Solve the equation 6x = 72 for x.
x=

The distance between point P and line L is 16/9√(13).

To find the distance between point P and line L, we can use the formula for the distance between a point and a line in two-dimensional space. The formula is as follows:

Let P = (x1, y1) be the point and L be the line ax + by + c = 0. Then the distance between P and L is:

|ax1 + by1 + c|/√(a² + b²)

To find a, b, and c for the given line, we need to put it in slope-intercept form y = mx + b by solving for y.

2x - 3y = 12=> 2x - 12 = 3y=> (2/3)x - 4 = y

The slope of the line, m, is the coefficient of x, which is 2/3. Therefore, the line is:

y = (2/3)x - 4The values of a, b, and c are: a = 2/3b = -1c = -4

Now we can substitute the coordinates of P and the values of a, b, and c into the formula for the distance between a point and a line.

Let P = (3, 5).|a(3) + b(5) + c|/√(a² + b²)= |(2/3)(3) - 1(5) - 4|/√[(2/3)² + (-1)²]= |-4/3 - 4|/√(4/9 + 1)= 16/9√(13).

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Answer:

the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.

Step-by-step explanation:

o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").

Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:

m = -12% / 100 = -0.12

20

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

cuz itz IRRATIONAL

Answer:

1,3,4,6,8} { 1 , 3 , 4 , 6 , 8 }. Range:{2,4,5,7,9}

Step-by-step explanation:

The domain is the set of all the values of x x . The range is the set of all the values of y y .

Answer:

Let's start by assigning a variable to Susan's present age. Let's call it "x".

According to the problem, in seven years, Susan will be "x + 7" years old.

Three years ago, Susan was "x - 3" years old.

The problem tells us that Susan will be 2 times as old in seven years as she was 3 years ago. So we can set up the following equation:

x + 7 = 2(x - 3)

Now we can solve for x:

x + 7 = 2x - 6

x = 13

Therefore, Susan's present age is 13 years old.

Let's assume Susan's present age is "x" years. According to the information provided, "Susan will be 2 times old in seven years as she was 3 years ago."

Seven years from now, Susan's age would be x + 7, and three years ago, her age would have been x - 3. According to the given statement, her age in seven years will be two times her age three years ago:

x + 7 = 2(x - 3)

Let's solve this equation to find Susan's present age:

x + 7 = 2x - 6

Subtracting x from both sides:

7 = x - 6

Adding 6 to both sides:

13 = x

Therefore, Susan's present age is 13 years.

Answer:

42 dollars

Step-by-step explanation:

The perimeter and area of the square are 16√5 mm and 80 mm²

Perimeter of a square = 4L

where

Therefore,

Perimeter of a square = 4 × 4√5

Perimeter of a square = 16√5 mm

Area of a square = l²

Area of a square = (4√5)²

Area of a square = 16 × 5

Area of a square = 80 mm²

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a) Proportionately, when the speed of the bottle is 3 m/s, the average maximum height of the beanbag is 0.15 m.

b) Proportionately, when the speed of the bottle is 4 m/s, the average maximum height of the beanbag is 0.2 m.

c)  Proportionately, when the speed of the bottle is 5 m/s, the average maximum height of the beanbag is 0.25 m.

d) Proportionately, when the speed of the bottle is 6 m/s, the average maximum height of the beanbag is 0.3 m.

Proportion represents the quantity of a variable contained in another.

Proportions are like ratios that depict the relationships between two values.

As an equation, proportions are two ratios equated to each other.

Speed      Height

2 m/s         0.10

Unit rate = 0.5 m (0.10/2)

3 m/s         0.15 (0.5 x 3)

4 m/s         0.2 (0.5 x 4)

5 m/s         0.25 (0.5 x 5)

6 m/s         0.3 (0.5 x 6)

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The greatest common factor of 15 , 50 and 25 is A = 5

The Greatest Common Divisor is the highest number that divides exactly into two or more numbers. It is also expressed as GCF

Given data ,

Let the greatest common factor of the numbers be represented as A

Let the first number be a = 15

Let the second number be b = 50

And , the third number be c = 25

Now , the factors of 15 = 1 , 3 , 5 and 15

The factors of 50 = 1 , 2 , 5 , 10 , 25 and 50

The factors of 25 = 1 , 5 , and 25

Therefore, the GCF is 5

Hence , the greatest factor is 5

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The function that describes the table of values is y = 4x + 7

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

The table of values

From the table, we can see that

As x increases by 1

The y values increase by 4

So, we have

m = Slope = 4/1 = 4

The equation is calculated as

y = mx + c

So, we have

y = 4x + c

Using the other points, we have

c = 7

This gives

y = 4x + 7

Hence, the function that describes the table of values is y = 4x + 7

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Answer:

6

Step-by-step explanation:

-6 to 6 is 12 units

The equation of the line containing the paints A and B is y = -1/3x + 4

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

The graph

Where, we have

(6, 2) and (0, 4)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 4

Using the other points, we have

6m + 4 = 2

So, we have

6m = -2

Evaluate

m = -1/3

So, we have

y = -1/3x + 4

As an equation, we have

y = -1/3x + 4

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The ounces of ground sumac = 12

The ounces of ground thyme =8

From the question, we have

Let the ounces of ground sumac = x

Let the ounces of ground thyme = y

x+y=20...............(i)

1.25x+2.25y=20*1.65

1.25x+2.25y=33...............(ii)

Solving, we get

x = 12

y =8

Subtraction:

Subtraction serves as a representation for the act of removing items from a collection. The negative symbol stands for subtraction. For example, if four of the nine oranges that are stacked together (as in the above illustration) are then transported to a basket, the stack will now contain five oranges rather than nine. Therefore, the difference between 9 and 4 is 5, which equals 9 minus 4. In addition to applying it to natural numbers, subtraction can also be used with other kinds of numbers. The letter "-" represents subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation.

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Answer:

Step-by-step explanation:

cos = adjacent / hypotenuse

Correct choice is B

Answer:

The correct answer is "1668". A further solution is provided below.

Step-by-step explanation:

According to the question,

Estimated proportion,

\(\hat{p} = \frac{574}{1007}\)

  \(=0.57\)

Margin of error,

E = 0.02

Level of confidence,

= 90%

= 0.90

Critical value,

\(Z_{0.10}=1.65\)

Now,

⇒  \(0.02=1.65\times \sqrt{\frac{0.57\times 0.43}{n} }\)

 \(0.0004=2.7225\times \frac{0.2451}{n}\)

         \(n=\frac{2.7225\times 0.2451}{0.0004}\)

             \(=1668.21\)

or,

         \(n \simeq 1668\)

Answer:12.25

Step-by-step explanation:

Step-by-step explanation:

3^6  = 3 * 3^5

 = 3 * 243 =  729

Answer:

do the butterfly method if you don't know how to do that comment and I'll show you a screenshot

Answer:

3c

Step-by-step explanation:

3c im pretty sure. Since it is 3 times classic. classic is c. so rock must be R. so R=C3.

The number of employees with petrol cars is 423

In exponential decay, a quantity initially drops gradually before decreasing quickly. Finding the exponential drop of a fast reduction over time is made easier by the exponential decay formula.

The exponentially decreasing formula is used to calculate the radioactivity decay, population decay, and half-life.

The formula for Exponential Decay is given by

Here we have

In 2010, a total of 2187 of the employees at Zoe's company owned a petrol car.

In 2013, there were 1029 employees with petrol cars.  

The number of cars decreases exponentially,  

As we know the formula for Exponential Decay, A = P (1 - r)^t

From the given data,  a = 2187 and t = 3

The number of cars decreased = 2187 (1 - r)³

=> 2187 (1 - r)³ = 1029  

=> (1 - r)³ = 1029/2187

=> (1 - r)³ = 343/729  

=> (1 - r)³ = 7³/ 9³

=> 1 - r = 7/9

=> r = 1 - 7/9

=> r = 2/9

=> r = 0.2222

The Number of cars in 2017 i.e after 4 years from 2013

=> (1029)(1 - 0.2222)⁴

=> 423.0721516 ≅ 423          

Therefore,

The number of employees with petrol cars is 423

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The answer is x4 = input.nextDouble() and double avgnumber = (x1 + x2 + x3 + x4) / 4.

Declare the double variables x1, x2, x3, and x4.
double x1, x2, x3, x4;
Read each variable from input in that order.
Scanner input = new Scanner(System.in);
System.out.println("Enter x1:");
x1 = input.nextDouble();
System.out.println("Enter x2:");
x2 = input.nextDouble();
System.out.println("Enter x3:");
x3 = input.nextDouble();
System.out.println("Enter x4:");
x4 = input.nextDouble();
To Find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
double avgnumber = (x1 + x2 + x3 + x4) / 4;

//This code takes four double variables from input and calculates the average by adding the four numbers together and dividing by four. The result is stored in the double variable avgnumber.

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Answer:

a = - 27

Step-by-step explanation:

- \(\frac{2}{3}\) a - 6 = 12 ( add 6 to both sides )

- \(\frac{2}{3}\) a = 18 ( multiply both sides by 3 to clear the fraction )

- 2a = 54 ( divide both sides by - 2 )

a = - 27

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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Answer:

The Answer is B

Step-by-step explanation:

Answer: x < 10

Step-by-step explanation: Just like any of your two-step equations, in this inequality, start by isolating the x term which in this case is 6x by adding 5 to both sides.

That leaves you with 6x < 60 and now just divide both sides by 2 and x < 10.

Notice that because we divide both sides of the inequality

by a positive number, not a negative, we did not change the

direction of the inequality sign.

Finally, put your answer in set notation, {x: x < 10}.

Unlike an equation which normally has one solution, the answer to an inequality must be stated as a solution set because an entire set of answers will work. In this problem, it's any number less than 10.

The derivative of y relative to x is given as follows:

dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).

The function for this problem is defined as follows:

y = 4x²sin(x)cos(x)

The function is a product of three functions, hence the product rule is applied, as follows:

dy/dx = [4x²]'sin(x)cos(x) + 4x²[sin(x)]'cos(x) + 4x²sin(x)[cos(x)]'.

The derivatives are given as follows:

Hence the derivative of the function is defined as follows:

dy/dx = 8xsin(x)cos(x) + 4x²cos²(x) - 4x²sin²(x)

dy/dx = 8xsin(x)cos(x) + 4x²(cos²(x) - sin²(x)).

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The result of the number 1 trillion to the 10th power as required to be determined is; 10¹²⁰.

The result of the number 1 trillion to the 10th power is as follows;

Recall; 1 trillion = 1,000,000,000,000 = 10¹²

Hence; 1 trillion to the 10th power is; ( 10¹² )¹⁰.

From the laws of indices; we therefore have that;

= 10¹²⁰

Ultimately, the result is; 10¹²⁰.

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