How do you find the center of dilation and scale factor in geometry?

Answers

Answer 1

Answer:

See below

Step-by-step explanation:

Centre of dilation

Dilation gives you a new shape that is either larger or smaller than the original.

In either case, every ray that  passes through corresponding points of the two shapes will converge at the centre of dilation (Point O in the diagram).

Scale factor

To get the scale factor, you measure the ratio of lengths of corresponding sides in the  shapes.

For example, a line in the red figure below may be four times as long as the corresponding line in the other.

If the dilation converts the blue shape into the red one, the scale factor is 4:1.

If the dilation converts the red shape into the blue one, the scale factor is 1:4.

How Do You Find The Center Of Dilation And Scale Factor In Geometry?
Answer 2

Final answer:

To find the center of dilation and scale factor in geometry, identify the fixed point and multiply the actual size by the scale factor. Using Calvin's map, with a scale factor of 1/800, the 80-meter distance between houses translates to 10 centimeters on the map.

Explanation:

To find the center of dilation in geometry, you need to identify a fixed point in the plane around which all other points are either expanded or contracted. The scale factor determines how much larger or smaller the image will be compared to the original figure. A scale factor greater than 1 indicates an enlargement, while a scale factor between 0 and 1 indicates a reduction.

Let's use Calvin's map problem as an example. Calvin has a scale factor of 1/800 for his map, and the actual distance between his house and his best friend Frank's house is 80 meters. To find the scale dimensions, we use the following steps:

Convert the actual distance to a compatible unit with the map's scale. Here, we convert meters to centimeters since the map is likely in centimeters (80 meters = 8000 centimeters).

Multiply the actual distance by the scale factor: 8000 cm * (1/800) = 10 cm.

The distance between the two houses on the scale drawing should be 10 centimeters.


Related Questions

A prism has the surface area of 100 cm². What sentence describes the effect of measuring the surface area in square millimeters?

A. The Surface area increases

B. The Surface area decreases

C. The surface area stays the same, but the number representing the surface area increases.

D. The surface area stays the same, but the number representing the surface area decreases.

Answers

Answer:

 A. The surface area stays the same, but the number representing the surface area increases.

Answer:

C

Step-by-step explanation:

Which two wholes numbers does 3 2/10 lie between?

Answers

Answer:

3 and 4

Step-by-step explanation:

On a number line, 3 2/10 is greater than 3, by 1/5, but less than 4, by 4/5.

3 and 4 are two whole numbers that come after each other.

Answer:

3 and 4

Step-by-step explanation:

3 2/10 is in-between the numbers 3 and 4

You plan to invest $350 $350 in a growth fund that has a rate of 1.5% 1.5% compounded quarterly. How much money will this investment be worth after 50 50 years? Round to the nearest cent.

Answers

Is this a scatterproblem?

If so then 350×((1.5)^4)^50 would be an answer?

Answer:

the answer is 739.91

Step-by-step explanation:

i put this problem for my question and got it right on the test.

good luck!

Emmanuel added 8 links per minute to his chain mail. Allesia started 20 minutes after Emmanuel and added 13 links per minute to her chain mail. How long had Emmanuel worked when Allesia caught up to him, and how many links had he added?

Answers

Answer: 52 minutes, 416 links

Step-by-step explanation:

8*20=160

13-8=5

160/5=32

32+20=52

52*8=416

Use the quadratic model y=-4x^2-3x+4 to predict y if x equals 5.

Answers

Answer:

y = - 111

Step-by-step explanation:

Substitute x = 5 into the quadratic for y

y = - 4(5)² - 3(5) + 4 = - 100 - 15 + 4 = - 111

Z varies inversely with x and directly with y. When x=6 and y=2 z=5 what is the value of a when x=4 and y=9

Answers

Answer:

        15·9

z = --------- = 135/4

         4

Step-by-step explanation:

The general formula here is as follows:

        ky

z = ---------

         x

We must find the value of the constant of proportionality.  To do this, subst. 6 for x, 2 for y and 5 for z and compute k:

        k·2

5 = ---------

         6

Multiplying both sides by 6 results in 30 = 2k.

Thus, k = 30/2, or k = 15.

Our formula becomes:

        15y

z = ---------

         x

if x = 4 and y = 9, we get:

        15·9

z = --------- = 135/4

         4

Answer:

[tex]z=33.75[/tex]

Step-by-step explanation:

We are given that z varies inversely with x and directly with y when x=6 and y=2 then z=5

We have to find the value of z when x=4 and y=9

According to question

[tex]z\propto\frac{1}{x}[/tex]

and [tex]z\proptoy[/tex]

Therefore, we have [tex]z\propto\frac{y}{x}[/tex]

[tex]z=k\frac{y}{x}[/tex]

k=proportionality constant

Substitute x=6 , y=2 and z=5 then we get

[tex]5=k\times \frac{2}{6}[/tex]

[tex]5=\frac{k}{3}[/tex]

[tex]k=5\times3[/tex]

By division  poperty of equality

k=15

Now, substitute the value x=4,y=9 and k=15 then the value of z

[tex]z=15\times \frac{9}{4}[/tex]

[tex]z=\frac{135}{4}[/tex]

[tex]z==33.75[/tex]

find the mode for a data set. 18,24,24,24,25,37,37,46

Answers

Answer:

24 is the mode

Step-by-step explanation:

Mode is the number that is most often seen.

18 is seen 1 time

24 is seen 3 times

25 is seen 1 time

37 is seen 2 times

46 is seen 1 time

24 is the mode because it is seen the most often.

Answer:

24

Step-by-step explanation:

The mode is the number that appears the most times in a data set.  Here, 24 occurs the most (3 times)

On a coordinate plane, what is the distance between the points (-4, -3) and (-1, 5)? Round your answer to the nearest hundredth.

Answers

Answer:

8.54

Step-by-step explanation:

To find the distance between 2 points

d = sqrt( y2-y1)^2 + (x2-x1)^2)

where (x1,y1) and (x2,y2) are the two points

d = sqrt((5--3)^2+ (-1--4)^2)

  = sqrt((5+3)^2+ (-1+4)^2)

  =  sqrt((8)^2+ (3)^2)

   = sqrt(64+ 9)

    =sqrt (73)

    =8.544003745

Rounding to the nearest hundredth

   =8.54

ANSWER

The distance between the two points is 8.54 to the nearest hundredth.

EXPLANATION

We want to find the distance between the the points (-4, -3) and (-1, 5).

We use the distance formula;

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d=\sqrt{( - 1 - -4)^2+(5- - 3)^2}[/tex]

[tex]d=\sqrt{( 3)^2+(8)^2}[/tex]

[tex]d=\sqrt{9+64}[/tex]

[tex]d = \sqrt{73} [/tex]

[tex]d = 8.544[/tex]

To the nearest hundredth the distance is 8.54 units.

if n/5=45/75.find the value of n.

Answers

Start with

[tex]\dfrac{n}{5}=\dfrac{45}{75}[/tex]

Multiply both sides by 5:

[tex]n = \dfrac{45\cdot 5}{75} = \dfrac{45}{15} = 3[/tex]

Answer:

n = [tex]\frac{9}{5}[/tex]

Step-by-step explanation:

Simplify the fraction on the right side

[tex]\frac{n}{5}[/tex] = [tex]\frac{45}{75}[/tex] = [tex]\frac{3}{5}[/tex] ( cross-  multiply )

5n = 15 ( divide both sides by 5 )

n = 3

What is the surface area of the regular pyramid?

Answers

You would have to do 18x2 then 14x2.

Answer:

Step-by-step explanation:

Surface area = [tex]lw+l\sqrt{(\frac{w}{2})^2+h^2}+w\sqrt{(\frac{l}{2})^2+h^2}[/tex]

just put the values in the formula h=18,w=14,l=14

A used motorcycle is on sale for $3,600. Erik makes an offer equal to 3/4 of this price. How much does Erik offer for the motorcycle?

Answers

2,700 I'm pretty sure.

Please help we with all

Answers

Step-by-step explanation:

[tex]1)\ \dfrac{10}{100}=0.10=0.1\\\\2)\ \dfrac{5}{10}=0.5\\\\3)\ \dfrac{6}{10}=0.6\\\\4)\ \dfrac{93}{100}=0.93\\\\5)\ \dfrac{1}{10}=0.1\\\\6)\ \dfrac{40}{100}=0.40=0.4\\\\7)\ \dfrac{56}{100}=0.56\\\\8)\ \dfrac{7}{10}=0.7\\\\9)\ \dfrac{3}{10}=0.3\\\\10)\ \dfrac{98}{100}=0.98\\\\11)\ \dfrac{4}{10}=0.4\\\\12)\ \dfrac{78}{100}=0.78[/tex]

what is the correct first step to solve this system of equations. 4x-3y=-10, 2x+3y=4

a) add the 2 equations together
b) subtract the 2 equations
c) multiply the second equation by 3
D) divide the first equation by 4

Answers

Answer:

best bet is c

The correct first step is : " add the 2 equations together "

What is Equation?

An equation is a mathematical statement with an '=' symbol between two expressions that have equal values.

Here, given equations are

  4x - 3y = -10

  2x + 3y = 4

In given equation the coefficient of y is equal with opposite sign, so for simplification of these equation we need to add these equation.

Thus, the correct first step is : " add the 2 equations together "

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A child’s toy harp is in the shape of a trapezoid as shown.
In square inches, what is the area of the harp?

Answers

Hello! your answer is going to be 64 square inches.

The equation to get this is as listed:

[tex]Area = \frac{Base1+Base 2}{2} * Height[/tex]

I hope this helps, and have a nice day!

Answer:

a = 64 ft²

Step-by-step explanation:

a = a + b   (h)

       2

a = 4 + 12/2 (8)

a = 16/2 (8)

a = 8 (8)

a = 64 ft²

The growth of a new strain of bacteria is represented by y=79.31(1,48)^x,where x represents the number of days a y represents the number of bacteria.which is the best prediction for the number of bacteria on day 6

Answers

Answer:

Choice D; 833

Step-by-step explanation:

The best prediction for the number of bacteria on day 6 will be given by substituting x with 6 in the exponential growth model;

[tex]y=79.31(1.48)^{x}\\y=79.31(1.48)^{6}\\y=833[/tex]

you bought a video game for 50$,but it loses 25% of its value every six months. how much will the video game be worth after two years​

Answers

keeping in mind that two years is 24 months, and we know that cyclically it's losing 25% every 6 months.

[tex]\bf \textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &24\\ c=period\dotfill &6 \end{cases} \\\\\\ A=50(1 - 0.25)^{\frac{24}{6}}\implies A=50(0.75)^4\implies A\approx 15.82[/tex]

There are 4 periods of 6 months in 2 years so 50x0.75^4= $15.82

which equation describes the porportion: the number of chickens (c) is four times as many the number of horses (h) on the farm​

Answers

Answer:

c4:h1

Step-by-step explanation:

Answer:

c=4h

Step-by-step explanation:

If f(x) = x+4 and g(x) =x^3, what is (g•f)(-3)

Answers

ANSWER

[tex](g\circ f)( - 3) = 1[/tex]

EXPLANATION

The given functions are

[tex]f(x) = x + 4[/tex]

and

[tex]g(x) = {x}^{3} [/tex]

The composite function,

[tex](g\circ f)(x) = g(f(x))[/tex]

[tex](g\circ f)(x) = g(x + 4)[/tex]

[tex](g\circ f)(x) = ( {x + 4)}^{3} [/tex]

We now substitute x=-3 to obtain:

[tex](g\circ f)( - 3) = ( { - 3 + 4)}^{3} [/tex]

[tex](g\circ f)( - 3) = ( {1)}^{3} = 1[/tex]

Answer:

The answer is 1

What is the solution to the following system of equations?

Answers

Answer:

(3,2)

Step-by-step explanation:

Make sure you use substitution to solve the equation for either x or y first. Then once you have the value of one, plug it into the equation to solve for the value of the other.

The answer is the third one.

PLEASE HELP
Triangle FGH was dilated to create triangle ABC.
What is the scale factor of the dilation?
3
1/3
2
1/2

Answers

Answer:

1/2

Step-by-step explanation:

Triangle FGH was dilated to create triangle ABC

The image is a reduction so scale factor is between 0 and 1

2.5/5 = 3.5/7 = 4.3 / 8.6

= 0.5  

= 1/2

Answer

1/2

The scale factor of the dilation is,

⇒ 1 / 2

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Triangle FGH was dilated to create triangle ABC.

Hence, For scale factor,

Since, Triangle FGH was dilated to create triangle ABC

So, We get;

The scale factor is,

2.5/5 = 3.5/7 = 4.3 / 8.6

2.5 / 5 = 1/2

3.5/7 = 1/2

4.3/8.6 = 1/2

Therefore, The scale factor of the dilation is,

⇒ 1 / 2

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The formula for calculating annual insurance premiums is _____.

Answers

Final answer:

The formula for calculating annual insurance premiums is based on several factors, including historical data, statistical analysis, and risk assessment.

Explanation:

The formula for calculating annual insurance premiums is based on several factors. Insurance companies use a combination of historical data, statistical analysis, and risk assessment to determine the premium amount. The general formula for calculating insurance premiums is:

Premium = (Average Person's Claims + Costs of Running the Company + Firm's Profits) / Number of Insured Individuals

For example, if there are 100 drivers and the insurance company needs to collect $186,000 to cover the costs of accidents, each driver would pay a premium of $1,860 per year.

The formula for calculating annual insurance premiums is Annual Premium = Base Rate [tex]\times[/tex] Coverage Amount [tex]\times[/tex] Adjustment Factors.

The formula for calculating annual insurance premiums is not a one-size-fits-all equation because it depends on various factors such as the type of insurance, the coverage amount, the deductible, the policyholder's risk profile, and other personal and policy-specific details.

However, a general form of the formula that can be used as a starting point is:

[tex]\[ \text{Annual Premium} = \text{Base Rate} \times \text{Coverage Amount} \times \text{Adjustment Factors} \][/tex]

Here, the base rate is the initial cost of insurance per unit of coverage, which is determined by the insurer based on the type of insurance and the average risk associated with it.

The coverage amount is the total amount of coverage the policyholder is purchasing. Adjustment factors are multipliers that reflect the policyholder's individual risk factors, such as age, health, driving record, credit score, etc.

Find the area of the polygon.

Answers

Answer:

2,400 cm²

Step-by-step explanation:

You can solve for x because you know that 40cm=x²+4cm:

36 cm = x²

x = 6cm.

Therefore the width is 2(6)²-12, which is 60cm.

So the area is 40 cm x 60 cm, which is 2,400 cm².

How do you solve -3x-4>5

Answers

Answer:

x<−3

Step-by-step explanation:

−3x−4>5

Step 1: Add 4 to both sides.

−3x−4+4>5+4

−3x>9

Step 2: Divide both sides by -3.

−3x

−3

>

9

−3

x<−3

Answer:

x < -3

Step-by-step explanation:

We must isolate x.

Start by adding 4 to both sides, obtaining -3x > 9.

Next, divide both sides by -3, remembering to reverse the direction of the > symbol:

-3x       9

------ > -----  ↔  x < 9/(-3), or x < -3

 -3       -3

An element with mass 570 grams decays by 26.9% per minute. How much of the element is remaining after 14 minutes, to the nearest 10th of a gram?

Answers

Answer:

7.1

Step-by-step explanation:

Exponential Functions:

y=ab^x

y=ab  

x

 

a=\text{starting value = }570

a=starting value = 570

r=\text{rate = }26.9\% = 0.269

r=rate = 26.9%=0.269

\text{Exponential Decay:}

Exponential Decay:

b=1-r=1-0.269=0.731

b=1−r=1−0.269=0.731

\text{Write Exponential Function:}

Write Exponential Function:

y=570(0.731)^x

y=570(0.731)  

x

 

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=570(0.731)^{14}

y=570(0.731)  

14

 

y= 7.091174

y=7.091174

Evaluate

y\approx 7.1

y≈7.1

round

Final answer:

To calculate the remaining amount of an element undergoing exponential decay, use the formula A = A0 * (1 - r)^t, where A is the remaining amount, A0 is the initial amount, r is the decay rate per minute, and t is the time in minutes. In this case, approximately 12.3 grams of the element is remaining after 14 minutes.

Explanation:

To calculate the amount of the element remaining after 14 minutes, we need to use the formula for exponential decay, which is A = A0 * (1 - r)t, where A is the remaining amount, A0 is the initial amount, r is the decay rate per minute (in decimal form), and t is the time in minutes.

In this case, the initial amount is 570 grams, the decay rate is 26.9% or 0.269 per minute, and the time is 14 minutes.

Plugging these values into the formula, we get:

A = 570 * (1 - 0.269)14 = 570 * (0.731)14 = 570 * 0.0221 = 12.27 grams.

Therefore, approximately 12.3 grams of the element is remaining after 14 minutes.

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Who reads at the same rate?

Answers

Answer:

Alexis and Jon reads at the same rate, 0.67 page by min

Step-by-step explanation:

Rate Alexis = 30/45 pages/min = 0.67 page by min

Rate Jon = 40/60 pages/min = 0.67 page by min

Rate Sal = 45/90 = 0.5 page by min

Rate Andre = 15/25 = 0.6 page by min

Then

Alexis and Jon reads at the same rate, 0.67 page by min

Best regards

What is an IQR? Help Please!

Answers

Answer:

in math it should be Interquartile Range

Step-by-step explanation:

Answer:

Interquartile range

Step-by-step explanation:

In descriptive statistics, the interquartile range, also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q₃ − Q₁.

convert 18/5 to a decimal using long division

Answers

Answer:

3.60

Step-by-step explanation

you need to turn it to 100 then move the decimal 2 places to the left

Answer:

A. 3.6

Step-by-step explanation:

Ben says 7 9/100 must be less than 7. 2/10 because 9 hundredths is less than 2 tenths. Do you agree? Draw a line to support your answer

Answers

Yes, I cannot draw a line because this is online. Sorry

A parallelogram-shaped tile has an area if 48 in.2. The base of the tile measures 12in. What is the measure of bits height

Answers

Answer:

height = 4 in

Step-by-step explanation:

The area (A) of a parallelogram is calculated using the formula

A = base × height ← substitute values

48 = 12 × height ( divide both sides by 12 )

4 = height

How old am i if 500 reduced by 3 times my age is 266

Answers

Hey there!

Let's start by making an equation to represent this.

500 - 3a = 266

Reduced by is the same as subtracting, and a represents age.

Subtract 500 from both sides.

-3a = -234

Divide each side by -3.

a = 78

Check.

500 - 3(78) = 266

500 - 234 = 266

266 = 266

You are 78 years old.

Hope this helps!

Answer: Age=78

Step-by-step explanation:

500-(3xAge)=266

500-266=3xAge

(500-266)/3 = Age

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