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Murrr4er [49]
2 years ago
9

The scale of the room design shows that 1" = 3 feet. How big is the actual room if the design shows a square that is 6 inches wi

de?
Mathematics
1 answer:
adoni [48]2 years ago
4 0

Answer:

arah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:

1 inch=30 feet.

If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?

In this concept, you will learn how proportions are used to find actual and scale dimensions using a scale ratio.

Using Proportions to Find Dimensions

A scale is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.

A scale drawing is a drawing that is used to represent and object that is too large to be drawn in its actual dimensions. If a drawing is to scale, you can use proportions to determine the actual dimensions of the scale drawing.

Let’s look at a scale drawing of a sculpture. In the drawing, the sculpture is 4 inches tall. The scale is 1 inch : 4 feet. It scale can be written as

1 in4 ft

(Note: Inch is abbreviated “in.” or with the double prime mark, ″. Foot/feet is abbreviated “ft” or with the single prime mark, ′.)

A drawing with this scale tells you that 1 inch on paper is equal to 4 feet in real life. If the drawing is 4 inches tall, use the scale to find the actual height of the sculpture.

First, create a proportion using equivalent ratios. Remember to write the corresponding units in the numerator and in the denominator. The actual height of the sculpture is represented by the variable x.

1 in.4 ft.=4 in.x ft.

Then, cross multiply and simplify the equation to find the value of x.

xx==4(4)16

The sculpture will be 16 feet tall.

Let’s make a scale drawing. Use the scale 1′′=2′. Draw a room that is 8′×12′.

First, write a proportion to find the measurement of the width.

1′′2′=x′′8′

Next, cross multiply and simplify the equation to find the value of x.

2x2xx===1(8)84

The drawing will be 4

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0 + 1 = 1
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Go to the horizontal line (x) and find 0.
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Then match up the the x and y to plot the coordinate.

You would continue with this equation with the rest of the xs. 

This is a hard concept to explain in just words, so feel free to comment with any more questions. :D

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3 years ago
Jenny earned a 77 on her most recent test. Jenny’s score is no less than 5 points greater than Four-fifths of Terrance’s score.
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Step-by-step explanation:

7 0
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<span>3x+2y+4+9y=


Combine like terms:
2y+9y=11y


I believe the answer is 3x+11y+4

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Anika [276]

The chairs in the auditorium illustrates an arithmetic sequence

  • The recursive rule is:  an = an-1 + 8; a1 = 26
  • The explicit rule is:  an = 18 + 8n
  • There are 74 seats in the 7th row
  • 840 chairs can fit the auditorium

<h3>The recursive rule</h3>

From the question, we have the following sequence:

Seats: 18, 26, 34

Rewrite as:

26 = 18 + 8

34 = 26 + 8

The above means that:

The number of seats on a row is 8 added to the the number of seats on the previous row.

Hence, the recursive rule is:

an = an-1 + 8; a1 = 26

<h3>The explicit rule</h3>

In (a), we have:

a1 = 26 and d = 8

The explicit rule is calculated using:

an = a1 + (n -1) * d

This gives

an = 26 + (n - 1) * 8

Expand

an = 26 - 8 + 8n

Evaluate the difference

an = 18 + 8n

Hence, the explicit rule is:

an = 18 + 8n

<h3>The number of seats in the row 7</h3>

This means that n = 7.

So, we  have:

a7 = 18 + 8 * 7 = 74

Hence, there are 74 seats in the 7th row

<h3>The sigma notation</h3>

We have the maximum number of rows to be 12.

So, the sigma notation would be:

\sum\limits^{12}_{n=1} {18 + 8n}

The total number of seats is:

Sn = n/2(2a + (n -1) * d)

This gives

S12 = 12/2(2 * 26 + (12 -1) * 8)

S12 = 840

Hence, 840 chairs can fit the auditorium

Read more about arithmetic sequence at:

brainly.com/question/6561461

7 0
2 years ago
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