Solve |2x - 2 ≥ 6.
A. x≤-2 or x ≥ 4
B. x ≤3 or x ≥ 5
C. x ≤-2 or x ≥ 5
D. x ≤-2 or x ≥ 6

Answer:

  none

Step-by-step explanation:

All of the numbers in the set shown here have a finite number of digits, hence are rational.

There are no irrational numbers in the set.

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The amount of the sale of the home is $2090181.82

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

Commission = 5.5% on the sale of a home

Also, we have

Commission  = 114960

using the above as a guide, we have the following:

5.5% on the sale of a home = 114960

So, we have

5.5% * sale of a home = 114960

Divide both sides by 5.5%

sale of a home = 114960/(5.5%)

Evaluate

sale of a home = 2090181.82

Hence, the sale of the home is $2090181.82

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Answer:

câu này là 500 nhen

Step-by-step explanation:

To calculate the population of the town in 2025, we need to add the changes in population over the next five years to the population in 2020.

Starting population in 2020 = 70,230

Change in population over 5 years:

Net migration = 6556 - 4096 = 2460

Natural increase (births - deaths) = 5225 - 4978 = 247

Total change in population = 2460 + 247 = 2707

Population in 2025 = 70,230 + 2,707 = 72,937

Therefore, the population of the town in 2025 is 72,937.

Based on the limited information provided, it is not possible to definitively determine the type of economy in Country A. More specific details and factors would be necessary to make a conclusive determination.

The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

  80

Step-by-step explanation:

The cube Peggy wants to build will require 5×5×5 = 125 unit cubes. Since she has 45, she will need 80 more.

____

Peggy's cube will have 5 cubes along one edge. Then one layer will be 5 times that many, so 25 cubes. The 5 layers will be 5 times that many, so 125 cubes.

Answer:

B is the answer foks thanks for looking

Step-by-step explanation:

They looked around and then rushed toward each other.  A cry of alarm surged through Tompkins Square Park.  Was this a fight to the death instead of a boxing match?

 The fear soon gave way to wave upon wave of cheering as the two amigos embraced.

 No matter what the decision, they knew they would always be champions to each other.

(continued)

Based on the passage, how do the boys resolve their conflict?

They decide to fight to the death.

They decide not to care who the winner is.

They decide to fight a rematch.

They decide to end their friendship.

Answer:

b

Step-by-step explanation:

The range of the function on the graph would be: D. all real numbers greater than or equal to 2

To obtain the range, observe the y values whose result can be obtained by the function of x. To obtain this range, we examine the graph and note that the range begins from 2 on the y-axis and extends upwards.

So, if we wish to define our range, we will enter all real numbers that are equal to or greater than 2 as seen in the direction of the graph.

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Answer:

c

Step-by-step explanation:

if she filled it 4/5 and the next morning 3/4 of the water was gone the birds drank 1/4

Step-by-step explanation:

the area of a parallelogram is

baseline × height = 5 × 3.2 = 16 m²

Answer:

0.7

Step-by-step explanation:

this is the answer because the zero means less in this equation.

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Answer:

23.9894949495cm is the depth of the container.

Step-by-step explanation:

Cylindrical container:

height: 28

radius: 9 (or 18/2)

pi * 9² = 254.4690049408

254.4690049408 * 28 = 7,125.1321383424 cm²

cylidrical container area: 7,125.1321383424cm²

Container:

length: 27cm

width: 11cm

27 * 11 = 297

7,125.1321383424 / 297 = 23.9894949495cm

I assume that the container with rectangular base is precisely full when tou pour the water into it.

And that your question was how deep the container was.

Answer:

x = 7

Step-by-step explanation:

Answer:

x= 1

Step-by-step explanation:

Add four to both sides of the equation:

10x-4+4 = 2x+4+4

Simplify:

10x = 2x+8

Subtract 2x from both sides:

8x = 8

Cancel out terms:

x=

Simplify:

x=1

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Answer: See the graph below!

I hope this helped!

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The equation  5x+7 = 4x+8+x-1 is true for all real numbers.

Solution for the equation is 5x + 7 = 5x + 7.

Given,

The equation;  5x+7 = 4x+8+x-1

We have to find the solution for this equation.

Here,

5x + 7 = 4x + 8 + x - 1 = 5x + 7

The equation is true for all real numbers;

Lets check;

 5 x 6+7 = 4 x 6 + 8 + 6 - 1

30 + 7 = 24 + 13

37 = 37

 5 x 15 + 7 = 4 x 15 + 8 + 15 - 1

75 + 7 = 60 + 22

82 = 82

That is,

The equation 5x + 7 = 4x + 8 + x - 1  is true for all real numbers.

The solution for the equation is  5x + 7 = 5x + 7.

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Answer:

24 is the number. The sum of its digits is 6.

Step-by-step explanation:

There are four two-digit numbers the product of whose digits is 8: 18, 24, 42, and 81. Of these numbers, 24 is four times the sum of its digits:

24 = 4 × 6 = 4 × (2 + 4)

Answer:

43.6 has 3 significant figures.

As we have proved that if one pair of opposite sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram.

To prove this, we can use the concept of alternate angles. Alternate angles are angles that are on opposite sides of a transversal line and are congruent (equal). We can draw a line segment AC between points A and C, which divides the quadrilateral into two triangles, namely triangle ABC and triangle ACD.

Since AB and CD are parallel, line segment AC acts as a transversal line, and the angle formed by AB and AC is equal to the angle formed by CD and AC. These angles are alternate angles, and therefore they are equal. Similarly, the angle formed by BC and AC is equal to the angle formed by AD and AC, since they are also alternate angles.

Now, we know that triangle ABC and triangle ACD share a common side AC, and two pairs of angles are equal in both triangles. Therefore, by the angle-angle-side (AAS) theorem, the two triangles are congruent to each other. Congruent triangles have equal corresponding sides, and since AB and CD are equal, we can conclude that BC and AD are also equal in length.

Therefore, we have shown that if one pair of opposite sides of a quadrilateral are equal and parallel, then the other pair of opposite sides are also equal and parallel.

This means that the quadrilateral is a parallelogram. In this case, we can conclude that quadrilateral ABCD is a parallelogram.

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The complete expression is (2 × x) + (2 × 6). This is an equivalent expression to the given expression.

What is an expression?

A number, a variable, or a combination of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.

Given expression is

2 (x+6)

Distributive property: The same outcome is obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend by the number separately and combining the resulting products.

The mathematical representation is a(b+c) = ab + ac.

Apply the Distributive property in the given expression:

(2×x) + (2×6)

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The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.

The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.

The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.

An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.

In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).

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Answer:

(a) \(PQ \sim ST\)

Step-by-step explanation:

Given

See attachment

Required

Which must be true

\(\triangle PQR \simeq \triangle STU\) implies that:

The following sides are corresponding

\(PQ \sim ST\)

\(PR \sim SU\)

\(QR \sim TU\)

The following angles are corresponding

\(\angle P \sim \angle S\)

\(\angle Q \sim \angle T\)

\(\angle R \sim \angle U\)

From the given options, only option (a) is true because:

\(PQ \sim ST\)

Answer:

Step-by-step explanation:

The events are not independentd) The events are not mutually exclusiveStep-by-step explanation:Hi!Lets call: Gar = {homes with garage}Pool

By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.

We are given that,

No. of children who stayed at school is 27,

Also, 70% of the children went on an excursion.

Suppose, the total number of children in percentage is 100%

Out of which 70% went on an excursion

Thus, the children who stayed at school is 100% - 70% = 30%

By using the Unitary method, we can find out the number of 70% of children.

If 30% of the children are 27

Then 70% of the children are = 27 × 100

                                                        30

                                                 = 63

∴ the total no. of children in the school = 27 + 63

                                                                 = 90

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