Solve x2 - 8x = 3 by completing the square. Which is the solution set of the equation?

O {4 - V19, 4 + V19}
O {4 - V11, 4 + V11}
O {4 - V8,4 + V8}
O {4 - V3, 4 + V3}

Answer:

y = - 3

Step-by-step explanation:

Given

\(\frac{y}{9}\) = \(\frac{y+2}{3}\) ( cross- multiply )

9(y + 2) = 3y ← distribute left side

9y + 18 = 3y ( subtract 3y from both sides )

6y + 18 = 0 ( subtract 18 from both sides )

6y = - 18 ( divide both sides by 6 )

y = - 3

Answer:

-1/43

Step-by-step explanation:

The slope of a line that is perpendicular to another line will always be the opposite reciprocal of that line; it will change from negative to positive and vice versa and it will switch the numerator and denominator.

If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5

Given the line A, B and C

The constant of proportionality is the ratio of the y coordinates to the x coordinate

k = y /x

Where k is the constant of proportionality

Consider the line A

One point on the line = (1, 5)

Constant of proportionality K = 5/1

= 5

Consider the line B

One point on the line = (3, 5)

Constant of proportionality k = 5/3

Consider the line C

One point on the line = (7, 5)

Constant of proportionality = 5/7

Therefore, the line A has the constant of proportionality of 5

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The given question is incomplete, the complete question is

Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?

(a) The number of choices with no restriction is 10,000.

(b) The number of choices with no repeated digits is 5,040.

(c) The number of choices with no repeated digits and the third digit as 0 is 648.

(a) With no restriction, there are 10 choices for each digit, ranging from 0 to 9. Since a 4-digit pin code consists of four digits, the total number of choices is 10^4 = 10,000.

(b) When no digit is repeated, the number of choices for the first digit is 10. For the second digit, there are 9 choices remaining (as one digit has been used). Similarly, for the third digit, there are 8 choices remaining, and for the fourth digit, there are 7 choices remaining. Therefore, the total number of choices is 10 × 9 × 8 × 7 = 5,040.

(c) When no digit is repeated and the third digit is fixed as 0, the number of choices for the first digit is 9 (excluding 0). For the second digit, there are 9 choices remaining (as one digit has been used, but 0 is available).

For the fourth digit, there are 8 choices remaining (excluding 0 and the digit used in the second position). Therefore, the total number of choices is 9 × 9 × 8 = 648.

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Answer:

Step-by-step explanation:

triangles PWR and AWB are equivalent (AAS/angle angle side)

RW and BW are equivalent (CPCT)

For any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

To determine the values of h and okay for which the device of equations has no answer, we want to locate the situations underneath which the equations are inconsistent or parallel.

The given system of equations is:

Equation 1: x + 3y = h

Equation 2: -4x + ky = -9

For the gadget to haven't any answer, the lines represented with the aid of these equations should be parallel and in no way intersect. In different phrases, the slopes of the traces need to be equal, but the y-intercepts should be specific.

Let's first discover the slopes of the traces. The slope-intercept form of Equation 1 is y = (-1/3)x + (h/3), wherein the slope is -1/3. The slope-intercept shape of Equation 2 is y = (4/k)x - (9/k), wherein the slope is 4/k.

For the strains to be parallel, the slopes should be equal. Therefore, we have the condition: -1/3 = 4/k.

To locate the values of h and okay for which the gadget has no answer, we need to locate the values of h that satisfy the situation -1/3 = 4/k.

Solving this equation for ok, we've got:

-1/3 = 4/k

-1 = 12/k

k = -12

Substituting k = -12 returned into the equation -1/3 = 4/k, we've:

-1/3 = 4/(-12)

-1/3 = -1/3

Since the equation holds real for any value of h, there aren't any restrictions at the price of h.

Therefore, for any price of h and k = -12, the system x + 3y = h and -4x + ky = -9 will haven't any answer.

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The system of equations has no solution when k is equal to 12. The value of h can be any real number.

To determine the values of h and f for which the system has no solution, we need to analyze the coefficients of the variables and the constants in the equations.

The given system of equations is:

x + 3y = h

-4x + ky = -9

We can rewrite the second equation as:

-4x + ky = -9

Dividing both sides of the equation by -4, we get:

x - (k/4)y = 9/4

Comparing the coefficients of x and y in the two equations, we can see that the slopes of the lines represented by the equations are different when k is not equal to 12.

Therefore, for the system to have no solution, k must be equal to 12.

As for the value of h, it can be any real number since it does not affect the slopes of the lines.

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The possible values of x according to the give. equation are; 0, ±√3i, ±2i, i, -1.

The possible values of x in the equation given in the task content represent the zeroes of the equation and can be determined as follows;

(x²+3) (x³+4x) (x²+x-i-xi) = 0.

Hence, by further factorisation; we have;

x(x²+3) (x²+4) (x-i) (x+1) = 0.

The possible values of x are therefore;

x = 0;

x²+3 = 0; x = ±√3i

x² +4 = 0; x = ±2i

x -i = 0; x = i.

x +1 = 0; x = -1

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Answer:

They are similar

Step-by-step explanation:

They are similar because angle MW connects and LV does to.

Answer:

midpoint equation

Step-by-step explanation:

Answer:

17.3

Step-by-step explanation:

To solve this equation, you need to use the pythagorean theorem which is:

\(a^{2} +b^{2}= c^{2}\)

a= length

b= height

c= hypotenuse

First, substitute in your values for the equation:

\(10^2+b^{2} =20^{2}\)

Then, use the squares in the equation:

\(100+b^{2} =400\)

Then, subtract 100 from both sides to isolate b:

\(b^{2} =300\)

Finally, square root both sides to get your answer:

\(b=17.3205080757\)

Then round to the nearest tenth which gives you 17.3.

Answer: 17.3 ft

Step-by-step explanation:

Consider the following argument: "Companies use free samples to encourage sales, I help them."

Perform your own analysis of the argument using the concept of negative/positive rights.

Companies using free samples to encourage sales is a positive right, while assisting companies to provide samples is a corresponding positive right.

The argument "Companies use free samples to encourage sales, I help them" can be analyzed using the concept of negative and positive rights. What are negative rights? Negative rights are rights that entail an obligation on other people not to interfere with one's activities. In other words, negative rights are rights that impose an obligation on others to refrain from doing something that restricts another person's activities. What are positive rights? Positive rights, on the other hand, are rights that require others to act in a specific way, providing goods or services to ensure that rights are upheld. Analysis of the argument in terms of negative/positive rights: The argument "Companies use free samples to encourage sales, I help them" is an example of a positive right. Companies' right to use free samples to encourage sales can only be upheld if someone assists them in giving out the samples. This means that for companies to exercise their right to use free samples to encourage sales, they need someone to provide the samples.To sum up, companies using free samples to encourage sales is a positive right, while assisting companies to provide samples is a corresponding positive right.

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now, this is assuming the compounding period is annually, so

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases} \\\\\\ A=2000\left(1+\frac{0.02}{1}\right)^{1\cdot 7}\implies A=2000(1.02)^7\implies A\approx 2297.37\)

Answer:

-4 I think

Step-by-step explanation:

The total number of views the video got over the course of the first 17 days is approximately 17,536.

To solve this problem, we can use the formula for the sum of a geometric sequence, which is given by:

Sn = a(1 - r^n) / (1 - r)

where

Sn is the sum of the first n terms

a is the first term

r is the common ratio between the terms

In this case, a = 800 (the first day's views), r = 1.05 (the 5% increase in views per day), and n = 17 (the number of days).

Substituting these values into the formula, we get:

Sn = 800(1 - 1.05^17) / (1 - 1.05) ≈ 17,536

Therefore, the video got approximately 17,536 views over the course of the first 17 days.

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The probability that none are broken as calculated from the data given is 0.96.

No of eggs = 12

percentage of broken eggs = 4%

=4/100 * 12 = 0.48 eggs

therefore , probability of getting broken egg

= no of favorable outcome/ no of outcomes

=0.48/12

=0.04

hence probability of not getting any broken egg

= 1 - P(broken)

= 1- 0.04

= 0.96

There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

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The volume of Prism B is approximately 1717.

To find the volume of Prism B, we need to use the information provided and the concept of similarity between the prisms.

Prism A and Prism B are similar, their corresponding sides are proportional.

Let's assume the scale factor between Prism A and Prism B is 'k'. This means that each side of Prism B is 'k' times larger than the corresponding side of Prism A.

Since the surface area is directly proportional to the square of the side length, we can write the following equation:

\((k * side length of Prism A)^2\)= surface area of Prism B

Plugging in the values we have, we get:

\((k * sqrt(588))^2 = 768\)

Simplifying the equation:

\(k^2 * 588 = 768\)

Dividing both sides by 588:

\(k^2 = 768 / 588\)

\(k^2 ≈ 1.306\)

Taking the square root of both sides:

k ≈ sqrt(1.306)

k ≈ 1.143

Now, we can find the volume of Prism B. Since volume is directly proportional to the cube of the side length, we have:

Volume of Prism B =\(k^3 *\) Volume of Prism A

Volume of Prism B ≈ \((1.143)^3 * 1052\)

Volume of Prism B ≈ 1717

The volume of Prism B is approximately 1717.

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The diagram of water cycle is attached below.

The best describes the process occurring at U and X is Water changes from a liquid to a gas.

The process that occurs at the position of U and X is discussed when water transforms from a liquid to a gas. This is called Evaporation.

The following are the situations that should not be arisen at the location U and X:

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Given statement solution is :-  P(5) = 1/6.

The probability of rolling a 5 is 1/6 or approximately 0.1667.

The probability of getting any side of the die is 1/6. The probability of obtaining a 1 is 1/6, the probability of obtaining a 2 is 1/6, and so on. The number of total possible outcomes is equal to the total numbers of the first die (6) multiplied by the total numbers of the second die (6), which is 36.

A standard die has six sides printed with little dots numbering 1, 2, 3, 4, 5, and 6. If the die is fair (and we will assume that all of them are), then each of these outcomes is equally likely. Since there are six possible outcomes, the probability of obtaining any side of the die is 1/6.

Since a standard die has six sides numbered from 1 to 6, the probability of rolling a specific number, such as 5, is equal to the probability of getting that number out of the total possible outcomes.

The total number of possible outcomes when rolling a die is 6 (one for each side). Since each side has an equal chance of landing face-up, the probability of rolling a 5 is 1 out of 6.

Therefore, P(5) = 1/6.

The probability of rolling a 5 is 1/6 or approximately 0.1667.

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The theorem that provides a method for revising probabilities to reflect new information is Bayes' theorem.

Bayes' theorem is a fundamental concept in probability theory and statistics that provides a way to update or revise probability estimates based on new or additional information.

It is named after the English statistician Thomas Bayes, who first formulated the theorem in the 18th century. Bayes' theorem is widely used in various fields such as science, engineering, medicine, finance, and artificial intelligence.

It is an essential tool for solving problems related to decision making, prediction, and classification.

Bayes' theorem is based on conditional probability, which describes the probability of an event given that another event has occurred. The theorem provides a formula for calculating conditional probabilities and allows for the incorporation of new information or evidence into the probability estimate.

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The given statement "An algorithm is a calculation that determines how long it will take to solve a problem." is False.

An algorithm is not just a calculation that determines how long it will take to solve a problem. An algorithm is a step-by-step set of instructions or a process used to solve a problem or perform a specific task. It is a systematic approach that allows a computer or human to break down a problem into smaller, manageable parts and reach a solution effectively.

Algorithms are the foundation of computer programming and can be applied in various fields such as mathematics, data processing, and problem-solving. They can be simple, like finding the largest number in a list, or complex, like solving a Rubik's Cube.

Efficiency is a key factor in evaluating algorithms. The time and resources required for an algorithm to solve a problem can vary greatly depending on the method used. However, the primary purpose of an algorithm is to provide a clear and concise procedure to reach a solution, rather than just estimating the time needed to solve a problem.

In summary, an algorithm is a well-defined process designed to perform a specific task or solve a problem, rather than just calculating the time required to do so. Its effectiveness depends on its efficiency, accuracy, and the simplicity of the steps involved.

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Answer:

6,30 9,45 12,60

Step-by-step explanation:

This is a question that go on and on and on.

3,15

6,30

9,45

12,60

The points that lie on the line will be (2, 10), (6, 30), (9, 45), and (8, 20). Then the correct options are B, D, F, and G.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

\(\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)\)

A student graphs a line that passes through (3, 15) and the origin. Then the equation of the line is given as,

(y - 0) = [(15 - 0) / (3 - 0)](x - 0)

y = 5x

At x = 2, the value of y is calculated as,

y = 5 (2)

y = 10

At x = 6, the value of y is calculated as,

y = 5 (6)

y = 30

At x = 9, the value of y is calculated as,

y = 5 (9)

y = 45

At x = 8, the value of y is calculated as,

y = 5 (8)

y = 40

The points that lie on the line will be (2, 10), (6, 30), (9, 45), and (8, 20). Then the correct options are B, D, F, and G.

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Answer:

\(x_1=0,x_2=7,x_3=-5\)

Step-by-step explanation:

\(0=x^3-2x^2-35x\)

\(0=x(x^2-2x-35)\)

\(0=x(x-7)(x+5)\)

\(x_1=0,x_2=7,x_3=-5\)

Answer:

first equation : 3y + 6×=12

second equation : 4y + 8x = 16

Step-by-step explanation:

first equation

3y + 6× = 12

now take the common ,

3( y + 2x ) = 12

so, y + 2x = 4

second equation

4y + 8x = 16

4 ( y + 2x ) = 16

so, y + 2x = 4

two lines with same equation have infinitely many solution . these two equations are the same so there are infinitely many solution .

Answer:

0.969

Step-by-step explanation:

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (18 - 31) / 7

= -1.857

area in z-score table (this is area to left of <18) is 0.0314.

P(>18) = 1 - 0.0314 = 0.969

Answer:

1887.6 ft³

Step-by-step explanation:

What is the volume of a cylinder with a height of 6.8 ft and a base with a radius of 9.4 ft, to the nearest tenth of a cubic foot?

The formula for the volume of a cylinder is given as:

πr²h

From the above question,

r = 9.4 ft

h = 6.8 ft

The volume of the cylinder =

π × 9.4² × 6.8

= 1887.61966 ft³

Approximately = 1887.6 ft³

Answer:

60-x

Step-by-step explanation:

a number = x

Answer:

vertical angles

Step-by-step explanation:

vertical angles is the angles opposite each other when two lines across

Answer:

When x is -6, y will be 18

When x is -5 y will be 15

Step-by-step explanation:

Create a proportion

y/x

-9/3 = x/-6  What do we need to multiply 3 by to get 6?  -2, so we will multiply -9 by -2 to get 18

Some people like to solve by cross multiplying.

That would give us

(-9)(-6) = 3x  

54 = 3x  divide both sides by 3

18 = x

Set up the second problem as a proportion

-9/3 = x/-5  This is a little trickier.  I am trying to think what I have to multiply 3 by to get -5.  3(-5/3)  will give me -5, so I will multiply the top number that I know (-9) by (-5/3) to find my x.

(-9)(-5/3) = 45/3  or 15

The domain for the function in this problem is given as follows:

0 ≤ x ≤ 5.

The domain of the function in this problem is the number of hours, which is represented by numbers between 0 and 5, as the hours cannot be negative and they played for 5 hours, hence the interval is given as follows:

0 ≤ x ≤ 5.

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