All categories

4 years ago

What is the image of (-9, 2) after a dilation by a scale factor of 3 centered at the origin?

Mathematics

1 answer:

Burka [1]4 years ago

3 0

Answer:

The image of the point is (-27, 6)

Step-by-step explanation:

<em>Let us talk about the dilation</em>

Dilation is a transformation that changes the size of a figure. It can become larger or smaller, but the shape of the figure does not change.
The scale factor of dilation measures how much larger or smaller the image will be. If the scale factor greater than 1, then the image will be larger. If the scale factor between 0 and 1, then the image will be smaller
If the point (x, y) is dilated by scale factor k and the center of dilation is the origin, then its image will be (kx, ky)

∵ Point (-9, 2) is dilated by a scale factor 3

∴ k = 3

∵ The center of dilation is the origin

→ Multiply the coordinates of the point by 3 to find the image

∴ The image = (3 × -9, 3 × 2)

∴ The image = (-27, 6)

The image of the point is (-27, 6)

You might be interested in

Christina must run around the rectangular soccer field during practice. The football field It measures 60 meters long by 45 mete

Reika [66]

Answer:

210 meters

Step-by-step explanation:

4 0

3 years ago

An experiment consists of tossing a coin and drawing a card, with the card-drawing stage dependent on the result of the coin tos

belka [17]

Well .5 for coin toss and with 52 cards in deck and clubs and spades makes it 26 so its 1/26 then those are your probabilities.<span>
</span>

3 0

3 years ago

Read 2 more answers

Hello:) anyone able to explain how to solve the equestrian for part (d) ? Thank youu

Anna007 [38]

Answer:

see explanation

Step-by-step explanation:

Given

4 $a^{4}$ - 5a² + 1 = 0

Use the substitution u = a², then equation is

4u² - 5u + 1 = 0

Consider the product of the coefficient of the u² term and the constant term

product = 4 × 1 = 4 and sum = - 5

The factors are - 4 and - 1

Use these factors to split the u- term

4u² - 4u - u + 1 = 0 ( factor the first/second and third/fourth terms )

4u(u - 1) - 1(u - 1) = 0 ← factor out (u - 1) from each term

(u - 1)(4u - 1) = 0

Equate each factor to zero and solve for u

u - 1 = 0 ⇒ u = 1

4u - 1 = 0 ⇒ 4u = 1 ⇒ u = $\frac{1}{4}$

Convert u back into terms of a, that is

a² = 1 ⇒ a = ± 1

a² = $\frac{1}{4}$ ⇒ a = ± $\frac{1}{2}$

Solutions are a = ± 1 , a = ± $\frac{1}{2}$

7 0

4 years ago

New streetlights will be installed along a section of the highway. The posts for the streetlights will be 7.5 m tall and made of

SIZIF [17.4K]

First, we determine the volumes of the posts may it be cylindrical in shape or rectangular prism.

(A) cylindrical:
( π(26.7/100)² - π(24.2/100)²)*(7.5) = 0.3 m³
(B) rectangular prism:
(40/100)²(7.5) - (35/100)²(7.5) = 0.28125 m³

Then, we calculate for the amount of substance
(A) cylindrical: (0.3 m³)(2700 kg/m³) = 810 kg
(B) rectangular prism : (0.28125 m³)(2700 kg/m³) = 759.375 kg

Then, calculate for the costs
(A) (810 kg)($0.38/kg) = $307.8
(B) (759.375 kg)($0.38/kg) = $288.56

Thus, the answer for A is rectangular post
B. About $19.24 can be saved.

6 0

3 years ago

Which of the pairs of events below is mutually exclusive?

Nady [450]

Answer:

Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

Step-by-step explanation:

Given four pair of events:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards

To find:

Which of the pairs is mutually exclusive?

Solution:

First of all, let us have a look at the definition of mutually exclusive events.

Mutually exclusive events do not have any case in common.

In other words, two events are known as mutually exclusive when both the events can not occur at the same time.

Now, let us have a look at the given options one by one:

1. Drawing an ace of spades and then drawing another ace of spades without replacement from a standard deck of cards.

We know that there is only one ace of spades in a standard deck.

Therefore, the two events can not occur one after the other, so these are mutually exclusive events.

2. Drawing a 2 and drawing a 4 with replacement from a standard deck of cards.

The two events can occur one after the other, so these are not mutually exclusive.

3. Drawing a heart and then drawing a spade without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

4. Drawing a jack and then drawing a 7 without replacement from a standard deck of cards.

Separate cards are drawn one after the other, so not mutually exclusive.

3 0

3 years ago