms of y and solve for t: x = e^t - t => t = ln(x + t); y = 4e^(t/2) => t = 2ln(y/4). Now, we can set up the integral to calculate the volume of the region: V = ∫[a,b] 2πrhΔx. The limits of integration, a and b, are the x-values where the curves intersect.

Setting the expressions for t equal to each other, we have: ln(x + t) = 2ln(y/4); (x + t) = (y/4)^2; x + t = y^2/16. Solving for t: t = y^2/16 - x. Substituting the values into the integral: V = ∫[a,b] 2πx(y^2/16 - x) dx.  Integrating with respect to x from the lower limit a to the upper limit b will give us the volume of the region formed by revolving the curves about the x-axis.

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a. Optimal solution: X1 = 140, X2 = 0, X3 = 80, Objective Function Value = 4700.000.

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding.

c. The dual price for the second constraint is 2.333, indicating that for each unit increase in its right-hand side value, the objective function value increases by 2.333.

d. The objective function coefficient of X2 can vary between 30 and 40 without changing the optimal solution

a. The complete optimal solution is:

X1 = 140

X2 = 0

X3 = 80

Objective Function Value = 4700.000

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding because it has a slack/surplus value of 0.

c. The dual price for the second constraint (9X1 + 15X2 + 3X3 < 1500) is 2.333. This means that for each unit increase in the right-hand side value of the second constraint, the objective function value will increase by 2.333 units, assuming all other variables and constraints remain constant.

d. The objective function coefficient of X2 can vary between 30 and 40 before a new solution point becomes optimal. This means that as long as the coefficient remains within this range, the current solution will still be optimal. However, if the coefficient of X2 goes below 30 or above 40, a new optimal solution may be obtained.

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