What is the solution to this system of linear equations?

y − 4x = 7

2y + 4x = 2

A. (3, 1)
B. (1, 3)
C. (3, −1)
D. (−1, 3)

I WILL MARK AS BRAINLIEST IF CORRECT!

\(y = (1/5) x^5 + Ce^ {(-x^5)}\) is the general solution of the given differential equation.

The given differential equation is:

y' + 5x⁴ y = x⁴

To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is \(e^{(int 5x^4 dx)}\):

\(e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}\)

The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is \(e^{(x^5)}\):

\(e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)\)

Now we can recognize the left-hand side as the product of the derivative of the product of \(e^{(x^5)\)and y:

\((d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}\)

Integrating both sides with respect to x, we get:

\(e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C\)

where C is the constant of integration. Dividing both sides by \(e^{(x^5)}\), we get the general solution:

\(y = (1/5) x^5 + Ce^(-x^5)\)

where C is an arbitrary constant.

\(y = (1/5) x^5 + Ce^{(-x^5)}\) is the general solution of the given differential equation.

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The completed two column table in the question showing that the measure of the angle m∠GKB = 120° can be presented as follows;

Statement \({}\)                                                Reason

\(\overline{AB}\) || \(\overline{EF}\)         \({}\)                                          Given

m∠ELJ = 120°

m∠ELJ + m∠ELK = 180°     \({}\)                        Linear pair Postulate

m∠BKL + m∠GKB = 180°   \({}\)                        Linear pair Postulate

m∠ELJ + m∠ELK = mBKL + m∠GKB  \({}\)      Transitive property

∠ELK ≅ ∠BKL                         \({}\)                   1. Alternate Interior Angles

m∠ELK = m∠BKL \({}\)                                      2. Definition of congruent angles

m∠ELJ + m∠ELK = m∠ELK + m∠GKB\({}\)      Substitution property

m∠ELJ = m∠GKB\({}\)                                      Subtraction property

m∠GKB = m∠ELJ \({}\)                                     Symmetric property

m∠GKB = 120° \({}\)                                          Substitution

An angle is the figure formed at the point of intersection of two rays that have the same starting point. The parts of an angle includes; The vertex, which is the point of intersection of the rays, and the sides or arms of the angle, which are the two rays forming the angle.

The details of the the statements that completes the above table used to prove the measure of the angle m∠GKB = 120° are as follows;

Alternate interior angles theorem

The alternate interior angles theorem states that the alternate interior angle formed by the two parallel lines and their shared transversal are congruent.

Definition of congruent angles

Congruent angles are angles that have the same measure.

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Answer:

Step-by-step explanation:

You want the explicit formula for each of the geometric sequences, and the 7th term.

The explicit formula for a geometric sequence with first term a[1] and common ratio r is ...

  a[n] = a[1]·r^(n-1)

The explicit formula is ...

  a[n] = -4·(-3)^(n-1)

The 7th term is ...

  a[7] = -4·(-3)^(7-1) = -2916

The explicit formula is ...

  a[n] = 12·(1/4)^(n -1)

The 7th term is ...

  a[7] = 12·(1/4)^(7-1) = 3/1024

We can use Coulomb's law to calculate the magnitude of the electric field at a distance r away from a point charge Q:

E = k * Q / r^2

where k is Coulomb's constant, Q is the charge of the point charge, and r is the distance from the point charge.

In this problem, we have a point charge Q of -10 nC located at (1.2 cm, 0 cm), and we want to find the x-component of the electric field at a distance r = 5.3 cm away at position (-4.1 cm, 0 cm).

To find the x-component of the electric field, we need to use the cosine of the angle between the electric field vector and the x-axis, which is cos(180°) = -1.

So, the x-component of the electric field at position (-4.1 cm, 0 cm) is:

E_x = - E * cos(180°) = - (k * Q / r^2) * (-1)

where k = 9 x 10^9 N*m^2/C^2 is Coulomb's constant.

Substituting the given values, we get:

E_x = - (9 x 10^9 N*m^2/C^2) * (-10 x 10^-9 C) / (0.053 m)^2

E_x ≈ -30,566.04 N/C

Rounding this to two significant figures and including the appropriate units, we get:

The x-component of the electric field is about -3.1 x 10^4 N/C (to the left).

The probability that the reporter gets an assignment in the United States or Asia is 15/37.

To find the probability that the reporter gets an assignment in the United States or Asia, we first need to determine the total number of assignments in the pool.

Total number of assignments = 8 + 29 + 15 + 22 = 74

Next, we need to determine the number of assignments that are in the United States or Asia.

Number of assignments in the United States or Asia = 8 + 22 = 30

Finally, we can calculate the probability of the reporter getting an assignment in the United States or Asia by dividing the number of assignments in the United States or Asia by the total number of assignments:

Probability of getting an assignment in the United States or Asia = (Number of assignments in the United States or Asia) / (Total number of assignments)

Probability of getting an assignment in the United States or Asia = 30/74

Therefore, the probability of the reporter getting an assignment in the United States or Asia is 30/74, which can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which in this case is 2:

Probability of getting an assignment in the United States or Asia = 15/37

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Debt is usually expected in all of the following cases except for option A, which is the purchase of a house.

Debt refers to an amount of money that is owed by one party (the borrower) to another party (the lender). It can be incurred through borrowing money, using credit cards, or other forms of financing. Debt can take many different forms, including personal loans, mortgages, credit card balances, student loans, and other types of financial obligations.

Debt is usually expected in all of the following cases except for option A, which is the purchase of a house. Purchasing a house with a mortgage involves taking on debt, but it is often considered a necessary and responsible investment for many people. The other options - credit card purchases, purchasing a car, and educational loans - often involve taking on debt as well, but they are not typically seen as long-term investments like a house.

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Answer:

\(3m^4-m^3+2m^2\)

Step-by-step explanation:

Given the expression:

\(\frac{(-7m^4 + 15m^3-12m^2)+(3m^5-12m^4-7m^3)}{m-6} \\\\Firstly\ simplify\ the\ bracket\ should\ be\ :\\\\=\frac{-7m^4 + 15m^3-12m^2+3m^5-12m^4-7m^3}{m-6}\\\\collect\ like\ terms\ together:\\\\=\frac{3m^5-7m^4-12m^4 + 15m^3-7m^3-12m^2}{m-6}\\\\=\frac{3m^5-19m^4 + 8m^3-12m^2}{m-6}\\\\=\frac{m^2(3m^3-19m^2+8m-12)}{m-6}\\\\=\frac{m^2(m-6)(3m^2-m+2)}{m-6} \\\\=m^2(3m^2-m+2)\\\\=3m^4-m^3+2m^2\)

Answer:

c

Step-by-step explanation:

Answer:

Convergent

Step-by-step explanation:

One method to determine if  \(\displaystyle \sum^\infty_{k=1}ke^{-k^2}\)is convergent or divergent is the Integral Test.

Suppose that the function we use is \(f(x)=xe^{-x^2}\). Over the interval \([1,\infty)\), the function is always positive and continuous, but we also need to make sure it is decreasing before we can proceed with the Integral Test.

The derivative of this function is \(f'(x) = e^{-x^2}(1-2x^2)\), so our critical points will be \(\displaystyle x=\pm\frac{1}{\sqrt{2}}\), but we can drop the negative critical point as we are starting at \(k=1\). Using some test points, we can see that the function increases on the interval \(\bigr[0,\frac{1}{\sqrt{2}}\bigr]\) and decreases on the interval \(\bigr[\frac{1}{\sqrt{2}},\infty\bigr)\). Since the function will eventually decrease, we can go ahead with the Integral Test:

\(\displaystyle \int_{{\,1}}^{{\,\infty }}{{x{{{e}}^{ - {x^2}}}\,dx}} & = \mathop {\lim }\limits_{t \to \infty } \int_{{\,1}}^{{\,t}}{{x{{{e}}^{ - {x^2}}}\,dx}}\hspace{0.5in}u = - {x^2}\\ & = \mathop {\lim }\limits_{t \to \infty } \left. {\left( { - \frac{1}{2}{{{e}}^{ - {x^2}}}} \right)} \right|_1^t\\ & = \mathop {\lim }\limits_{t \to \infty } \left( {-\frac{1}{2}{{e}}^{ - {t^2}}-\biggr(-\frac{1}{2e}\biggr)}} \right) = \frac{1}{2e}\)

Therefore, since the integral is convergent, the series must also be convergent by the Integral Test.

Answer:

the graph has a positive slope with a y-intercept of 5

y = 1/4x + 5

Step-by-step explanation:

i found the slope by using points (0,5) and (4,6)

slope formula says to subtract the y-values and divide by difference of x-values:

(6-5) / (4-0) = 1/4

Answer:

Just use math-way or des-mos  and it will graph them for you.

By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)

In this question we have a power function with two variables and which has to be simplified by using power properties. The detailed procedure is shown below:

By using power properties, the expression y⁸ · y³ · x⁰ · x⁻² is equivalent to the expressions 1 / (x² · y⁵) and x⁻² · y⁻⁵. (Correct choices: C, D)

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The ascending order of the expression from smallest to highest is: -39, -11, -8, -6, 2.

In the above case, we need to first break down or simplify the expressions and thus it will be:

9 + 3 = -6

-4 + 6 = 2

2(-4) = -8

1 - 7 - 31 = -39

-5 - 3 x 2 = -11

So now, we need to arrange them and this will be in ascending order from smallest to highest  and it will be: -39, -11, -8, -6, 2

Therefore, the ascending order of the expression is : -39, -11, -8, -6, 2.

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See correct question below

17. Arrange -9 +3, -4+6, 2(-4), 1-7-31, -5-3x2 in ascending order.

Answer:

The answer is "\(\bold{9.19- 9.19\ i}\)"

Step-by-step explanation:

When the value of \(z_1\) has the following properties:

\(\to |z_1| =13\)

\(\theta = 315^{\circ} \\\\ = 1.75 \pi\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ _{where} \ \ (\pi = 180^{\circ})\)

Calculating the value of \(z_1\) :

\(= 13 \times [ \cos(1.75 \pi ) + i \sin(1.75 \pi) ] \\\\= 13 \times[\cos(1.75 \pi - 2\pi ) + \ i \sin(1.75 \pi - 2\pi )]\\ \\= 13 \times [\cos(-0.25 \pi ) +\ i \sin(-0.25 \pi) ]\\\\= 13 \times [0.707106781 - 0.707106781]\\\\ =9.19 - 9.19\ i \\\\\)

Answer:

356.53

Step-by-step explanation:

Calculate the semicircle and square areas separately. For the semicircle, A = πr²/2, so 100.53

And for the square, A = a², so 256

Hope this helps

Answer:

x = 3

Step-by-step explanation:

7x-8=13

Add 8 to each side

7x-8+8=13+8

7x = 21

Divide each side by 7

7x/7 = 21/7

x = 3

fractions with the same denominator added together

You must add the numerators and keep the same denominator when adding fractions with the same denominator. Since the denominators of the two fractions are the same, we must add the numerators while maintaining the same denominator, which is 4.

What are the parts of fraction?

A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.

The number below the bar is called the denominator . It tells the number of equal parts into which the whole has been divided. The number above the bar is called the numerator. It tells how many of the equal parts are being considered.

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Answer:

37

Step-by-step explanation:

Okay! Hi there! I can help you with joy!

The answer is 37. We have a 50-degree angle and it's obvious that we have a 90-degree angle (there's a square).

So, we solve the following math problem;

90-53=37

I hope it's correct!

Good luck on your assignment! Enjoy your day, please!

\(*ROSALINDCORDELIA*\)

The probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution.

To calculate the probability, we need to assume that the sample proportion follows a normal distribution. This assumption holds true when the sample size is sufficiently large and the conditions for the central limit theorem are met.

First, we need to calculate the standard error of the sample proportion. The standard error is the standard deviation of the sampling distribution of the sample proportion and is given by the formula sqrt(p(1-p)/n), where p is the estimated proportion and n is the sample size.

Next, we convert the sample proportion range into z-scores using the formula z = (x - p) / SE, where x is the given proportion and SE is the standard error. In this case, we use z-scores of 0.2 and 0.42.

Once we have the z-scores, we can use a standard normal distribution table or a statistical software to find the corresponding probabilities. The probability of the sample proportion falling between 0.2 and 0.42 is equal to the difference between the two calculated probabilities.

Alternatively, we can use the z-table to find the individual probabilities and subtract them. The z-table provides the cumulative probabilities up to a certain z-score. By subtracting the lower probability from the higher probability, we can find the desired probability.

In conclusion, the probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution and z-scores. This probability represents the likelihood of observing a sample proportion within the specified range.

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The value of the game would be 13.33 dollars.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Value of the game = E(x)

                               \(= [(60\times\frac{5}{6}) + (-10\times\frac{1}{6})]\\\\=50 -1.66\\\\= 48.33\)

P(Plain surface) = 2/6 and

P(Not plain surface) = 1 - 2/6 = 2/3

Let x: Value won/lost in the game

Value of the game

                          \(= [(60\times\frac{2}{6}) + (-10\times\frac{2}{3})]\\\\=20 -6.66\\\\= 13.33\)

Hence, the value of the game would be 13.33 dollars.

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Answer:

x = 8

Step-by-step explanation:

The sum of the measures of two complementary angles is 90°.

m<C + m<D = 90°

5x + 7x - 6 = 90

12x = 96

x = 8

Answer:

without doing the math, we can affirm that the percent in decrease in the price of the gloves is not the same as the percent increase of the goggles. decreasing $2 from $10 will have a lower decrease than an increase of $2 from $8 since $2 represents a higher portion of $8 compared to $10

Step-by-step explanation:

(please give brainliest, much appreciated)

The area of the square, which has an apothem measuring 2.5 cm and a perimeter of 20 cm is 25 cm².

Area of square is the square of its side's length. It can be given as,

\(A=a^2\)

Here, (a) is the length of the side of the square

A square has an apothem measuring 2.5 cm and a perimeter of 20 cm. The perimeter of the square is 4 times the sides of the square.

Let suppose the side of this square is a cm. thus,

\(4a=P\\4a=20\\a=\dfrac{20}{4}\\a=5\rm\; cm\)

The area of the square is,

\(A=5^2\\A=25\rm\; cm^2\)

Hence, the area of the square, which has an apothem measuring 2.5 cm and a perimeter of 20 cm is 25 cm².

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Answer:

25cm

Step-by-step explanation:

e2020

From the given data which shows the length of fish in a pond, there is an outlier at 7.

Hence, the correct option is B.

To determine if the data contains any outliers, we can use the interquartile range (IQR) method. First, we need to find the median and the quartiles of the data set

Arrange the data in order 7, 9, 11, 13, 15, 15, 19, 28.

Median (Q2) = the middle value = 15.

Q1 (the first quartile) = the median of the lower half of the data set = 9.

Q3 (the third quartile) = the median of the upper half of the data set = 19.

Next, we can calculate the IQR as the difference between the third and first quartiles

IQR = Q3 - Q1 = 19 - 9 = 10.

Finally, we can identify any outliers as values that are more than 1.5 times the IQR above the third quartile or below the first quartile.

The upper outlier bound is Q3 + 1.5 x IQR = 19 + 1.5 x 10 = 34.

The lower outlier bound is Q1 - 1.5 x IQR = 9 - 1.5 x 10 = -6.

Since the minimum value in the data set is 7, which is greater than the lower outlier bound, we have an outlier at 7. The maximum value in the data set is 28, which is less than the upper outlier bound, so it is not an outlier.

Hence, the correct option is B.

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The overall average of the 9 numbers is 13 and the average of the last 4 numbers is 20.

To find the overall average of the 9 numbers, we can use the formula for the weighted average:

overall average = (sum of all numbers) / (number of numbers)

We know that the average of the first 5 numbers is 10, so their sum is 5 * 10 = 50. We also know that the average of the next 4 numbers is 15, so their sum is 4 * 15 = 60. The sum of all 9 numbers is then 50 + 60 = 110. Therefore, the overall average is:

overall average = 110 / 9 ≈ 13

To find the average of the last 4 numbers, we can subtract the sum of the first 5 numbers from the sum of all 9 numbers, and then divide by 4:

average of last 4 numbers = (sum of all 9 numbers - sum of first 5 numbers) / 4

= (110 - 50) / 4

= 60 / 4

= 15

Therefore, the average of the last 4 numbers is 15, which is option C.

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Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

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To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:

Let u = y,

v = y',

w = y".

Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:

du/dx = y' = v,

dv/dx = y" = w,

dw/dx = y"'.

Now we can rewrite the given differential equation in terms of u, v, and w:

u - w - 4u + 4u = 0.

Simplifying the equation, we get:

-3u - w = 0.

This equation can be expressed as a system of first-order linear differential equations as follows:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

Now we have a companion system of linear equations:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.

The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.

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Answer:

13.5-6.6= 6.9 (nice)

a^2+b^2=c^2

6.9^2+b^2=7.7^2

b=3.41760149813

13.5+7.7+6.6+3.41760149813= 31.2176014981

( i might be wrong)

Answer:

7.75

Step-by-step explanation:

Answer:  (6.75,0)

Step-by-step explanation:

The x-intercept of a line is when it's y coordinate is 0, so input 0 into the equation for y and solve for x.

4x + 9(0) = 27

4x = 27  

 x= 6.75