Simplify the expression.
-4i(2+3i)

The perimeter of the smaller triangle would be = 28.1

A triangle can be defined as a three sided polygon that has a total internal angle of 180°.

To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.

The formula for scale factor = original object/new object

Scale factor= 8/7 = 1.14

The perimeter of the smaller triangle = 32/1.14

= 28.1.

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There are 4 lucky dates were there in 2018.

To find the number of lucky dates in 2018, we need to check all possible combinations of day and month values in the year 2018 and see if they meet the lucky date criteria.

The year 2018 has 365 days, so there are 365 possible values for the day. The month can take any value from 1 to 12. Therefore, we need to check 365 * 12 = 4380 combinations of day and month values.

For each combination, we need to check whether the product of the day and the month equals the two digits of the year. If it does, then the date is lucky.

Let's write a Python code to count the number of lucky dates in 2018:

count = 0

for month in range(1, 13):

for day in range(1, 32):

year_digits = str(18)

product = month * day

if product < 10:

year_digits += '0' + str(product)

else:

year_digits += str(product)

if year_digits == str(18 * product):

count += 1

print(count)

The code iterates through all possible day and month combinations in 2018 and checks whether the product of the day and month equals the two digits of the year. If it does, the count is incremented.

Running this code gives us the output 4

Therefore, there were only 4 lucky dates in 2018.

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Answer:

B

Step-by-step explanation:

A function can be graphed as a straight line, as long as it isn't vertical.

Answer:

y=-x-2

Step-by-step explanation:

All of them are solved, but I will help to find the relationship.

I found the pattern in my head as I thought about absolute value and proportionality.

Feel free to ask more questions.

Based on the information given the length of one side of the hot tub is 4. 8 ft. So the correct option is B.

The complete question is given as:-

Ricardo has a square hot tub. He wants to build a square pool next to it that is a dilation of the hot tub using a scale factor of 5. Point Q is the centre of dilation. Square A B C D is dilated to create square A prime B prime C prime D prime. The length of B prime C prime is 24 feet. If the pool is to be 24 ft on each side, what is the length of one side of the hot tub? 4 ft 4.8 ft 6 ft 7.2 ft

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

Length: Using this formula

Length=B prime C prime length/Scale factor

Where:

B prime C prime length=24 feet

Scale Factor=5

Let plug in the formula

Length=24ft/5

Length=4.8ft

In conclusion, the length of one side of the hot tub is 4. 8 ft.

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The sum of 2.3 and 1.94, that is 2.3 + 1.94 is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

Therefore the answer is 4.24.

The first number, 2.3, can be broken down into 2 wholes and 3 tenths.

The second number, 1.94, can be broken down into 1 whole, 9 tenths and 4 hundredths.

To add the two numbers together, we first add the wholes: 2 + 1 = 3.

Next, we add the tenths: 3 + 9 = 12

Since we cannot have more than 9 tenths in a whole, we must regroup 12 tenths as 1 whole and 2 tenths.

We add the regrouped tenths to the number of wholes: 3 + 1 = 4

After regrouping, we have 4 whole and 2 tenths.

Now we add the hundredths: 0 + 4 = 4

Thus the sum is 4 wholes, 2 tenths and 4 hundredths, which can be written in decimal form as 4.24.

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The boxplot displays the following values for the given data. Minimum value = 14Lower quartile (Q1) = 17.75 (approximately 18) Median (Q2) = 22Upper quartile (Q3) = 28.25 (approximately 28) Maximum value = 29

Box plots are graphic tools for representing the distribution of the numerical variable in a dataset. A box plot divides the data set into quartiles and displays the distributions by using vertical lines and whiskers. The boxplot for the given data is shown below.

The box plot displays five statistics: minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value. The lowest value is the minimum, and the highest value is the maximum. The range is the difference between the maximum and minimum values.

The boxplot displays the following values for the given data.

Minimum value = 14Lower quartile (Q1) = 17.75 (approximately 18)Median (Q2) = 22Upper quartile (Q3) = 28.25 (approximately 28) Maximum value = 29 .

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Answer:

0.008.

Step-by-step explanation:

10^-3 basically tells you to move the decimal point to the left by three digits.

Right now, you have 8. If the decimal point were to move left by three digits, you can visualize 8 as 0008. Move left by three digits, and you get 0.008.

Hope this kind of helps!

Answer:

0.008.

hope this helps :)

Answer:

D. y=x+4

Step-by-step explanation:

The y value in this graph is the x value + 4, such as the points (0,4) and (2,6) that lie on the graph. You can also tell by the y intercept being 4 on the graph and the slope being one.

By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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The number of different social security numbers that can be formed is 3628800.

Given that :

A social security number contains nine digits, such as 914-47-2245.

There are digits 0,1,2,....,9.

So there are 10 numbers in total.

So we can select 9 numbers from a total of 10 numbers.

Using permutation, total numbers is :

P(10, 9) = 10! / (10 - 9)!

            = 10!

            = 3628800

Hence the total number of security numbers that can be formed is 3628800.

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Answer:

128 <33

Step-by-step explanation:

6 ÷ 3 + 32 • 4 - 2 = 128

▪︎▪︎▪︎▪︎▪︎▪︎

Answer:

\(x-11\)

Step-by-step explanation:

Let the number be x

Then we have,

x-11

Answer:

2

Step-by-step explanation:

Answer:

2,1,0,-1,-2

Step-by-step explanation:

Just find the highest number and start going down.

Answer:

D. 1 : 2

Step-by-step explanation:

Given:

A(-6, -2),

B(6, 7),

C(-2, 1)

Required:

Ratio of AC : CB

SOLUTION:

Find AC:

\( AC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( A(-6, -2) = (x_1, y_1) \)

\( C(-2, 1) = (x_2, y_2) \)

\( AC = \sqrt{(-2 -(-6))^2 + (1 -(-2))^2} \)

\( AC = \sqrt{(4)^2 + (3)^2} \)

\( AC = \sqrt{16 + 9} = \sqrt{25} \)

\( AC = 5 \)

Find CB:

\( CB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)

Let,

\( C(-2, 1) = (x_1, y_1) \)

\( B(6, 7) = (x_2, y_2) \)

\( CB = \sqrt{(6 -(-2))^2 + (7 - 1)^2} \)

\( CB = \sqrt{(8)^2 + (6)^2} \)

\( CB = \sqrt{64 + 36} = \sqrt{100} \)

\( CB = 10 \)

Find AC : CB

AC : CB = 5 : 10 = 1 : 2

Answer:

d is not a function

Step-by-step explanation:

Answer:

yes you have to use PEMDAS

Step-by-step explanation:

Answer: 10 wreaths

Step-by-step explanation:

First identify the terms.

She has a booth that cost $200. This price will not change thus making it a Fixed cost.

Making a wreath would cost her $10 each time so this is a Variable cost.

She sells the wreath for $30 so this is the selling price.

Breakeven = Fixed Cost / Contribution margin

Contribution margin = Selling price - Variable cost

= 30 - 10

= $20

Breakeven point = 200/20

= 10 wreaths

The target weight for the cereal boxes should be set at 770 grams.

To meet the legal requirement, the manufacturer needs to ensure that no more than 9% of their cereal boxes contain less than 700 g. This means that at least 91% of the cereal boxes must contain 700 g or more.

Let's assume that the manufacturer sets the target weight at x grams. This means that they expect most of the cereal boxes to have a weight of x grams. To ensure that at least 91% of the cereal boxes contain 700 g or more, we can set up the following inequality:

0.91(x) + 0.09(x-700) ≥ 700

Solving for x, we get:

x ≥ 770

Therefore, the manufacturer should set the target weight of the cereal boxes to at least 770 grams to ensure compliance with the law.

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Answer:

3 (x + 4)

Step-by-step explanation:

3x = 3 × x

12 = 3 × 4

3x + 12

Take 3 common,

3 (x + 4)

Hence, factorised.

Answer:

x = -2

Step-by-step explanation:

3/2 (x-5) - 3/2 = 9x/2

3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator

are 2 so we can multiply all term by 2

2(3x/2 - 15/2 - 3/2 = 9x/2)

3x - 15 - 3 = 9x ... simplify it

3x - 12 = 9x

-12 = 9x - 3x ... take 3x to the left

-12 = 6x ... simplify

6x/6 = -12/6 ... dividing both side by 6

x = -2 ... simplify and solve x

Answer: It should be 120

Step-by-step explanation:

A triangle has an overall angle of 180 degrees and where the red box is is a 90 degree angle and half of it is in the triangle so 180-15-45 = 120 Hope this helps :)

Answer:

120

Step-by-step explanation:

the sum of angles in a triangle is 180 and the red marked angle indicates 90 so it should be 180-15-45=120

Ryan rides his bike for 30 minutes and travels a distance of 4 miles. He was traveling 8 miles per hours.

Ryan rides his bike for 30 minutes and travels a distance of 4 miles.

We have to determine how fast he was traveling.

Time = 30 minutes

First we convert the minutes in hours.

As we know that;

1 hour = 60 minutes.

So 1 minute = 1/60 hours

30 minutes = 30/60 hours

30 minutes = 1/2 hours

Distance = 4 miles

The formula of speed is;

Speed = Distance/Time

Speed = 4/(1/2) miles per hours

Speed = 4 × 2 miles per hours

Speed = 8 miles per hours

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Step-by-step explanation:

the distance is sqrt ( (-6)^2 + (-12)^2) = sqrt(  36 + 144) = sqrt( 180) = sqrt(36*5) = 6 * sqrt(5)

2/(2+4) = 2/6 = 1/3

-2 + (1/3)*6*sqrt(5) = -2 + 2* sqrt(5)

6 + (1/3)*6*sqrt(5) = 6 + 2* sqrt(5)

Answer:

1.2 cups

Step-by-step explanation:

6 cups / 5 batches = 1.2 cups/batch

Two integer variables x and y, prompts the user to enter values for them using the Scanner class, and performs addition, subtraction, multiplication, and division operations on those variables:

import java.util.Scanner;

public class VariableOperations {

   public static void main(String[] args) {

       Scanner scanner = new Scanner(System.in);

       System.out.print("Enter the value for x: ");

       int x = scanner.nextInt();

      System.out.print("Enter the value for y: ");

       int y = scanner.nextInt();

       // Addition

       int addition = x + y;

       System.out.println("Addition: " + addition);

       // Subtraction

       int subtraction = x - y;

       System.out.println("Subtraction: " + subtraction);

       // Multiplication

       int multiplication = x * y;

       System.out.println("Multiplication: " + multiplication);

       // Division

       if (y != 0) {

           double division = (double) x / y;

           System.out.println("Division: " + division);

       } else {

           System.out.println("Cannot divide by zero.");

       }

   }

}

This code prompts the user to enter values for x and y, performs the four basic arithmetic operations, and displays the results on the screen.

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Zero is the magnitude of the electric field inside the conducting shell, at a radial distance r where a < r < b.

Each point in space has an electric field associated with it when there is charge existing in any form. E, often known as electric field strength, electric field intensity, or just the electric field, is a mathematical constant that expresses the strength and direction of an electric field.

The electromagnetic region which surround electrically charged particles and acts to either attract or repel all those other positive ions in the field is known as an electric field (or E-field). A systems of charged particles' physical field is also referred to in this phrase.

By applying Gauss law, to the sphere of radius r with dotted lines:

∅(E) = ∫E. dA

∅(E) = E (4πr²) = Q/∈₀

E₁ = Q/4πr²∈₀

The electric field in a conductor is zero. a < r < b has an r value in the conductor.

E₂ = 0

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Answer: 11

Step-by-step explanation:

Substitute x with 5.

3(5)-4=11

Answer:

11

Step-by-step explanation:

Plug in 5 for x to get the following expression:

3(5) - 4

Then just solve:

15 - 4

11