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$Polygon Y is a scaled copy of Polygon X using a scale factor of (1)/(3). Polygon Y^(') 's area is what fraction of Polygon X 's area?$

Polygon $Y$ is a scaled copy of Polygon $X$ using a scale factor of $\frac{1}{3}$ . $\newline$ Polygon $Y^{\prime}$ 's area is what fraction of Polygon $X$ 's area?

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Scale drawings: word problems

Full solution

Q. Polygon

Y

is a scaled copy of Polygon

X

using a scale factor of

\frac{1}{3}

.

\newline

Polygon

Y^{\prime}

's area is what fraction of Polygon

X

's area?

Scale Factor Explanation: When scaling a two-dimensional figure, the area of the scaled figure is the square of the scale factor times the area of the original figure. In this case, the scale factor is $\frac{1}{3}$ .
Area Comparison Calculation: To find the area of Polygon $Y$ in relation to Polygon $X$ , we square the scale factor $(\frac{1}{3})^2$ .
Square of Scale Factor: Calculating the square of $\frac{1}{3}$ gives us $(\frac{1}{3}) \times (\frac{1}{3}) = \frac{1}{9}$ .
Final Area Ratio: Therefore, the area of Polygon $Y$ is $\frac{1}{9}$ the area of Polygon $X$ .

More problems from Scale drawings: word problems

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Rosie went on a hiking trip. The first day she walked

18

kilometers. Each day since, she walked

90 \%

of what she walked the day before.

\newline

What is the total distance Rosie has traveled by the end of the

10^{\text {th }}

\newline

Round your final answer to the nearest kilometer.

\newline

\mathrm{km}

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Question

A monkey is swinging from a tree. On the first swing, she passes through an arc of

10 \mathrm{~m}

. With each swing, she passes through an arc

\frac{9}{10}

the length of the previous swing.

\newline

What is the total distance the monkey has traveled when she completes her

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swing? Round your final answer to the nearest meter.

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Question

S E=\frac{\sigma}{\sqrt{n}}

\newline

The given equation relates the standard error,

S E

, of a sample mean to the population standard deviation,

\sigma

, and the size of the sample,

n

. Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?

\newline

1

\newline

n=\left(\frac{\sigma}{S E}\right)^{2}

\newline

n=\frac{\sigma^{2}}{S E}

\newline

n=\sqrt{\left(\frac{\sigma}{S E}\right)}

\newline

n=\frac{\sqrt{\sigma}}{S E}

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Question

Avery is designing a large rectangular sign. They want the sign to have an area of

2 \mathrm{~m}^{2}

\frac{4}{5} \mathrm{~m}

\newline

How tall should the sign be?

\newline

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Question

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

\newline

The relationship between the elapsed time

t

, in minutes, and the number of bacteria,

B(t)

, in the Petri dish is modeled by the following function.

\newline

B(t)=10 \cdot 2^{\frac{t}{12}}

\newline

How many bacteria will make up the culture after

120

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

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Question

A large brine tank containing a solution of salt and water is being diluted with fresh water.

\newline

The relationship between the elapsed time,

t

, in hours, after the dilution begins, and the concentration of salt in the tank,

S(t)

, in grams per liter

(\mathrm{g} / \mathrm{l})

, is modeled by the following function.

\newline

S(t)=500 \cdot e^{-0.25 t}

\newline

What will the concentration of salt be after

10

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

1

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Question

After the closing of the mill, the town of Sawyerville experienced a decline in its population.

\newline

The relationship between the elapsed time,

t

, in years, since the closing of the mill, and the town's population,

P(t)

, is modeled by the following function.

\newline

P(t)=12,000 \cdot 2^{-\frac{t}{15}}

\newline

In how many years will Sawyerville's population be

9000

? Round your answer, if necessary, to the nearest hundredth.

\newline

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Question

Carlos has taken an initial dose of a prescription medication.

\newline

The relationship between the elapsed time

t

, in hours, since he took the first dose, and the amount of medication,

M(t)

, in milligrams (

\mathrm{mg}

), in his bloodstream is modeled by the following function.

\newline

M(t)=20 \cdot e^{-0.8 t}

\newline

In how many hours will Carlos have

1 \mathrm{mg}

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\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

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Question

To take a taxi, it costs

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\newline

How many miles did you travel?

\newline

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Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

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and then picking a

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\newline

Write your answer as a percentage.

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