Given 2 (x + 3) - 4x = x
Prove x= 2

Answer:

100 degrees

Step-by-step explanation:

To determine if a differential form is exact, we need to check if its partial derivatives satisfy the condition of equality. If the differential form is not exact, we can multiply it by an integrating factor to make it exact.

Given a differential form of the form M(x, y)dx + N(x, y)dy, we can determine if it is exact by checking if ∂M/∂y = ∂N/∂x. If this condition is not satisfied, the differential form is not exact. However, we can multiply the differential form by an integrating factor to make it exact.

By multiplying the original differential form by an integrating factor, which is usually a function of either x or y, the resulting form will have equal partial derivatives, satisfying the condition for exactness. The integrating factor effectively "corrects" the form and makes it exact.

By finding the appropriate integrating factor and multiplying it with the given differential form, we can transform it into an exact form. This process is a fundamental technique in solving certain types of differential equations and allows us to find solutions that would otherwise be challenging to obtain.

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You're basically trying to get here is the limit as x approaches negative infinity, of (5ˣ -1)/(x¹⁰ -1).

What you're basically trying to get here is the limit as x approaches negative infinity, of (5ˣ -1)/(x¹⁰ -1).

Let's look at the numerator and denominator of this function separately. First, in the numerator, as x goes toward -infinity, the value of 5ˣ gets closer and closer to 0 with ever increasing negative powers. You then subtract 1 from that, so the entire numerator will tend closer and closer to -1 with decreasing x.

Step2:

Then, in the denominator, recall that any number, negative or positive, to an even power will be positive. As x goes lower and lower, x¹⁰ will go higher and higher, to the point where subtracting 1 from it will have no effect. In other words, the denominator will tend closer and closer to infinity.

In the end, you basically have a real number being divided by ever larger and larger numbers, making it approach zero. So the final answer is, y will approach zero as x approaches -infinity.

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The option that is NOT an augmented functional dependency is: Q --> P, because it removes the attribute from the left-hand side of the existing functional dependency, which is not allowed in an augmented dependency.

Functional dependency: It is a concept in database management systems that describes the relationship between two attributes or sets of attributes in a table. In a functional dependency A → B, A is the determinant or the attribute(s) that uniquely determines the value of B.

Augmented functional dependency : It is formed by adding one or more attributes to the determinant side of an existing functional dependency.

From the given options, the only one that is not an augmented functional dependency is "Q → P". This is because it does not involve adding any attributes to the determinant side of an existing functional dependency.

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Answer:

384 cm^3

Step-by-step explanation:

the volume formula:

     V = a*b*c,

where a - length, b - width, c - height

so, the volume of the solid is V = 4*8*12 = 384 cm^3

The volume of the solid, if the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters is 384 cm³.

To find the volume of the solid, we need to multiply the length, width, and height together. So, the volume of the solid is:

V = l x w x h
V = 4 cm x 8 cm x 12 cm
V = 384 cm³

Therefore, the volume of the solid is 384 cubic centimeters (cm³).

To find the volume of a solid with given dimensions, you can use the formula for the volume of a rectangular prism, which is Volume = Length × Width × Height. In this case, the length is 4 centimeters, the width is 8 centimeters, and the height is 12 centimeters.

Now, let's plug these values into the formula:

Volume = (4 cm) × (8 cm) × (12 cm)

By multiplying these numbers together, you'll get the volume of the solid:

Volume = 384 cubic centimeters (cm³)

So, the volume of the solid with the given dimensions is 384 cm³.

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Answer:

3(x+6)(x-3)

Step-by-step explanation:

3x^2+9x-54

3(x^2+3x-18)

3[(x^2-3x+6x-18)]

3[x(x-3)+6(x-3)]

3[(x+6)(x-3)]

3(x+6)(x-3)

Answer:

His total sales is equal to $1,312.

Step-by-step explanation:

To find his commission cost you have to multiply 6 1/2% by 4,800. So your equation would look like 4800×.065[You have to convert your percentage to decimal form]. Your answer would be 312. You then add it to your salary to get a total of $1,312.

Hope this helps!

Answer:

5

Step-by-step explanation:

9.1875 are the mean and variance of depth in random variable.

What is random variable in math?

The mean of the random variable X is

                                                E(X) =b+a/2

                                                        = 19 + 8.5/2

                                                       = 13.75

The variance of the random variable X is,

                                                       V(X) = ( b - a)²/12

                                                               = ( 19 - 8.5 )²/12

                                                             = 9.1875

If the random variable X is uniformly distributed on the interval [8.5, 19], then the mean of the random variable X is 13.75 and the variance of the random variable X is 9.1875.

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In the trash can, there are 648 bricks. when the measurements are 8 by 4 by 2 The right response is so (C).

This same total mass of a three-dimensional shape is referred to as its porous structure. A cuboid with six rectangular faces has a surface area equal to the sum of the areas of each face. The cuboid's length, width, and height can also be labeled, and indeed the surface area (SA) can indeed be calculated using the equation SA=2lw+2lh+2hw.

Based on this equation, surface area is equivalent to two times overall combination of width and length, two times its products of length and height, and two times the ratio of both height and width.

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Answer:

x - y = 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

x + y = - 5 ( subtract x from both sides )

y = - x - 5 ← in slope- intercept form

with slope m = - 1

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-1}\) = 1 , thus

y = x + c ← is the partial equation

To find c substitute (7, 3) into the partial equation

3 = 7 + c ⇒ c = 3 - 7 = - 4

y = x - 4 ← equation in slope- intercept form

subtract y from both sides

0 = x - y - 4 ( add 4 to both sides )

4 = x - y , that is

x - y = 4 ← equation in standard form

Answer:

Step-by-step explanation:

Its either a or b

Answer:

(6 - 2) / 3

Step-by-step explanation:

First, use parenthesis to declare that whatever is inside will be done first. This is saying to subtract 2 from 6. Next, add / 3 after to show you are dividing the answer of 6-2 by 3.

Answer:

deductive reasoning?

Step-by-step explanation:

The equation tan(θ) = 2 has two solutions in the interval from 0 to 2π. The approximate values of these solutions, rounded to the nearest hundredth, are θ ≈ 1.11 and θ ≈ 4.25.

The tangent function is defined as the ratio of the sine to the cosine of an angle. In the given equation, tan(θ) = 2, we need to find the values of θ that satisfy this equation within the interval from 0 to 2π.

To solve for θ, we can take the inverse tangent (arctan) of both sides of the equation. However, we need to be cautious of the periodicity of the tangent function. Since the tangent function has a period of π (or 180 degrees), we need to consider all solutions within the interval from 0 to 2π.

The inverse tangent function gives us the principal value of the angle within a specific range. In this case, we're interested in the values within the interval from 0 to 2π. By using a calculator or trigonometric tables, we can find the approximate values of the solutions.

In the interval from 0 to 2π, the equation tan(θ) = 2 has two solutions. Rounded to the nearest hundredth, these solutions are θ ≈ 1.11 and θ ≈ 4.25.

Therefore, the solutions to the equation tan(θ) = 2 in the interval from 0 to 2π are approximately θ ≈ 1.11 and θ ≈ 4.25.

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Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test

Asking subject matter experts to rate each item in a test would be most helpful in strengthening the content validity of a test. Content validity refers to the extent to which a test accurately measures the specific content or domain it is intended to assess. By involving subject matter experts, who are knowledgeable and experienced in the domain being tested, in the evaluation of each test item, we can gather expert opinions on the relevance, representativeness, and alignment of the items with the intended content. Their input can help ensure that the items are appropriate and adequately cover the content area being assessed, thus enhancing the content validity of the test.

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Answer:

A(-4.5;2) B(0;-3.5).......

Answer:

8 1/3 liters

Step-by-step explanation:

create a proportion from water : yard

let 'y' = water for entire yard

5/3 ÷ 1/5 = y ÷ 5/5

5/3 · 5/1 = y/1

25/3 = y/1

3y = 25

y = 8 1/3

Esi would receive 36 and Kwasi 24 from the 60 oranges

Ratio of their ages :

12 : 8

express to lowest term by dividing both sides by 4

3 : 2

Given the amount of oranges = 60

Esi = 3/5(60) = 36

Kwasi = 2/5(60) = 24

Therefore, Esi would receive 36 and Kwasi 24.

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Answer:

39°

Step-by-step explanation:

To answer this question it's important to remember that all triangles have 3 angles which sum to 180. This means that we can set up an equation to find the missing angle

Create the equation

Combine like terms

Subtract 141 from both sides

This means that the missing angle is 39 degrees. Since two of the angles are equal to 39, this also means that this triangle is isosceles.

If c = 7, then

12 - 2c

= 12 - 2(7)

= 12 - 14

= -2

c - 5

= (7) - 5

= 2

=》+2 > -2.

So, c - 5 has greater value than 12 - 2c, if c = 7.

______

Hope it helps ⚜

Answer:1: no 2: They probably measured the speed and they added up all the points they got and divided it by the total number of points and it ended up with the mean, and average speed for the rider

Step-by-step explanation:

Based on the Gauss-Jordan Elimination method, and the matrix given, the next step would be to b. divide R2 by 2 and R3 by 3.

The first row has already gone as low as it can so rows two and three need to be worked on.

The best way to do this is to divide Row 2 by 2 and Row 3 by 3. This then leads to the augmented matrix becoming:

[1    0     0   I  5]

[0    1     0   I  4]

[0    0    1    I  3]

In conclusion, option B is correct.

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In the given image, \(a_{23}\) is 5. The correct option is the first option 5

From the question, we are to determine which entry in the given matrix represents \(a_{23}\)

NOTE: For any entry denoted as \(a_{mn}\), it represents the entry in the m-th row and n-th column.

Thus,  

 \(a_{23}\) represents the entry in the 2nd row and 3rd column.

In the given image, the entry in the 2nd row and 3rd column is 5.

Hence, in the given image, \(a_{23}\) is 5. The correct option is the first option 5

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Displacement at t = 0 :

Displacement at t = 1 :

Displacement between t = 0 and t = 1 :

∴ The displacement between t = 0 and t = 1 is -4√2 meters.

Answer:

\(-4\sqrt{2} m\)

Step-by-step explanation:

Similar question to the previous one you asked, and I swear I will not make the same mistake again :)

First we will find the displacement at t = 0 and t = 1 to find both displacements.

t = 0,

\(x(0)=4cos(\pi (0)+\frac{\pi }{4} )=4cos(\frac{\pi }{4} )\\=4(\frac{\sqrt{2} }{2} )\\=2\sqrt{2} m\)

t = 1,

\(x(1)=4cos(\pi (1)+\frac{\pi }{4} )=4cos(\pi +\frac{\pi }{4} )\\=4(-\frac{1}{\sqrt{2} } )\\=-\frac{4}{\sqrt{2} }\)

Total Displacement = Final Position - Initial Position

= x(1) - x(0)

= \(-\frac{4}{\sqrt{2} } -2\sqrt{2} \\=-4\sqrt{2} m\)

\(4.4\%\) interest rate would be required in order for Jack to end up with \(\$840\).

Jack is going to invest \(\$650\) and leave it in an account for \(6\) years.

The interest is compounded continuously.

We have to find  interest rate, would be required in order for Jack to end up with \(\$840\).

As we know that,

In the compound interest we get interest also in the interest.

The formula of Amount in compound interest is

\(A = P(1+\frac{r}{100})^n\)

where \(A=\) Amount after interest

\(P=\) Principal Amount

\(r=\) Rate

\(n=\) Time

From the question we know that,

Amount after interest \(A=\$840\)

Principal Amount \(P=\$650\)

Time \(n=6\)

We have to find the rate of interest.

Now putting the value in formula

\(A = P(1+\frac{r}{100})^n\)

\(840 =650(1+\frac{r}{100})^6\)

Divide by \(650\) on both side

\(\frac{840}{650}=\frac{650}{650}(1+\frac{r}{100})^6\)

\((1+\frac{r}{100})^6=\frac{84}{65}\)

\((1+\frac{r}{100})^6=1.2923\)

taking root power of six on both side and using calculator to solve the value

\(1+\frac{r}{100}=1.044\)

Subtract \(1\) on both side

\(1+\frac{r}{100}-1=1.044-1\)

\(\frac{r}{100}=0.044\)

Multiply by \(100\) on both side

\(\frac{r}{100}\times100=0.044\times100\)

\(r=4.4\)

Hence, \(4.4\%\) interest rate would be required in order for Jack to end up with \(\$840\).

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Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.

In mathematics, an inequality is a connection that does not have an equal sign between equations or values. Inequality precedes imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Have used the not equal symbol, which is most often used, when values are not similar (). No issue how little or huge the values, variable inequalities are employed to contrast them.

Here,

Given:

Lacrosse balls cost $10 per pack

while golf balls price $25 per pack.

Total funds equal $250.

In order to create an inequality,

we must multiply g by the quantity of golf balls you bought and I by the quantity of lacrosse balls.

So, the inequality is:

25g + 10l ≤ 250

Therefore , the solution of the given problem of inequality comes out to be the inequality is: 25g + 10l ≤ 250.

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