Triangle ABC, with coordinates A(2, 3), B(3, 5), C(7, 4), is dilated by a scale factor of 2. What are the coordinates of the dilated figure, triangle A′B′C′?

Answer:

Solving the equation \(\frac{a^2-b^2}{2+d^3}\) by putting a=6, b=4 and d=1/2 we get \(\frac{160}{17}\)

Step-by-step explanation:

We are given formula: \(\frac{a^2-b^2}{2+d^3}\)

and values a=6, b=4 and d=1/2

We need to put the values of a, b and d in the given equation \(\frac{a^2-b^2}{2+d^3}\) and find their result

Putting values in the equation:

\(\frac{a^2-b^2}{2+d^3}\\=\frac{(6)^2-(4)^2}{2+(\frac{1}{2})^3}\\=\frac{36-16}{2+\frac{1}{8}}\\=\frac{20}{\frac{2*8+1}{8}}\\=\frac{20}{\frac{17}{8}}\\=\frac{20*8}{17}\\=\frac{160}{17}\)

So, solving the equation \(\frac{a^2-b^2}{2+d^3}\) by putting a=6, b=4 and d=1/2 we get \(\frac{160}{17}\)

Answer:

Y=⅘X+2. the picture not clear so i hesitate

Answer:

Explicit formula *******

Answer: 25%

Step-by-step explanation: The total number of city council is 80 and 20/80 is 1/4

The general solution of an exact differential equation can also be found by solving the associated homogenous equation and adding the particular solution obtained from the original equation.

1. Identify the exact differential equation.

2. Find the integrating factor by multiplying the equation by an expression of the form e^(f(x)).

3. Multiply the integrating factor with the equation to make it exact.

4. Integrate both sides of the equation to obtain the general solution.

5. Check the solution by differentiating it to confirm that it satisfies the original equation.

6. Add the particular solution obtained from the original equation to the homogenous solution to get the general solution.

The general solution of an exact differential equation can be found by using an integrating factor. An integrating factor is a function of the independent variable which can be multiplied with the equation in order to make it exact. Once the equation has been made exact, it can be solved using the standard integration techniques. In addition, the general solution can be found by solving the associated homogenous equation and then adding the particular solution obtained from the original equation.

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer: 3,250

Step-by-step explanation:

1) Find the sample space for the experiment of tossing a six-sided die three times and recording the sum:
The minimum sum occurs when you roll a 1 on each toss (1+1+1=3), and the maximum sum occurs when you roll a 6 on each toss (6+6+6=18). So, the sample space for this experiment is {3, 4, 5, ..., 18}.

2) Find the sample space for the experiment of a taste tester ranking three varieties of yogurt, A, B, and C, according to preference:
The taste tester can rank the yogurts in any order, so there are 3! (3 factorial) or 6 possible rankings. The sample space for this experiment is {ABC, ACB, BAC, BCA, CAB, CBA}.

3) Find the sample space for the experiment of selecting two county supervisors from five supervisors, A, B, C, D, and E, to study a recycling plan:
There are C(5, 2) or 10 possible combinations of supervisors. The sample space for this experiment is {AB, AC, AD, AE, BC, BD, BE, CD, CE, DE}.

To know more about"Sample space" refer here:

https://brainly.com/question/24273864#

#SPL11

Answer:

39

Step-by-step explanation:

4 cubed is 64 and 64-25 is 39

Good luck!

After solving the given expression, the value obtained for the difference between 4³ and 25 will be equal to 39.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers.

Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given statement in the question,

The difference between 4³ and 25 will be,

4³ = 64

Then,

64 - 25 = 39

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ5

The terminal point of sin t, cost, and tan t is:

sin t = 3/5
cos t = 4/5
tan t = 3/4


To find sin t, cos t, and tan t for the terminal point P(x, y) = (4/5, 3/5) determined by a real number t, we need to use the trigonometric ratios of sine, cosine, and tangent.

First, we need to find the values of x and y from the given coordinates of P. Since P is on the unit circle, we know that the distance from the origin to P is 1.

Therefore, we can use the Pythagorean theorem to find the value of the missing side:
x^2 + y^2 = 1^2
(4/5)^2 + (3/5)^2 = 1
16/25 + 9/25 = 1
25/25 = 1

So, x = 4/5 and y = 3/5.

Next, we can use the definitions of sine, cosine, and tangent to find their values for t:
sin t = y/1 = 3/5
cos t = x/1 = 4/5
tan t = y/x = (3/5)/(4/5) = 3/4

Then, we obtain:
sin t = 3/5
cos t = 4/5
tan t = 3/4

Know more about the terminal point  here:

https://brainly.com/question/1621860

#SPJ11

a. The probability that  X is less than 94 is 0.0808.
b. The probability that  X is between 94 and 96.5 is 0.1033.
c. The probability that  X is above 102.8 is approximately 0.3569.



a. To find the probability that  X is less than 94, we need to standardize the value using the formula z = ( X- u) / (σ / √n).

Substituting the given values, we have z = (94 - 101) / (15 / √9) = -2.14. Using a standard normal distribution table or calculator, we find that the probability associated with z = -2.14 is 0.0162.

However, since we want the probability of  X being less than 94, we need to find the area to the left of -2.14, which is 0.0808.

b. To find the probability that  X is between 94 and 96.5, we can standardize both values. The z-score for 94 is -2.14 (from part a), and the z-score for 96.5 is (96.5 - 101) / (15 / √9) = -1.23.

The area between these two z-scores can be found using a standard normal distribution table or calculator, which is 0.1033.


c. To find the probability that  is above 102.8, we can calculate the z-score for 102.8 using the formula z = ( X- u) / (σ / √n).

Given:
u = 101
σ = 15
n = 9
X = 102.8

Substituting the values into the formula, we have:

z = (102.8 - 101) / (15 / √9)
z = 1.8 / (15 / 3)
z = 1.8 / 5
z = 0.36

To find the probability associated with z = 0.36, we need to find the area to the left of this z-score using a standard normal distribution table or calculator.

P(z < 0.36) = 0.6431

However, we want to find the probability that  X is above 102.8, so we need to subtract this value from 1:

P(X > 102.8) = 1 - P(z < 0.36)
P(X > 102.8) = 1 - 0.6431
P(X > 102.8) = 0.3569

Therefore, the probability that  X is above 102.8 is approximately 0.3569.


Learn more about Probability click here :brainly.com/question/30034780
#SPJ11

Answer:

x > - 1

Step-by-step explanation:

- 10 < x - 9 ( add 9 to both sides )

- 1 < x , therefore

x > - 1

Answer:

x > -1

Step-by-step explanation:

why:

-10  < x-9         for exemple 2< 3

x-9  > -10                 3 > 2      

just add 9 to both sides

x-9 +9 > -10 +9

x > -1

meth2

x-9  > -10  

x > -10 +9       left  to right

x> -1

Answer:

250 minutes.

Step-by-step explanation:

1/5=50/x

cross product

5*50=1*x

250=x

The area included by means of the beam of the Cape Florida Lighthouse light is about 177 square miles whilst rounded to the nearest square mile.

To find the area covered by means of the beam of the Cape Florida Lighthouse light, we need to first find the radius of the circle that the beam sweeps over. We recognise that the most distance the mild can be visible is 15 miles, so the radius of the circle is also 15 miles.

Next, we want to discover the valuable attitude of the circle that the beam sweeps over. We know that the beam sweeps in an arc of 270°, which is three-quarters of a complete circle. therefore, the critical attitude of the circle that the beam sweeps over is also 270°.

Now, we are able to use the formula for the area of a sector of a circle to discover the area covered through the beam:

area of sector = (central angle/360°) x π x radius^2

Substituting the given values, we get:

Thus, the area included by means of the beam of the Cape Florida Lighthouse light is about 177 square miles whilst rounded to the nearest square mile.

Learn more about area of a sector of a circle:-

https://brainly.com/question/9406374

#SPJ4

We know that all three terms are important in supervisory experience, but "content" is one that is more crucial than the others

The terms mentioned in your question are "content", "loaded", and "important". In the context of supervisory experience, these terms refer to the quality and quantity of information and tasks assigned to subordinates.

"Content" refers to the information and tasks that are communicated by the supervisor to the subordinate. This includes instructions, feedback, and guidance on how to perform tasks effectively.

"Loaded" refers to the amount of information and tasks that are assigned to subordinates. This can be overwhelming if the workload is too heavy, which can lead to stress and burnout.

"Important" refers to the significance of the information and tasks assigned to subordinates. This relates to the impact that these tasks have on the overall success of the team or organization.

When it comes to supervisory experience, all three terms are important. However, the term "content" is one that is more important than the others. This is because the quality of information and guidance provided by the supervisor has a significant impact on the subordinate's ability to perform tasks effectively. A lack of clear guidance can result in confusion, mistakes, and delays in completing tasks.

The amount of information and tasks assigned to subordinates also has an impact on the supervisory experience. If the workload is too heavy, it can lead to stress and burnout, which can negatively impact job performance. Therefore, supervisors need to balance the workload to ensure that subordinates are not overwhelmed.

The significance of the information and tasks assigned to subordinates also plays a crucial role in supervisory experience. If tasks are not important or relevant, subordinates may feel demotivated or disengaged. Therefore, supervisors need to ensure that tasks are aligned with the team's goals and contribute to the overall success of the organization.

In terms of the subordinate's experience, all three terms play a critical role. Clear and concise instructions (content) can help subordinates perform tasks effectively. A balanced workload (loaded) can help subordinates manage their time and reduce stress. Assigning important tasks (important) can help subordinates feel valued and motivated to contribute to the team's success.

In conclusion, all three terms are important in supervisory experience, but "content" is one that is more crucial than the others. Providing clear guidance and instructions can help subordinates perform tasks effectively, which ultimately leads to team success.

To know more about  supervisory refer here

https://brainly.com/question/30753003#

#SPJ11

Answer:

the answer would be B: 4x=3y

Step-by-step explanation:

this is perimeter which means that you add the side lengths all together.

5x-3y+x+4y-2x+2y

then you just add the like terms

Answer:

b) 4x + 3y

Step-by-step explanation:

add all equations (perimeter = side + side + side)

P= 5x-3y + x+4y -2x+2y

combine like terms

5x + x - 2x = 4x and -3y + 4y + 2y = 3y

P = 4x + 3y

The correct statement among the given options is "Qualitative data is usually nonnumeric.

Qualitative data is the data that are in the form of non-numerical data, which are usually words, images, or objects.

It refers to data that has a descriptive attribute such as color, smell, shape, or texture.

Qualitative data is collected through methods such as surveys, interviews, observations, and focus groups.

Qualitative data is typically associated with the social sciences such as anthropology, sociology, history, and psychology.

The study of qualitative data is a relatively new field of research that has gained popularity in recent years.

It is used in a variety of disciplines, including marketing research, social science research, and health research.

So, the correct statement is that Qualitative data is usually nonnumeric.

https://brainly.com/question/1417786?referrer=searchResults

#SPJ11

The number of homes in a community of 12, 000 which would be heated by electricity, given the rate of houses heated, is c. 3,360 homes

To find the number of homes in the community which would be heated by electricity, first find the percentage of homes that are heated according to the U.S. Census :

= Number of houses heated / Total number

= 7 / 25

= 28 %

When given a community of 12, 000 homes therefore, the number of homes which would be heated are:

= Percentage of houses heated x Community size

= 28 % x 12, 000

= 3,360 homes

Find out more on homes heated at https://brainly.com/question/26441119

#SPJ1

Answer:

c. 3,360 homes

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

25x + 200 > 1,200

Subtract 200 from each side

25x + 200-200 > 1,200-200

25x> 1000

Divide by 25

25x/25 >1000/25

x>40

Answer:

26

Step-by-step explanation:

w = 5 so 7w is 7 x 5 = 35 and x = 9 so it’s 35 - 9 which is 26

Yes, from the attached diagram triangle ABC and triangle ADC are congruent to each other by SSS congruency.

As given in the question,

In the attached diagram,

In triangle ABC and triangle ADC,

As given in the diagram we have,

AD ≅ AB ( given )

CD ≅ BC ( given )

AC ≅ CA ( Common side )

By SSS ( Side - Side - Side ) congruent theorem we have,

Triangle ABC is congruent to the triangle ADC.

ΔABC ≅ ΔADC

Therefore, the triangle ABC, and triangle ADC are congruent to each other using SSS( Side - Side - Side ) congruent theorem.

Learn more about triangle here

brainly.com/question/2773823

#SPJ4

In linear equation, 157 did Terry's front wheel complete.

What is a linear equation example?

Terry goes for a cycle and travels 60.32km.

 so, 60.32 * 1000 ÷ ( 2 * 3.14 * 61 )

   = 60320 ÷ 2 * 3.14 * 61

   = 60320 ÷ 6.28  * 61

    = 60320 ÷ 383.08

     = 6032000/ 38308

     = 1508000/9577

    = 157

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

Answer:

\(x {}^{3} \)

Step-by-step explanation:

\(\frac{(x {}^{5} )}{( {x}^{2} )}\)

\(x {}^{3} \)

Answer:

Different cuts can produce cross sections that are congruent to the base, a side, or even triangles if the cut is through the corner of a prism. A slice that is not parallel to the base and contains points from the four vertical edges of the prism reveals a parallelogram.

Step-by-step explanation:

hope this helps

Answer:

An irregular pentagonal prism

The angle measurement would remain as 40 degrees

No, when a geometric figure, such as a line or an angle, is translated (moved) to a new position without being rotated, reflected, or scaled, its shape and size do not change, and therefore its angle measure remains the same.

This property is a fundamental concept in geometry and is known as the "invariance of angle measure under translation". It means that if two angles are congruent (have the same measure) in their original position, they will remain congruent after being translated to a new position.

Hence The angle measurement would remain as 40 degrees

Read more on translation in mathematics here:https://brainly.com/question/1046778

#SPJ1

To prove the SSS Inequality Theorem using an indirect proof, we need to assume the opposite of what we are trying to prove and show that it leads to a contradiction.

The SSS Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Assume that there exists a triangle ABC where the sum of the lengths of two sides is not greater than the length of the third side. Without loss of generality, let's assume that AB + BC ≤ AC.

Now, consider constructing a triangle ABC where AB + BC = AC. This would mean that the triangle is degenerate, where points A, B, and C are collinear.

In a degenerate triangle, the sum of the lengths of any two sides is equal to the length of the third side. However, this contradicts the definition of a triangle, which states that a triangle must have three non-collinear points.

Therefore, our assumption that AB + BC ≤ AC leads to a contradiction. Hence, the SSS Inequality Theorem holds true, and for any triangle, the sum of the lengths of any two sides is greater than the length of the third side.

Learn more about Inequality here

https://brainly.com/question/30238989

#SPJ11

The answer is (C) newspapers. Convenience products are low-cost consumer goods and services that are readily available and easily accessible to consumers.

These products are typically purchased frequently, with minimal effort and little thought or research. Examples of convenience products include bread, gasoline, newspapers, and other everyday items that consumers purchase without much consideration.

Cars, furniture, large appliances, and a cruise are not typically considered convenience products. These are generally higher-cost items that require more thought and research before purchase.

Learn more about  bread here:

https://brainly.com/question/13001375

#SPJ11

Answer:

\(f(x)=0.5x^2-4x+7.5\)

Step-by-step explanation:

The general form of a quadratic function is:

\(y=ax^2+bx+c\)

We'll find the general form of the function:

\(f(x)=0.5(x-3)(x-5)\)

Multiplying the expressions in parentheses:

\(f(x)=0.5(x^2-5x-3x+15)\)

Simplifying:

\(f(x)=0.5(x^2-8x+15)\)

Operating:

\(\mathbf{f(x)=0.5x^2-4x+7.5}\)

1.Confidence level/Confidence coefficient

2.Estimation rule/Estimator

3.Margin of error

4.Point estimate

5.Confidence interval

6.Unbiased

7.Minimum

8.Efficiency

9lSample mean

10.Sample size

The degree of confidence attached to an interval estimate is called the confidence level or confidence coefficient. It represents the probability that the interval estimate contains the true parameter value.

A rule that calculates an estimate of a parameter of interest is called an estimation rule or an estimator. It is a mathematical formula or method used to calculate an estimate based on sample data.

The size of the error of estimation should not exceed the margin of error. The margin of error represents the maximum amount by which the estimate is expected to deviate from the true parameter value.

A single computed value used to represent an unknown parameter is called a point estimate. It is a specific value determined from the sample data and serves as an estimate for the population parameter.

An interval estimate with an attached level of confidence is called a confidence interval. It provides a range of values within which the true parameter is believed to lie with a certain level of confidence.

An estimator is unbiased if the mean of its sampling distribution is equal to the true value of the parameter. In other words, an unbiased estimator does not systematically overestimate or underestimate the parameter.

The best point estimator for a parameter of interest must have the minimum variance among all other estimators. A low variance indicates that the estimator provides more precise and reliable estimates.

Efficiency is a measure of how well an estimator performs compared to others. An efficient estimator has the smallest variance among a class of unbiased estimators.

The sample mean is the best point estimator for the population mean. It is unbiased and has the minimum variance among all unbiased estimators for the population mean.

To obtain a narrow interval estimate with a high confidence level, the sample size must be increased. A larger sample size reduces the margin of error and provides a more precise estimate.

Learn more about parameter here: brainly.com/question/12912389

$SPJ11

Answer:

B. 15

Step-by-step explanation:

Step by Step Solution

More Icon

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "11.3" was replaced by "(113/10)".

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                    b-((113/10))>0  

Step by step solution :

STEP

1

:

           113

Simplify   ———

           10  

Equation at the end of step

1

:

      113

 b -  ———  > 0  

      10  

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  10  as the denominator :

         b     b • 10

    b =  —  =  ——————

         1       10  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

b • 10 - (113)     10b - 113

——————————————  =  —————————

      10              10    

Equation at the end of step

2

:

 10b - 113

 —————————  > 0  

    10    

STEP

3

:

3.1    Multiply both sides by  10  

3.2    Divide both sides by  10  

     b-(113/10)  > 0

Solve Basic Inequality :

3.3      Add  113/10  to both sides

            b > 113/10

Inequality Plot :

3.4      Inequality plot for

        b  - 11.300  >  0

One solution was found :

b > 113/10

Which number is a solution of the inequality?

b > 11.3

The answers are 15,9,-14, and 4

15