Round off 4095 nearest hundreds​

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above, since a parallel line will have the same slope anyway

\((\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -3 } \implies {\Large \begin{array}{llll} \cfrac{ 4 }{ 3 } \end{array}}\)

The general solution to the given differential equation is:

y = (x/12) - (1/288)

How to solve the Differential Equation?

We want to solve the differential equation given as: y' - 24xy = -2x

The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is -24x. Therefore, the integrating factor is e^(-24x).

Multiplying the entire equation by the integrating factor, we get:

e^(-24x)y' - 24xe^(-24x)y = -2xe^(-24x)

The left side of the equation is the derivative of (e^(-24x)y) with respect to x:

(d/dx)(e^(-24x)y) = -2xe^(-24x)

Integrating both sides with respect to x, we have:

e^(-24x)y = ∫(-2xe^(-24x))dx

Integrating the right side, we get:

e^(-24x)y = -∫(2xe^(-24x))dx

To evaluate the integral on the right side, we can use integration by parts. Let's differentiate -2x and integrate e^(-24x):

u = -2x (differential of u = -2dx)

dv = e^(-24x) (integral of dv = -1/24e^(-24x)dx)

Using the integration by parts formula:

∫uv dx = uv - ∫v du

We can compute the integral as follows:

-∫(2xe^(-24x))dx = -[(-2x)(-1/24e^(-24x)) - ∫(-1/24e^(-24x))(-2dx)]

= -[x/12e^(-24x) + 1/12∫e^(-24x)dx]

= -[x/12e^(-24x) + 1/12(-1/24)e^(-24x)]

= -[x/12e^(-24x) - 1/(12*24)e^(-24x)]

= -[x/12e^(-24x) - 1/(288e^(-24x))]

= -[x/12 - 1/288]e^(-24x)

Substituting this back into the previous equation, we have:

e^(-24x)y = -[-(x/12 - 1/288)e^(-24x)]

Simplifying further:

e^(-24x)y = (x/12 - 1/288)e^(-24x)

Canceling out e^(-24x) on both sides:

y = x/12 - 1/288

Therefore, the general solution to the given differential equation is:

y = x/12 - 1/288

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Answer:

2y = 8x - 6

2y/2 = 8x/2 - 6/2

y = 4x - 3

Keegan's error is assuming that the product of the slopes of any two sides of a triangle should be -1 for the triangle to be a right triangle.

To determine if the triangle LMN is a right triangle, Keegan should instead calculate the lengths of the three sides of the triangle and check if they satisfy the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

To correct his approach, Keegan should calculate the lengths of sides LM, MN, and NL using the coordinates of the vertices and then check if the Pythagorean theorem holds true.

If the squared length of one side is equal to the sum of the squares of the other two sides, then the triangle LMN is a right triangle.

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Answer:

87 is what he took out after six weeks is that it or?

Answer:

7. 64

22. 12.9

12. 22

Step-by-step explanation:

x = 154    154 - 90 = 64

15% of 86 is 12.9

A triangle's angles must all add up to 180.

90 + 68 = 158    180 - 158 = 22

The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4  × 10³

From the question, we are to simplify the given expression

The given expression is

6 × 10⁻³ / 8 × 10⁻⁶

Simplifying the expression

6 × 10⁻³ / 8 × 10⁻⁶

This can be written as

6/8 × 10⁻³/10⁻⁶

Reduce the fraction

3/4  × 10⁻³/10⁻⁶

Apply the division law of indices

3/4  × 10⁻³ ⁻ ⁽⁻⁶⁾

3/4  × 10⁻³ ⁺ ⁶

3/4  × 10³

Hence, the value is 3/4  × 10³

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Answer: The ratio 18:26 simplified is 9:13.

Step-by-step explanation:

To simplify the ratio 18:26, we find the greatest common divisor of 18 and 26, and then we divide 18 and 26 by the greatest common divisor.

The greatest common divisor that you can use to simplify 18:26 is 2. Which means the answer to ratio 18:26 simplified is: 9:13

Answer:9/13

explanation: k12

Answer:

\(\displaystyle a = \frac{8}{5}\).

Step-by-step explanation:

Two vectors \((x_1,\, y_1)\) and \((x_2,\, y_2)\) are parallel to one another if and only if the ratio between their corresponding components are equal:

\(\displaystyle \frac{x_1}{x_2} = \frac{y_1}{y_2}\).

Equivalently:

\(\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}\).

For the two vectors in this equation to be parallel to one another:

\(\displaystyle \frac{a}{4} = \frac{2}{5}\).

Solve for \(a\):

\(\displaystyle a = \frac{8}{5}\).

\(\displaystyle \frac{8}{5}\) would be the only valid value of \(a\); no other value would satisfy the \(\displaystyle \frac{x_1}{y_1} = \frac{x_2}{y_2}\) equation.

Answer:107

Step-by-step explanation:

749 ➗ 7=107

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer:

30

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

lcm is 30

Explanation

Step 1

Let

positive number represents owes

so,

a checking account is overdrawn by $5=-5

then a 5$ is charged =-5

Step 2

the total balance is the sum of the movements

the balance is negative 10, it means you owe $10 to the bank

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

Answer:

Although doctor-centric dramas can be entertaining, they're usually filled with a number of inaccurate portrayals of the medical field.

To see where which popular shows get the details right and which ones are loaded with problems, Insider consulted with real doctors and nurses.

Here's how the experts really feel about popular medical shows.

Note: The Entertainment Value and Medical Accuracy scores on each slide are the averages of the scores (out of 10) that the experts provided for each show.

Step-by-step explanation:

please mark me as brainlest answer hope this helps

Answer:

C

Step-by-step explanation:

Hope it helps

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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Answer:

A

Step-by-step explanation:

Because when you are doing a reflection, You sort of see if you can fold it and it will still be the same. If you put the first triangle on the second one, they have the same shape.

Hope this helps :)

The quotient of - 3.32 / - 2.2 is 8 ÷5.

Given fraction:

-3.32 / -2.2

First step is to re-write the given fraction which is - 3.52 / - 2.2

3.52 / 2.2

Second step is to convert the decimal to fraction

352 ÷ 100 / 22 ÷10

Third step is to reduce the fraction

reducing 352/100

=(2^5 × 11)/(2^2 × 5^2)

= [(2^5 × 11) ÷ 2^2] / [(2^2 × 5^2) ÷ 2^2]

= (2^3 × 11)/5²

= 88/25

Reducing 22/10

Divide the numerator and denominator by the greatest common divisor

= 22 ÷ 2 / 10 ÷ 2

= 11 /5

Now let determine  or find the quotient

88 ÷ 25 × 11 ÷ 5

= 8 ÷ 5

Therefore we can conclude that 8 ÷ 5 is the quotient.

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The angle of the T in the ΔRST is 100° and the value of p is 11.

Define Triangle.

A triangle is a polygon that consists of three sides and three vertices. The fact that the interior angles of a triangle add up to 180 degrees is the most crucial aspect of triangles. This characteristic is known as the angle sum property of a triangle.

i.e., In a give ΔABC, ∠A + ∠B + ∠C = 180°.

Given:

∠R = 37°; ∠S = 43°; ∠T = 10p-10°

Let's take ∠T = x

In ΔRST,

∠R + ∠S + ∠T = 180°

37 + 43 + x =  180°

x = 180 - 80 ⇒ 100

∴ ∠T = 100°

To find the value of p,

 ∠T = 100

10p - 10 = 100

10p = 110 ⇒ 11

∴ p = 11

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Answer:

m = -3 ; c = 1

Step-by-step explanation:

y = -3x + 1

y = mx + c

m = -3

c = 1

slope= -3/2, y-intercept=8

y=mx+b m is the slope while b is the y-inteecept

Answer:

probability is 1/52 to be dealt with a ten of diamonds

It takes about 120 years for the graph to reach 100 million barrels per day whereas it takes 50 years to go from 100 million to 200 million.

As per the question the left axis indicates the amount of oil in the earth in trillions of barrels.

The right axis indicates the global consumption rate of oil in millions of barrels per day.

To the left of the red vertical line are model results that approximate reality whereas to the right are model-based predictions of the future.

The bottom axis is time in years.

The graph attached at the end of the solution.

Let the number of years of transition from using no oil to consuming 100 million barrels per day be a.

Let the number of years of transition from using 100 million to 200 million barrels per day be b.

From the given graph, we can see that initial consumption rate is low, and it takes 120 years for the graph to reach 100 million barrels.

But it takes 50 years to go from 100 million to 200 million.

This is known as exponential growth.

Therefore, the value of a is 120 and the value of b is 50.

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B; False

Here, we want to establish if there is a relationship between two variables

From the question, it was stated that at higher speeds, the ticket fee to be paid will be higher

So, what this mean is that the amount of ticket fee to be paid is a factor of the speed at which she was traveling

This directly makes the speed the independent variable while the ticket fee (value depends on the speed of travel) represents the dependent variable

Hence, we can establish that that the ticekt fee is a function of the speed and not the other way round

This makes the correct option FALSE