HELP ASAP WILL GIVE BRAINLIEST
Which type of transformation is shown?
• A. A rotation
• B. A dilation
O C. A reflection
• D. A translation

HELP ASAP WILL GIVE BRAINLIESTWhich Type Of Transformation Is Shown? A. A Rotation B. A DilationO C.

Answers

Answer 1

Answer:

Dilation

Step-by-step explanation:

The  a'b'c'    figure is larger than the original a b c


Related Questions

1 Total surface area = units?​

1 Total surface area = units?

Answers

Answer:

The answer is Thirty Six (36)

Answer:

36 g

Step-by-step explanation:

Which of the following is the correct sequence of project phases? O A. Concept - Planning - Definition O B. Definition - Planning - Performance O C. Postcompletion - Performance - Planning OD. Performance - Concept - Planning

Answers

The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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at the 0.01 significance level, do women save more money than men? what is the value of the test statistic for this hypothesis test? men 25 50

Answers

The value of the test statistic for this hypothesis test = 1%

Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis. Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.

When a discovery in statistical hypothesis testing is highly improbable to have occurred given the null hypothesis, it is said to have statistical significance.

\(H_{O}\) : Mean of mean = mean of women

\(H_{a}\) : means of men < mean of women

(Left tailed test)

Since population standard deviation is known but sample sizes are small t test is used.

The mean of Men minus Women equals = -5.00

standard error of difference = 2.201

t = 2.2721

\(df\)= 53

p value = 0.0136

since p >0.01 at 1% significance level we fail to reject \(H_{O}\) .

Both means are approximately equal at 1% level of significance.

Therefore,

The value of the test statistic for this hypothesis test = 1%

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Jason read a total of 8 books over 4 months. If Jason has read 16 books so far, how many months has he been with his book club? Solve using unit rates. its worth 100 points

Answers

Answer:

8 months

Step-by-step explanation:

I got it right

for what value of k will x+k/x have a relative maximum at x=-2

Answers

when k = 4, the function x + k/x will have a relative maximum at x = -2.

To find the value of k that will make x+k/x have a relative maximum at x=-2, we can use the first derivative test.

First, we find the derivative of x+k/x with respect to x:

f'(x) = 1 - k/x^2

Next, we set x = -2 and solve for k to make f'(-2) = 0:

f'(-2) = 1 - k/(-2)^2 = 1 - k/4

1 - k/4 = 0

k = 4

what is derivative?

A derivative is a mathematical concept that represents the rate at which a function changes over time or space. It is the slope of a tangent line to a curve at a particular point.

In other words, the derivative of a function f(x) at a point x=a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim[h→0] [f(a+h) - f(a)]/h

The derivative gives us information about how quickly the function is changing at a specific point.

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what is 560.6928631 feet to the nearest foot ?

Answers

Answer:

561

Step-by-step explanation:

skillz

ע\
How do I solve slopes

Answers

Answer:

Y\(\frac{y_{2}-y_{1}}{x_2-x_1}\) or Y2-Y1/X2-X1

Step-by-step explanation:

hope this helps

i will not be angry from you if you brainlisted me

What is the equation of the line through (2, –1) and (0, 5)?

Answers

Answer:

B

Step-by-step explanation:

To find the equation, we can use the point-slope form:

Where m is the slope and (x₁, y₁) is a point.

First, we will need to find the slope. Since we have two points, we can use the slope formula:

Let (2, -1) be (x₁, y₁) and let (0, 5) be (x₂, y₂). Substitute appropriately and evaluate:

Therefore, the slope m is -3.

Now, we can use the point-slope form. We also need a point. Let’s use (2, -1) for consistency. So, we will substitute -3 for m and (2, -1) for (x₁, y₁). This yields:

We will now convert this to slope-intercept form. Simplify the left and distribute the right:

Subtract 1 from both sides. Therefore, our equation is:

Thus, our answer is B.

Answer:

(y-y1)=m(x-x1)

y+1=5+1/0-2(x-2)

y+1=6/-2(x-2)

-2y-2=6x-12

6x+2y+14=0

If a road map has a scale of 3 in: 100 mi, find the following distances
How far is it between Cardwell and Claremont if they are 4.5 inches apart on the map?

Answers

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

If a road map has a scale of 3 inches to 100 miles.

Then the scale factor is given as,

Sclar factor = 100 / 3

Sclar factor = 33.33 miles per inch

Then the distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be given as,

Distance = 33.33 x 4.5

Distance = 150 miles

The distance between Cardwell and Claremont if they are 4.5 inches apart on the map will be 150 miles.

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what are the relationships of numerator and denominator coefficients with r, l, and c values of a circuit?

Answers

The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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Use the Distributive Property to solve the equation6(x-6)+6=8x-12. ​ The solution of the equation is nothing. ​(Type the value of​ x.)

Answers

Answer:

The solution of the equation is x = -9

Step-by-step explanation:

∵ The equation is 6(x - 6) + 6 = 8x - 12

→ Use the distributive property to simplift the left sid

∵ 6(x - 6) = 6(x) - 6(6) ⇒ Distributive property

6(x - 6) = 6x - 36

6x - 36 + 6 = 8x - 12

→ Add the like terms in the left side

∴ 6x + (-36 + 6) = 8x - 12

∴ 6x + (-30) = 8x - 12

6x - 30 = 8x - 12

→ Subtract 8x from both sides

∴ 6x - 8x - 30 = 8x - 8x - 12

∴ -2x - 30 = -12

→ Add 30 to both sides

∴ -2x - 30 + 30 = -12 + 30

∴ -2x = 18

→ Divide both sides by -2

∵ \(\frac{-2x}{-2}=\frac{18}{-2}\)

x = -9

∴ The value of x is -9

9514 1404 393

Answer:

  -9

Step-by-step explanation:

The distributive property is used to eliminate parentheses.

  6(x -6) +6 = 8x -12

  6x -36 +6 = 8x -12 . . . . . . . distribute 6 to x and -6

  -30 = 2x -12 . . . . . . . . . . . . .subtract 6x, collect terms

  -18 = 2x . . . . . . . . . . . . . . . . add 12

  -9 = x . . . . . . . . . . . . . . . . . . divide by 2

The value of x is -9.

_____

Check

6(-9 -6) +6 = 8(-9) -12

6(-15) +6 = -72 -12

-90 +6 = -84 . . . . . . . true

Solve the equation for t^2 +15t=-36.

Answers

Answer:

t=−3 or t=−12

Step-by-step explanation:

Step 1: Subtract -36 from both sides.

t2+15t−(−36)=−36−(−36)

t2+15t+36=0

Step 2: Factor left side of equation.

(t+3)(t+12)=0

Step 3: Set factors equal to 0.

t+3=0 or t+12=0

t=−3 or t=−12

Can you guys please help me again

Can you guys please help me again

Answers

Answer:

its D    1  7/8 also which is 1R7

Step-by-step explanation:

mark me as brainliest

Find the equation of the line with slope = 2 and y-intercept = -8.​

Find the equation of the line with slope = 2 and y-intercept = -8.

Answers

Answer: d

Step-by-step explanation:

Using the linear equation y=mx+b, you are given m (the slope) and b (the y-intercept). m=2 and b=-8. Therefore, y=2x-8

A sphere of radius 3 in is initially at a uniform temperature of 70 F. How long after being immersed in a liquid at 1000 F with an associated heat transfer coefficient h of 10BTU/(h−ft 2
−F) will the temperature at the center of the sphere reach 907 F if the sphere is made from (a) Copper, k=212BTU/(h−ft−F),rho=555lb/ft 3
,c p

=0.092BTU/(lb−F) (b) Asbestos, k=0.08BTU/(h−ft−F),rho=36lb/ft 3
,c p

=0.25BTU/(lb−F) In each case determine if a lumped analysis applies or a distributed analysis applies. Note that the Biot number is defined as Bi= k
h V
/A

. Consequently, for a sphere, Bi= 3k
hR

where R is the sphere radius. Also, there is no need to derive any results already derived in class or available in the textbook.

Answers

Using a numerical method such as the Newton-Raphson method, the first root of J₁(x)/x is found to be approximately 3.83.

Therefore, α = 3.83/3.

For a sphere of radius r, volume V, and surface area A (which is given by 4πr²), the Biot number can be defined as:

Bi=khV/A

where k is the thermal conductivity of the sphere material, h is the heat transfer coefficient and rho is the density of the material and cp is the specific heat of the material.

(a) For Copper, k = 212 BTU/(h-ft-F), rho = 555 lb/ft³, cp = 0.092 BTU/(lb-F)

The Biot number for copper can be calculated as:Bi = 3k/hR= (3 × 212)/(10 × 3 × 1) = 6.36

Therefore, a lumped analysis applies since Bi < 0.1.

Since a lumped analysis applies, the temperature of the sphere can be determined using the following equation:

T(t) - Ta = (Ti - Ta) × exp(-hAt/mc p

)where T(t) is the temperature of the sphere at time t, Ta is the ambient temperature of the surroundings (1000°F), Ti is the initial temperature of the sphere (70°F), m is the mass of the sphere, and t is the time.

The mass of the sphere can be calculated as:

m = rhoV= 555 × (4/3) × π × (3³) = 113097.24 lb

The specific heat capacity of copper is cp = 0.092 BTU/(lb-F).

Therefore, the product mc p is given by:

mc p = 113097.24 × 0.092 = 10403.0768

The temperature at the center of the sphere reaches 907°F after 53.06 seconds, which is calculated using:

T(t) = Ta + (Ti - Ta) × exp(-hAt/mc p)

= 1000 + (70 - 1000) × exp(-10 × 4π × (3)² × t/10403.0768)  

= 907

(b) For Asbestos, k = 0.08 BTU/(h-ft-F), rho = 36 lb/ft³, cp = 0.25 BTU/(lb-F)

The Biot number for asbestos can be calculated as:

Bi = 3k/hR= (3 × 0.08)/(10 × 3 × 1) = 0.072

Therefore, a distributed analysis applies since Bi > 0.1.

Thus, the temperature distribution within the sphere needs to be considered.

The temperature distribution is given by:

T(r,t) - Ta = (Ti - Ta) [I₀(αr) exp(-α²ht/ρcp)] / [I₀(αR)]

where I₀ is the modified Bessel function of the first kind of order zero, α is the first root of I₁(x)/x and R is the radius of the sphere.

The temperature at the center of the sphere can be determined by setting r = 0:

T(0,t) - Ta = (Ti - Ta) [I₀(0) exp(-α²ht/ρcp)] / [I₀(αR)]T(0,t) - Ta

= (Ti - Ta) exp(-α²ht/ρcp)T(0,t)

= Ta + (Ti - Ta) exp(-α²ht/ρcp)

The mass of the sphere can be calculated as:

m = rhoV= 36 × (4/3) × π × (3³) = 7322.4 lb

The specific heat capacity of asbestos is cp = 0.25 BTU/(lb-F).

Therefore, the product mc p is given by:

mc p = 7322.4 × 0.25 = 1830.6The temperature at the center of the sphere reaches 907°F after 72.6 seconds, which is calculated using:

T(0,t) = Ta + (Ti - Ta) exp(-α²ht/ρcp)

= 1000 + (70 - 1000) exp(-α² × 10 × 72.6/1830.6)

= 907

The value of α can be determined by solving the following equation:

J₁(x) = 0where J₁ is the Bessel function of the first kind of order one.

Using a numerical method such as the Newton-Raphson method, the first root of J₁(x)/x is found to be approximately 3.83.

Therefore, α = 3.83/3.

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PLSS I MADE IT CLEARER THIS TIME​

Answers

Maybe you did make it clearer but there’s no attachment this time lol

Answer:

There is still no attachment.

Step-by-step explanation:

What is 437 rounded to the nearest whole number

Answers

Answer:

437

437 is a whole number itself, so it would be 437.

Hope that helps!

Step-by-step explanation:

The number is 400 since it’s the nearest

If Hannah weights 29 pounds and her medicine says dosage of child weight 10-15 mg/kg what is Hannah weight in kilograms? Round to the nearest hundredth

Answers

Answer:

13.16

Step-by-step explanation:

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate?a. ​+1​b. 0​c. Infinity​d. -1

Answers

Answer:

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate b. 0​

Step-by-step explanation:

If the plots on a scatter diagram lie on a straight line in a simple linear regression model, it indicates a perfect fit between the predictor variable and the response variable. In this case, the standard error of the estimate would be 0.

The standard error of the estimate represents the average distance between the observed values and the predicted values by the regression model. When the scatter diagram forms a perfect straight line, it means that the regression model can precisely predict the response variable using the predictor variable without any error.

Consequently, the residuals, which are the differences between the observed and predicted values, become zero for all data points, resulting in a standard error of 0. It is important to note that this scenario of a perfect fit on a scatter diagram is rare in real-world data, as there are typically variations and uncertainties in the relationship between variables.

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According to a report done last year by the dental industry, 81% of dentists would recommend Starry Whites toothpaste. After some recent negative publicity, the sales team at Starry Whites suspects the proportion of dentists who now recommend the brand is lower. The team chooses 140 dentists at random and asks them whether they'd recommend the brand. Of those, 110 say they'd recommend it. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to conclude that the proportion, p, of all dentists who now recommend this brand is less than 81%. (a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test. (b) For your hypothesis test, you will use a Z-test. Find the values of np and n−1p to confirm that a Z-test can be used. (One standard is that np≥10 and ≥n(1−p)>=10 under the assumption that the null hypothesis is true.) Here n is the sample size and p is the population proportion you are testing. (c) Perform a Z-test and find the p-value.Here is some information to help you with your Z-test. i. The value of the test statistic is given by p-p/root p(1-p)/n. ii. The p-value is the area under the curve to the left of the value of the test statistic.

Answers

(a)The hypothesis' are

    H0: p = 0.81

    H1: p < 0.81

(b) Since np ≥ 10, this condition is satisfied.

(c) The p-value is 0.2814.

    The significance level of 0.10, we fail to reject the null hypothesis.

For(a)

According to the information given,

The null hypothesis H0 would be that the proportion of dentists who recommend Starry Whites toothpaste is still 81%,

While the alternative hypothesis H1 would be that the proportion of dentists who recommend this brand is less than 81%.

We can state the null and alternative hypotheses as,

H0: p = 0.81 (proportion of dentists who recommend Starry Whites toothpaste is still 81%)

H1: p < 0.81 (proportion of dentists who recommend Starry Whites toothpaste is less than 81%)

For(b)

Based on the information given, we can use a Z-test for proportions to conduct the hypothesis test.

To confirm that a Z-test is appropriate, we need to check if the following conditions are met:

   np ≥ 10

n(1-p) ≥ 10

Here,

n = 140 (sample size) and

p = 0.81 (population proportion under the null hypothesis).

⇒ np = 140 x 0.81

         = 113.4 Since

np ≥ 10, this condition is satisfied.

⇒ n(1-p) = 140 x (1-0.81) = 26.2

Since n(1-p) >= 10,

This condition is also satisfied.

Therefore, both conditions are met, and we can use a Z-test for proportions to conduct the hypothesis test.

For(c)

We can perform a Z-test using the formula you provided, which is,

⇒z = (p - p0) /√(p0 x (1 - p0) / n)

where:

p0 is the hypothesized proportion (in this case, p0 = 0.81)

p is the sample proportion (in this case, p = 110/140 = 0.786)

n is the sample size (in this case, n = 140)

Substituting the values, we get,

⇒ z = (0.786 - 0.81) / sqrt(0.81 x (1 - 0.81) / 140)

⇒ z = -0.58

To find the p-value, we need to look up the area under the standard normal distribution curve to the left of z = -0.58.

Using a standard normal distribution table or calculator, we find that the area is 0.2814.

Therefore, the p-value is 0.2814.

Since the p-value is greater than the significance level of 0.10, we fail to reject the null hypothesis.

This means we do not have enough evidence to conclude that the proportion of dentists who recommend Starry Whites toothpaste has decreased.

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check weather 6x2-5x - 14 is exactly divisible by (x-2) or not

Answers

Answer:

\(\large \boldsymbol {} 6x^2 -5x-14 =0 \\\\ D=25+14\cdot 4\cdot 6 =361=19^2 \\\\ x_1= \dfrac{5+19}{12} =2 \\\\\\ x_2 =\dfrac{5-19}{12} =-\dfrac{7}{6} \\\\ and \ \ we \ \ \ know \ \ that \\\\\ 6x^2 -5x-14 =6 (x-x_1) ( x- x_ 2) = 6 ( x-(-\frac{7}{6} ))\boldsymbol { ( x-2 ) } \\\\ as \ we \ can \ see \ , \ the \ \ expansion \ is \\\\\ x-2 ; therefore \ \ , \ \ the \ \ answer \ \ is \ \ yes\)

Answer: Yes: divisible

Step-by-step explanation:

\(P(x)=6x^2-5x-14\\\\P(2)=6*2^2-5*2-14=24-10-14=0\\\\P(x)\ is\ exactly\ divisible\ by\ x-2\\\)

Help plz answer 10,11,12 ASAP

Help plz answer 10,11,12 ASAP

Answers

Lack of attention to date issues can invalidate testing results. what is a good way to make sure data issues are property addressed?

Answers

A good way to ensure that data issues are properly addressed is by implementing robust data quality assurance and validation processes. These processes involve various steps and techniques to identify, prevent, and resolve data issues effectively. By following these best practices, you can minimize the risk of invalidating testing results due to date-related problems.

One essential step is to establish clear data quality standards and guidelines. This includes defining data formats, data integrity rules, and validation criteria specific to date-related fields. By setting these standards, you provide a framework for ensuring consistent and accurate data across the testing process.

Another important aspect is to perform comprehensive data profiling and analysis. This involves examining the data to identify anomalies, inconsistencies, or inaccuracies related to dates. By using data profiling tools or writing custom scripts, you can detect issues such as missing values, incorrect formats, or outliers within date fields. This analysis enables you to have an overview of the data quality and pinpoint potential problems.

To address data issues effectively, it is crucial to establish data cleansing procedures. This involves correcting errors, resolving inconsistencies, and standardizing date formats. For instance, you can use data cleaning techniques like imputation to fill in missing dates, transforming data into a consistent format (e.g., YYYY-MM-DD), or removing duplicate entries. By applying these cleansing techniques, you improve the accuracy and reliability of the data used in testing.

Furthermore, implementing data validation checks is essential to identify and flag potential issues during the testing process. This can involve writing automated tests or validation scripts that verify the integrity and correctness of date-related data. By performing validation checks at different stages of the testing process, you can detect anomalies promptly and take appropriate actions to address them.

Lastly, fostering a culture of data quality awareness and accountability is crucial. Promoting education and training on data handling best practices, emphasizing the importance of accurate dates, and encouraging open communication about data issues among team members can significantly contribute to ensuring data issues are adequately addressed.

In summary, to ensure data issues are properly addressed, it is important to establish data quality standards, perform data profiling and analysis, implement data cleansing procedures, incorporate validation checks, and foster a culture of data quality awareness. By following these practices, you can mitigate the risk of invalidating testing results due to date-related problems and enhance the overall reliability and integrity of your data.

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Hi! I need Help
What is the answer to (-37) - (+14)
Negative 37 minus positive 14

Answers

Answer: -51 my friend

Step-by-step explanation:

A Ferri Wheel ha a radiu of 16 feet. How far will you travel if you take a ride that goe around 5 time?

Round anwer to the nearet hundredth and for pi ue π=227

Answers

If we take a ride that goes around 5 times, we will travel for 502.86 feet. The result is obtained by using the formula for circumference.

How to find circumference?

Circumference is the perimeter of a circle. It can be calculated by the following formula.

C = 2πr

Where

C = circumferencer = radius of a circle

A Ferri wheel has a radius of 16 feet. If you take a ride that goes around 5 times, determine the distance you traveled!

(Round answer to the nearest hundredth and for pi use π = 22/7)

The shape of the wheel is round (a circle). The distance traveled is the circumference multiplied by the number of rounds.

We have

Radius, r = 16 feetNumber of rounds, n = 5

Distance traveled

= C × n

= 2πr × 5

= 2(22/7)(16) × 5

= 502.86 feet

Hence, the distance traveled by the wheel is 502.86 feet.

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The vertex of the parabola below is at the point (2, 4), and the point (3,6) is
on the parabola. What is the equation of the parabola?
10
(3,6)
(2,4)
-10
10
-10
O A. y=2(x-2)² +4
OB. x= 4(y-3)² +1
O C. y= 6(x-2)2 +4
OD. y=3(x-4)2 +2
← PREVIOUS

Answers

The equation of the parabola is y = 2(x - 2)^2 + 4

How to determine the parabola equation?

The given parameters are:

Vertex, (h,k) = (2,4)Point (x,y) = (3,6)

A parabola is represented as:

y = a(x - h)^2 + k

Substitute (h,k) = (2,4)

y = a(x - 2)^2 + 4

Substitute (x,y) = (3,6)

6 = a(3 - 2)^2 + 4

Evaluate the difference

6 = a(1)^2 + 4

This gives

6 = a + 4

Subtract 4 from both sides

a = 2

Substitute a = 2 in y = a(x - 2)^2 + 4

y = 2(x - 2)^2 + 4

Hence, the equation of the parabola is y = 2(x - 2)^2 + 4

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Okay which fraction is equal to 0.370?

Okay which fraction is equal to 0.370?

Answers

It should be B) because it the closest.

Solution:

\(Let \: \: \: \: x = 0.370370.... \\ therefore \: \: \: x \: = 0.370370... \\ = > 1000x = 370.370370... \\ = > 1000x - x = 370.370370... - 0.370370... \\ = > 999x = 370 \\ = > x = \frac{370}{999} \)

Answer:

B)

\( \frac{370}{999} \)

Hope it helps

Answer the question in the picture

Answer the question in the picture

Answers

9514 1404 393

Answer:

  D.  3.70 and 3.75

Step-by-step explanation:

Your calculator tells you that √14 ≈ 3.742.

The upper ends of the ranges of choices A, B, and C are all below this value, so the only interval that is applicable is choice D:

  √14 lies between 3.70 and 3.75

Please please please help asapp
question: in the movie lincoln lincoln says "euclid's first common notion is this: things which are equal to the same things are equal to each other. that's a rule of mathematical reasoning and it's true because it works - has done
and always will do. in his book euclid says this is self-evident. you see there it is even in that 2000 year old book of mechanical law it is the self-evident truth that things which are equal to the same things are equal to each other."
explain how this common notion is an example of a postulate or a theorem

Answers

The statement made by Lincoln in the movie "Lincoln" refers to a mathematical principle known as Euclid's first common notion. This notion can be seen as an example of both a postulate and a theorem.

In the statement, Lincoln says, "Things which are equal to the same things are equal to each other." This is a fundamental idea in mathematics that is often referred to as the transitive property of equality. The transitive property states that if a = b and b = c, then a = c. In other words, if two things are both equal to a third thing, then they must be equal to each other.

In terms of Euclid's first common notion being a postulate, a postulate is a statement that is accepted without proof. It is a basic assumption or starting point from which other mathematical truths can be derived. Euclid's first common notion is considered a postulate because it is not proven or derived from any other statements or principles. It is simply accepted as true. So, in summary, Euclid's first common notion, as stated by Lincoln in the movie, can be seen as both a postulate and a theorem. It serves as a fundamental assumption in mathematics, and it can also be proven using other accepted principles.

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(L2) A circle that contains a polygon so that it passes through each vertex of the polygon is a(n) _____ circle.

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(L2) An inscribed circle is one that encompasses a polygon so that it passes by each of the polygon's vertices.

A circumcircle, not an inscribed circle, is a circle that encircles a polygon at each vertex. A circle that is enclosed within a polygon and intersects each side of the polygon exactly once is said to be inscribed. A circumcircle, on the other hand, is a circle that goes through every vertex of the polygon, with its center located at the point where the perpendicular bisectors of the polygon's sides converge. The greatest circle that can be drawn within a polygon is the circumcircle, while the largest circle that can be drawn inside a triangle is the inscribed circle.

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