A toy train set includes a train station building which is a scale model of a real building. The area of
the front side of the toy building is 1 square foot. The real building's front side has an area of 400
square feet. If we view the real building as a dilation of the toy, what is the scale factor?
Your answer

Answers

Answer 1

Answer:

[tex]20[/tex]

Step-by-step explanation:

The area of the front side of the toy model is [tex]1\ \text{ft}^2[/tex]

The area of the real building's front side is [tex]400\ \text{ft}^2[/tex]

So

[tex]1\ \text{ft}^2[/tex] of the toy model is equivalent to [tex]400\ \text{ft}^2[/tex] of the real building.

Area scale factor is given by [tex]k^2[/tex], where [tex]k[/tex] is the scale factor of the sides.

So,

[tex]\dfrac{400}{1}=k^2\\\Rightarrow k=\sqrt{400}\\\Rightarrow k=20[/tex]

Hence, the scale factor is [tex]20[/tex].

Answer 2

The scale factor should be 20.

Important information:

The area of the front side of the toy building is 1 square foot. The real building's front side has an area of 400 square feet.

Calculation of the scale factor:

Since 1 square foot should be equal to 400 square feet

So,

[tex]400\div 1 = k^2[/tex]

[tex]K = \sqrt{400}[/tex]

k = 20

Learn more about the scale factor here: https://brainly.com/question/23908178


Related Questions

4 + 5 x (10 divided by 9 ) 4 = ?

Answers

Answer:

40

Step-by-step explanation:

4+5=9

9x(10/9)=10

10x4=40

This question has 2 parts. Please explain everything you did in order to answer the second question!

Answers

Answer:

41.8 units

Step-by-step explanation:

Property of the kite: diagonals are perpendicular

PQ = PS = √10²+6² = √136 = 11.7 roundedRS = RQ = √6²+7²= √85 = 9.2 rounded

Perimeter is the sum of the side lengths:

P = 2*(11.7 + 9.2) = 41.8

Drag and drop the correct terms to classify the triangles based on sides or angles.

Answers

1. Equilateral
2. Isosceles
3. Scalene
4. Right
5. Acute
6. Obtuse

The triangles are classified below.

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

An equilateral triangle is a triangle where all three sides are equal.

The right triangle is a triangle where one angle is 90 degrees.

An isosceles triangle is a triangle where two sides are equal.

An obtuse triangle is a triangle where the angle is greater than 90 degrees

An acute triangle is a triangle where the angles are less than 90 degrees.

A scalene triangle is a triangle where all three sides are different.

Now,

Side 5 cm, 5 cm, 5 cm, and 5 cm is an equilateral triangles.

Since all the sides are the same.

Sides of 3 cm, 5 cm, and 5 cm is an isosceles triangle.

Since the two sides are the same.

Sides of 3 cm, 5 cm, and 7 cm is a scalene triangle.

Since all three sides are different.

Angles of 40°, 50°, and 90° is a right triangle.

Angles of 40°, 60°, and 80° is an acute triangle.

Angles of 40°, 40°, and 100° is an abtuse triangle.

Thus,

The triangles are classified above.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ5

Which expression is the same as (2 x 7) x 3 ?

Answers

Answer:

[tex]42x^{2}[/tex]

which of the following is equivalent to 3(5+2i)-2(3-6i)^2

Answers

Umm im not sure maby like 1+1 or sum

Answer:

can u show me which following?

Step-by-step explanation:

show like (a, (b or something like that because it says *following and i think that it should have something like that ;-;

write the equation of the line that is parallel to y = 4x -7 and passes through the point (-2, -5). show your work.​

Answers

Answer:

y = 4x + 3

Step-by-step explanation:

To do this, put the new line into the form y = mx + b where m is the slope and b is the y-intercept.

When two lines are parallel, they have the same slope. Since, the slope of the first line is 4, that means the slope of the second line is also 4.

So far, the equation is y = 4x + b.

Then, since you know (-2, -5) is a solution, x = -2, y = -5 is a solution so you can plug this into the equation.

This would be:

-5 = 4 * -2 + b

-5 = -8 + b

3 = b

This means the equation is y = 4x + 3.

What is the area of the composite figure?

Answers

Hello! :)

[tex]\large\boxed{A = 32.5cm^{2}}[/tex]

We can use the following area to solve for the area of the trapezoid pictured:

[tex]A = \frac{1}{2}(b_{1} + b_{2})h[/tex]

Where:

h = height

b1 = bottom base

b2 = top base

Plug in the given values:

[tex]A = \frac{1}{2}(9 + 4)(5)[/tex]

Simplify:

[tex]A = \frac{1}{2}(65)\\\\A = 32.5 cm^{2}[/tex]

Can you help me please with this

Answers

-39/100 is the answer according to me ..

Plz mark me as brainliest if u found it helpful

(GIVING BRAINLYIST) 4 ÷ 1/2 YOU HAVE TO show your work on paper using fraction models!

Answers

Answer:

8

Step-by-step explanation:

so my school uses the method called kcf (keep change flip)

keep the 4

change the division sign to a multiplication sign

flip 1/2 to 2/1

4x2=8

Answer:

8 i first said two but used a caculater and found out it was 8

Step-by-step explanation:

help help meeee!!!!!

Answers

Answer:

The correct answer will be $725

Answer:I believe it is $725

Step-by-step explanation: 12.50(1+0.16)

= 14.5 then 14.5 times 50 = 725

Plz guys can you guys help me

Answers

Answer:

answer B is correct of this question

Answer:I believe the answer is C my dude

Step-by-step explanation:

Ricardo works as a real estate agent. he earns 6% commission for every how he sells. last month, Ricardo sold two homes. One sold for $135,000 and the other sold for $160,000. how much did Ricardo earn by selling these two homes?

Answers

Add the two houses together:

135000 + 160000 = 295,000

Multiply the total by the percentage:

295,000 x 0.06 = $17,700

He earned $17,700

Madison makes 4 types of hair ribbons. She makes 3 of each type of ribbon. How
many hair ribbons does Madison make?
A 12
B. 10
C. 9
D. 7

Answers

Answer:

D. 7

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

PLEASE HELP 22 POINTS

Answers

Answer:

y = 15 m<a = 78 m<b = 68

Step-by-step explanation:

(5y+3) + (4y+8) --> 9y + 11

9y + 11 = 146

y = 15

plug in 15 into the equations for the angles and you get

m<a = 78

m<b = 68

Which of the following lists of ordered pairs is a function?
O A. (2, 4), (0, 2), (2, -4), (5,3)
O B. (1,6), (2,7),(4,9), (0,5)
O c. (0, 2), (2, 3), (0, -2), (4,1)
O D. (1, 2), (1, -2), (3, 2), (3, 4)

Answers

Answer:

b

Step-by-step explanation:

Answer:

The option B i.e.(1,6), (2,7),(4,9), (0,5) represents the function.

Step-by-step explanation:

We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.

In other words, we can not have duplicated inputs as there should be only 1 output for each input.

Checking option A:

(2, 4), (0, 2), (2, -4), (5,3)

Here, the input x = 2 is repeated twice.

Thus, option A does not represent the function as the input x = 2 is duplicated and we can not have duplicated inputs as there should be only 1 output for each input.

Checking option B:

(1,6), (2,7),(4,9), (0,5)

It is clear that no input value is repeated. In other words, each input or x-value of the X set has a unique y-value or output of the Y set.

Thus, the option B represents the function.

Checking option C:

(0, 2), (2, 3), (0, -2), (4,1)

Here, the input x = 0 is repeated twice.

Thus, option C does not represent the function as the input x = 0 is duplicated and we can not have duplicated inputs as there should be only 1 output for each input.

Checking option D:

(1, 2), (1, -2), (3, 2), (3, 4)

Here, the input x = 1 is repeated twice, and also x = 3 is repeated twice,

Thus, option D does not represent the function as we can not have duplicated inputs as there should be only 1 output for each input.

Conclusion:

The option B i.e.(1,6), (2,7),(4,9), (0,5) represents the function.

An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.0 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 6 engines and the mean pressure was 5.4 pounds/square inch with a standard deviation of 0.7. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Answers

Answer:

Do no reject null hypothesis.  

Conclusion:

there is no sufficient statistical evidence at 0.025 level of significance to support the claim.

Step-by-step explanation:

Given that;

mean x" = 5.4

standard deviation σ = 0.7  

n = 6

Null hypothesis H₀ : μ = 5.0  

Alternative hypothesis H₁ : μ > 5.0    

∝ = 0.025    

now,

t = ( 5.4 - 5.0) / ( 0.7/√6) = 0.4 / 0.2857 = 1.4

degree of freedom df = n-1 = 6 - 1 = 5

T critical = 2.571

Therefore; t < T critical,

Do no reject null hypothesis.  

Conclusion:

there is no sufficient statistical evidence at 0.025 level of significance to support the claim.

Abdul earns $13.00 in interest each month for six months. How much interest will Abdul have earned at the end of six months?

Answers

answer:

78

-- please mark the brainliest and click the thanks button if correct :)

Answer:

$78

Step-by-step explanation:

13 * 6 is 78

I hope that helps broski

This question is geometry

Answers

Answer:

Its 138

Step-by-step explanation:

LOL

which expression is equivalent to 7a-8-12a+4​

Answers

Answer:

-5a-4

Step-by-step explanation:

7a-8-12a+4

7a-12a-8+4

=-5a-4

how much is 1/2÷8×57÷13+15

Answers

Answer:

Use the BODMAS method and at the end work the fraction left by adding it to 15

My answer was 15.274


[tex] \sqrt{361} [/tex]


Answers

Answer:

19

Step-by-step explanation:

Answer:

19

Step by step explanation:

HELP QUICK ILL GIVE TOU BRAINLIEST
find the surface area...

Answers

Answer: 483.09 in^2
Explanation: 12, 11, 10, 12

The bottom part of this block is a rectangular prism. The top part
is a square pyramid. How much paper is needed to completely
cover the block? Explain.​

Answers

Answer:

Check question number 9 in that file you may be able to understand the problem

Step-by-step explanation:

6x - 9x - 5 + 8 + 7x

Show your work.

Answers

Answer:

6x−9x−5+8+7x

=6x+−9x+−5+8+7x

Combine Like Terms:

=6x+−9x+−5+8+7x

=(6x+−9x+7x)+(−5+8)

=4x+3

Answer:

=4x+3

Step-by-step explanation:

I hope this helps

Answer:

=4x + 3

Step-by-step explanation:

Add the numbers

6

YOU HAD YOUR WORD TASTUMI YOU HAD YOUR WORD!2

Answers

Answer:

yes :(

Step-by-step explanation:

A store owner spends 7x + 13 dollars on two orders of boxes of light bulbs, including shipping.

Part A
If she spends 3x + 5 dollars on the first order of light bulbs, which of the following represents how much she spends on the second-order?
10x + 18
4x + 8
21x + 65
10x + 8
Part B
If the store owner spent a total of $90 on both orders, how much does a box of light bulbs cost in dollars? Enter the number in the box.

Answers

Answer:

[tex]B = 4x + 8[/tex]

A box = $11

Step-by-step explanation:

Given

[tex]Total = 7x + 13[/tex]

Represent the first order with A and the second with B.

So, we have:

[tex]A = 3x + 5[/tex]

Solving (a): Find B.

To find B, we make use of:

[tex]A + B = Total[/tex]

Make B the subject

[tex]B = Total - A[/tex]

Substitute values for Total and A

[tex]B = 7x + 13 - (3x + 5)[/tex]

Open bracket

[tex]B = 7x + 13 - 3x - 5[/tex]

Collect Like Terms

[tex]B = 7x - 3x + 13 - 5[/tex]

[tex]B = 4x + 8[/tex]

Solving (b): Cost of a box of light bulb

This means that:

[tex]Total = 90[/tex]

Substitute 7x + 13 for Total

[tex]7x + 13 = 90[/tex]

Collect Like Terms

[tex]7x = 90 - 13[/tex]

[tex]7x = 77[/tex]

Make x the subject

[tex]x = \frac{77}{7}[/tex]

[tex]x = 11[/tex]

What is the area of the triangle?
2
2
units2

Answers

Answer:

2

Step-by-step explanation:

you just multiply

Charlin got 20 questions correct on her exam and scored a 80%. How many (total) questions were on the exam

Answers

The answer would be 25

HELP HELP HELP HELP HELP PLEASE PLEASE!!!!!!

Answers

I did something very very similar to this bu it was couple years ago

9514 1404 393

Answer:

  84 = j × 7

Step-by-step explanation:

A product results from multiplying two numbers. Here, the two numbers are said to be "Julie's score" and 7. "Julie's score" is represented by j, so the product is ...

  j × 7

Then the translation can be ...

  84 is the product of j and 7

  84 = j × 7

__

In algebra, we can indicate a product without the multiplication symbol, simply by writing the factors next to each other. Generally, we write the numeric factor first:

  84 = 7j . . . . another way to write the answer

Note that this latter method does not seem to appear in the forms available for your answer box.

Isabella is making a display board for the school trip. The display board is 2.50m by 2m rectangle. She needs to cover the entire display board with card. How much card would she needs?

Answers

Answer:

5m^2

Step-by-step explanation:

Given data

Length of board= 2.50m

Width of board= 2m

The cover need should have the same area as the board

Area= Length*Width

Area= 2.5*2

Area=5m^2

Hence the area of the cover is 5m^2

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