Dilate a square with vertices $\left(0,\ 0\right)$(0, 0)​ , $\left(0,\ 4\right)$(0, 4)​ , $\left(4,\ 4\right)$(4, 4)​ , and $\left(4,\ 0\right)$(4, 0)​ using the scale factor $k=0.5$k=0.5​ . What is the value of the ratio (new to original) of the perimeters? the areas?

Answers

Answer 1

The ratio (new to original) of the perimeters is equal to 1/2 or 0.5. Also, the ratio (new to original) of the areas is equal to 1/4 or 0.25.

How to determine the value of the ratio (new to original)?

In Mathematics, the ratio of the perimeters of two (2) geometric figures would be equal to the scale factor when the two (2) geometric figures are similar;

Let z represent the scale factor.Let y represent the perimeter of the original square.Let x represent the perimeter of the new square.

Mathematically, the scale factor of a geometric figure can be calculated by using this formula:

Scale factor, z = Dimension of image/Dimension of original figure = y/x

Scale factor, z = 1/2 or 0.5.

In Geometry, the ratio of the areas of two (2) geometric figures would be equal to the square of scale factor when the two (2) geometric figures are similar.

Scale factor, z = (y/x)²

Scale factor, z = (1/2)²

Scale factor, z = 1/4 or 0.25.

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Complete Question:

Dilate a square with vertices (0, 0). (0, 4). (4, 4), and (4, 0) using the scale factor k = 0.5. What is the value of the ratio (new to original) of the perimeters? the areas?

The ratio of the perimeters is

The ratio of the areas is


Related Questions

For the data in the table, write an equation for the direct variation.

Answers

The equation of direct variation is,

[tex]\begin{gathered} y=kx \\ k=\frac{y}{x} \end{gathered}[/tex]

Substitute the values of y and x.

[tex]\begin{gathered} k=\frac{5.4}{4} \\ k=1.35 \end{gathered}[/tex]

So, the obtained equation will be y=1.35(x).

Let's check with the values of x.

1) If x=4

[tex]\begin{gathered} y=1.35x \\ y=1.35(4) \\ y=5.4 \end{gathered}[/tex]

2) If x=2

[tex]\begin{gathered} y=1.35x \\ y=1.35(2) \\ y=2.7 \end{gathered}[/tex]

3) If x=-2

Choose the statements that are true about a cube with side length 1 unit.
It has a volume of 6 cubic units.
It has a volume of 1 cubic unit.
It has a volume of 3 cubic units.
It is called a "one block."
It can be used to measure volume.
It is called a "unit cube."

Answers

The answer to the mentioned statement are :

first statement is WRONG

the second statement is RIGHT

The third statement is also WRONG

the fourth statement is RIGHT

fifth statement is RIGHT

sixth statement is WRONG

The side of the given cube is 1 unit.

This means that the Length= Breadth = Height = 1 unit because it is cube

This means that the volume can be described as

( side ) ³

that is 1 × 1 × 1 = 1 cubic unit

thus the first statement is WRONG

However the second statement is RIGHT

The third statement is also WRONG

since it is a cube whose volume is 1 cubic unit

thus we can say that it is one block

Thus the fourth statement is RIGHT

fifth statement is RIGHT

sixth statement is WRONG

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Question
Solve 2y−18x=−26 for y.

Answers

Answer:

-26

Step-by-step explanation:

Using Pythagoras' Theorem please solve it.​

Answers

[tex] \huge\underline\mathcal{Answer \: - }[/tex]

Pythagoras theorem states that the square of hypotenuse equals the sum of square of other two sides.

therefore ,

[tex](25) {}^{2} = (x + 3) {}^{2} + 4 { }^{2} (x + 2) {}^{2} \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16(x {}^{2} + 4 + 4x) \\ \\ \longrightarrow \: 625 = x {}^{2} + 9 + 6x + 16x {}^{2} + 64x + 64 \\ \\ \longrightarrow \: 625 = 17x {}^{2} + 70x + 73 \\ \\ \longrightarrow \: 17x {}^{2} + 70x + 73 - 625 = 0 \\ \\ \longrightarrow \: 17x {}^{2} + 70x - 552 = 0[/tex]

now using quadratic formula ,

[tex]x = \frac{ - b \: \pm \: \sqrt{b {}^{2} - 4ac} }{2a} \\ [/tex]

here , a = 17 , b = 70 , c = -552

substituting the values in the equation above ,

[tex]x = \frac{70 \: \pm \: \sqrt{70 {}^{2} - 4(17)( - 552)} }{2 \times 17} \\ [/tex]

after simplifying we get ,

[tex]\boxed{x = 4} \: \: or \:\boxed{ x = \frac{ - 138}{7} } \\ [/tex]

since length can't be negative , therefore the other value will be neglected and hence ,

[tex]\boxed{value \: of \: x \: = \: 4 \: cm}[/tex]

hope helpful ;-;

Answer:   x = 4

======================================================

Work Shown:

As you mentioned, we'll use Pythagoras' Theorem aka Pythagorean Theorem.

[tex]a^2+b^2 = c^2\\\\(x+3)^2+(4(x+2))^2 = 25^2\\\\(x+3)^2+16(x+2)^2 = 625\\\\(x^2+6x+9)+16(x^2+4x+4) = 625\\\\x^2+6x+9+16x^2+64x+64 = 625\\\\17x^2+70x+73 = 625\\\\17x^2+70x+73-625 = 0\\\\17x^2+70x-552 = 0\\\\[/tex]

Next, we'll use the quadratic formula with a = 17, b = 70, c = -552.

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-70\pm\sqrt{(70)^2-4(17)(-552)}}{2(17)}\\\\x = \frac{-70\pm\sqrt{42436}}{34}\\\\x = \frac{-70\pm206}{34}\\\\x = \frac{-70+206}{34} \ \text{ or } \ x = \frac{-70-206}{34}\\\\x = \frac{136}{34} \ \text{ or } \ x = \frac{-276}{34}\\\\x = 4 \ \text{ or } \ x \approx -8.1176\\\\[/tex]

Ignore the negative x value solution. The sides (x+3) and 4(x+2) will be negative values if we plugged in x = -8.1176, but negative side lengths do not make sense.

This makes x = 4 the only possible solution.

----------------

If x = 4, then,

vertical leg = x+3 = 4+3 = 7horizontal leg = 4(x+2) = 4*(4+2) = 4*6 = 24

This is a 7-24-25 right triangle.

We can confirm this using the pythagorean theorem

[tex]a^2+b^2 = c^2\\\\7^2+24^2 = 25^2\\\\49+576 = 625\\\\625 = 625 \ \ \ \checkmark[/tex]

3 movie tickets cost $36. At this rate, what is the cost per ticket?​

Answers

The cost per ticket is $12!

Answer:

12

Step-by-step explanation:

36 divided by 3 is 12

In the figure ZX = 2x + 1 YW = 3x - 1 and YX = 1, find perimeter of VYZ

Answers

The perimeter of triangle VYZ is 12 units.

How to find the perimeter of a triangle?

The perimeter of a triangle is the sum of the whole sides of the triangle.

In other words, the perimeter of a triangle is the total distance covered by its boundaries or the sides.

Therefore,

perimeter of ΔVYZ = VY + ZY + ZV

Therefore,

VY  =  ZY = ZV = XW

Hence,

YW = YX + XW

Therefore,

XW = YW - YX

YW  = 3x - 1

YX = 1

Hence,

XW = 3x - 1 - 1

XW = 3x - 2

Therefore,

perimeter of ΔVYZ = 3x - 2 + 3x - 2 + 3x - 2

perimeter of ΔVYZ = 9x - 6

ZX = YW

2x + 1 = 3x - 1

2x - 3x = - 1 - 1

-x = -2

x = 2

Therefore,

perimeter of ΔVYZ = 9(2) - 6

perimeter of ΔVYZ = 18 - 6

perimeter of ΔVYZ = 12 units

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what is 25 + 20x factor

Answers

Answer:

5(4x+5)

Step-by-step explanation:

25+20x

=5(5+4x)

:]

AGAIN PLS HELP ME I NEED IT

Answers

Answer: Yes, No, No, Yes

Step-by-step explanation:

Goal: Substitute all the ordered pairs into the equation.

1) (1,-3)

5(1) + 2(-3) = -1

5 + -6 = -1

-1 = -1

Yes

2) (2,8)

5(2) + 2(8) = -1

10 + 16 = -1

25 = -1

No

3) (-4, -6)

5(-4) + 2(-6) = -1

-20 + -12 = -1

-32 = -1

No

4) (-3, 7)

5(-3) + 2(7) = -1

-15 + 14 = -1

-1 = -1

Yes

What is the value of V?
V-22+v+32+v=180

Answers

V-22+v+32+v=180

V+v+v=170

3v=170

v=56.67

(5y-23) (2x+13) 47 (3x) find the values of c and y

Answers

The value of variable x and y are 24 and 19 respectively.

How to find angles?

We have to find the variables x and y of the angles.

Therefore,

using angles in a triangle,

2x + 13 + 47 + 5y - 23 = 180

2x + 5y = 180 - 13 - 47 + 23

2x + 5y = 143

Using corresponding angles,

180 - (2x + 13) = 47 + 3x

180 - 2x  - 13 = 47 + 3x

180 - 47 - 13 = 3x + 2x

120 = 5x

x = 120 / 5

x = 24

Hence,

2(24) + 5y = 143

5y = 143 - 48

5y = 95

y = 95 / 5

y = 19

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If the assumptions for the large sample confidence interval for the population proportion are not met, what adjustments can be made?.

Answers

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

A 95% confidence interval gives you a 5% chance of being wrong. A 90% confidence interval gives you a 10% chance of being wrong. In comparison to a 99% confidence interval, a 95% confidence interval is smaller (for example, plus or minus 4.5 percent instead of 3.5 percent).

When constructing a confidence interval for a propotion, if the condition of proportion requires 10 individuals in each category is not met, then confidence interval should be adjusted.

The number of individuals in each category is increased by 2 and sample size increases by 4.

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PLS PLS HELP ASAP!!!
translate the image using the rule below

Answers

Answer:

t=(1,-3) c=(-2,-2) r=(-3,-5)

Step-by-step explanation:

add 2 to each x value and subtract 4 from each y value

A diner serves a stack of potato slices that is 2.8 centimeters tall. The thickness of a potato is .35 centimeters. How many potato slices are in the stacks?

Answers

Given that a diner serves a stack of potato slices that is 2.8 centimeters tall. The thickness of a potato is 0.35 centimeters.

We have to determine the number of potato slices in the stacks.

The number of potato slices in the stack is given by:

[tex]\frac{2.8}{0.35}=8[/tex]

Thus, the number of potato slices in the stack is 8.

Which system is responsible for carrying this oxygen to the muscles?

Answers

Answer:

The circulatory system

Step-by-step explanation:

Is this math? lol

:]

Please help me find out what 758x92 is

Answers

Answer:69736

Step-by-step explanation:

69,736

is the answer

Select the correct answer.
-
The function f(x) has been transformed to give g(x). Which of the following functions represents g(x)?
A. 9(z) = 2z²
B. 9(2) = () z²
C. g(z)=()=²
D. g(z) = 42²

Answers

c.

Step-by-step explanation:

you can check the the correct answer by giving tables value for eg f(x)= 2 g(f(x))= 1/2(2)²=2

as you can see in the graph g(x) (2,2)

A veterinarian recorded a cat's resting heart rate to be 120 beats over a 45-second time period. Complete the table to find the constant of proportionally in beats per minute.
Btw I'm in 7th grade


Number of Minutes: 0.25 0.5 0.75 1

Number ofHeartbeats: ? ? ?

Answers

The table will be:

Number of Minutes: 0.25. 0.5. 0.75 1

Number of heartbeats: 0.6675 1.335 2 2.67

How to calculate the value?

The veterinarian recorded a cat's resting heart rate to be 120 beats over a 45-second time period. The constant will be:

= 120 / 45

= 2.67

Therefore, to find the heartbeat, we have to multiply the numbers of minutes by 2.67. This is illustrated as:

= 2.67 × 0.25 = 0.6675

This illustrates the concept of multiplication.

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If x is a positive integer, this expression is equivalent to what?

Answers

Given:

[tex]\text{ Th expression is }4x^{\frac{1}{2}},\text{ x is a positive integer.}[/tex]

Required:

Which option is equivalent?

Explanation:

The equivalent for is

[tex]\begin{gathered} =4x^{\frac{1}{2}} \\ =4\sqrt{x} \end{gathered}[/tex]

Answer:

Option B is correct answer.

Of 85 entries in the parade, 19 were
marching bands. How many entries were
not marching bands?

Answers

The answer is 66. Do 85-19 to get the answer

Question 5Which of the following is equivalent to (2 – 2) (x - 1)

Answers

[tex]\begin{gathered} (x-2)(x-1)=x^2-x-2x+2=x^2-3x+2 \\ \end{gathered}[/tex]

On a map of a campground, the Sleepy Bear cabin is located at (-14,-10) and the Deer Run cabin is located at (-14,-6). How far apart are the two cabins? (Just type in the number)

Answers

Answer: -4 over 0 (I think) I hope this helps a little bit

Step-by-step explanation: Finding the slope

(-14,-10) and (-14,-6)

Use your Y values and subtract them -10-(-6) or -10 + 6= -4 that will be your numerator

Use your 2 X values and subtract them -14-(-14) or -14+14=0  that will be your denominator

Slope will be  -4 over 0

what is an example of data organization and analysis

Answers

The answer choices which represents an example of data organisation and analysis are;

Choice A; Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation.

Choice C. Running a weather station.

Choice E; Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.

Data organisation and Analysis.

The concept above as the name implies involves the process of gathering data in a bid to further carry out analysis and consequently, draw inferences from such analysis.

Therefore, the answer choices A, C and E represent such activities which involve data organisation and analysis.

Complete question:

What is an example of data organisation and analysis?

Check all that apply.

A. Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation

B. Rejecting extreme data

C. Running a weather station

D. Transferring the weather data to a computer application

E. Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.

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An example of data organization and analysis include:

A. drawing a pie chart to show the percentage of sunny days rainy days and cloudy days without precipitation.

E. summing the number of days with precipitation summing the number of sunny days and summing the number of cloudy days without precipitation

What is data organization?

Data organization and analysis are accomplished by a process of categorizing and organizing data based on its category and how it is studied. A is an example of data organizing and analysis.

Drawing a pie chart to display the percentage of sunny days, rainy days, and cloudy days without precipitation - in this example, data organization is done through charts and graphs, with data classification visible. e is another example.

Summing the number of days with precipitation, sunny days, and cloudy days without precipitation - in this example, data organizing is done solely through summation of numbers, with no graphs or charts to graphically portray the data.

In conclusion, the correct options are A and E.

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Which of the following activities are examples of data organization and analysis?

Check all the apply.

A. Drawing a pie chart to show the percentage of sunny days, rainy days, and cloudy days without precipitation

B. Rejecting extreme data

C. Running a weather station

D. Transferring the weather data to a computer application

E. Summing the number of days with precipitation, summing the number of sunny days, and summing the number of cloudy days without precipitation.

what is 0.4111111… as a fraction

Answers

So there is a method to do this problem
Take 0.41111... as x
Thus 10x = 4.11111... and 100x= 41.1111...

=> 100x - 10x = 41.1111... - 4.111111
=> 90x=37
=> x= 37/90
=> 0.4111... = 37/90

What is the solution set of the following equation?
-8x + x + 15 = -7x + 12

a. Ø
b. {all reals}
c. {1/7}

Answers

Answer:

A

Step-by-step explanation:

(-8x  +  x) + 15  = -7x +12

   -7x    +15 = -7x + 12

      15 = 12          There are no solutions

Determine if the relation is a
function. Use set builder and
interval notation for the
domain and range.
Function: Yes No
Domain:
Range:

Answers

Answer:

It would be helpful if you add more info on the question

Step-by-step explanation:

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $456. What was the simple interest rate of the bonds?

Answers

5.7%

Explanaton:

let amount invested = Principal = $8000

time = 1 year

rate = ?

Interest = $456

To get the rate, we'll apply simple interest formula:

[tex]\begin{gathered} I\text{ = PRT} \\ I\text{ = interest, P = principal, R = rate, T = time} \end{gathered}[/tex][tex]\begin{gathered} 456\text{ = 8000}\times R\times1 \\ 456\text{ = 8000R} \\ \text{divide both sides by 8000:} \\ \frac{456}{8000}\text{ =}\frac{8000R}{8000} \\ \\ R\text{ = 0.057} \\ In\text{ percent, rate = 0.057}\times100 \\ \text{Rate = 5.7\%} \end{gathered}[/tex]

Hence, the simple rate of the bonds is 5.7%

0.8-2x=-1.4

Solve for x

Answers

Answer:

x= -0.3

Step-by-step explanation:

0.8-2x=1.4 Set up equation

-2x=1.4-0.8  Put Like terms together

-2x=0.6       Subtract like terms

x=0.6/-2     Divide

x=-0.3        Answer

If Sarah needs 3 cups of flour for 2 batches of cookies, How many cups of flour would she need for 18 batches of cookies?

Answers

Answer:

24 = 18

Step-by-step explanation:

3 cups = 2 cookies

Meaning she needs 24 cups of flower for 18 cookies

May I please get help with this. I have tried multiple times but still could not get the correct answers for them

Answers

ANSWER

[tex]\frac{2}{5}[/tex]

EXPLANATION

To find the scale factor of the model to the sculpture, we have to divide one set of measurements of the model and sculpture.

Let us divide the length of the model by that of the sculpture:

[tex]\begin{gathered} \frac{10}{25} \\ \Rightarrow\frac{2}{5} \end{gathered}[/tex]

That is the scale factor of the model to the real sculpture.

A =
h(a + b)/2 solve for b

Answers

Answer: b = (−ah+2a)/h

Step-by-step explanation:

Step 1: Flip the equation.

Step 2: Add (-1)/2ah to both sides.

Step 3: Divide both sides by h/2.

The answer is B= 2A/H-a
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