All categories

3 years ago

Given the preimage points: find the coordinates

Mathematics

1 answer:

m_a_m_a [10]3 years ago

8 0

Question 1)

Answer:

Please see the explanation.

Step-by-step explanation:

We know that the dilation of an original object shows how much bigger or smaller the image will really get, as compared to the original shape.

Also,

if the value of scale factor > 1, the image will get bigger.

if the value of scale factor < 1, the image will get smaller.

The new coordinates of the image can be determined by multiplying the scale factor with the coordinates of the original object.

Given the preimage points:

A(0, 5)

B(4, 9)

C(-1, -8)

The formula of the dilation by a scale factor of 3:

(x, y) → (3x, 3y)

As the scale factor > 1, so the image will be bigger.

Therefore, the coordinates of the dilated image after the dilation by a scale factor of 3 will be:

A(x, y) → (3x, 3y) = A(0, 5) → (3(0), 3(5)) = A'(0, 15)

B(x, y) → (3x, 3y) = B(4, 9) → (3(4), 3(9)) = B'(12, 27)

C(x, y) → (3x, 3y) = C(-1, -8) → (3(-1), 3(-8)) = C'(-3, -24)

Question 2)

Answer:

Please see the explanation.

Step-by-step explanation:

Given the preimage points:

A(0, 5)

B(4, 9)

C(-1, -8)

The formula of the dilation by a scale factor of 1/2:

(x, y) → (1/2x, 1/2y)

As the scale factor < 1, so the image will be smaller.

Therefore, the coordinates of the dilated image after the dilation by a scale factor of 1/2 will be:

A(x, y) → (3x, 3y) = A(0, 5) → (1/2(0), 1/2(5)) = A'(0, 5/2)

B(x, y) → (3x, 3y) = B(4, 9) → (1/2(4), 1/2(9)) = B'(2, 9/2)

C(x, y) → (3x, 3y) = C(-1, -8) → (1/2(-1), 1/2(-8)) = C'(-1/2, -4)

You might be interested in

HELP ASAP!!!!!!!PLEASE SHOW WORK!!!!!! !!!!!

DENIUS [597]

Answer:

Area = 12.82 miles²

Step-by-step explanation:

Area of a triangle with two adjacent sides and the inscribed angle between these side is given by,

Area = $\frac{1}{2}ab[\text{sin(C)}]$

By substituting the values of sides a, b and the angle C,

Area = $\frac{1}{2}(5.7\times 9.3)[\text{sin}(14^{\circ})]$

= 12.82 square miles

4 0

3 years ago

What is the volume of a cylinder with a height of 4.5 cm and a base with a radius of 5.2 cm, to the nearest tenth of a cubic cen

lawyer [7]

Answer:

382.3

Step-by-step explanation:

v=πr²h

v=π(5.2)²(4.5)

v=about 382.27

3 0

3 years ago

A class trip was 234 miles away from the school. If the bus driver drove at a constant speed of 70 mph, about how long did the t

puteri [66]

Answer:

A. 3 hours 20 minutes

Step-by-step explanation:

The distance divided by the speed gives you the time.

(234 miles)/(70 mph) = 3.343 hours.

3.343 hours is decimal hours. We need hours and minutes.

1 hour = 60 minutes. We separate the whole hours from the decimal part of the hours, and we multiply the decimal part of the hours by 60 to find minutes.

3.343 hours =

= 3 hours + 0.343 hours

= 3 hours + 0.343 hours * 60 minutes/hour =

= 3 hours + 20.6 minutes

The closest answer is:

A. 3 hours 20 minutes

5 0

3 years ago

Read 2 more answers

The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for t

nadezda [96]

Answer:

a. There is evidence that the population mean is above $300.

b. There is no evidence that the population mean is above $300.

c. There is no evidence that the population mean is above $300.

d. The director could ask for cheaper similar books.

Step-by-step explanation:

Let X be the random variable that represents the cost of textbooks. We have observed n = 25 values, $\bar{x}$ = 315.4 and s = 43.20. We suppose that X is normally distributed.

We have the following null and alternative hypothesis

$H_{0}: \mu = 300$ vs $H_{1}: \mu > 300$ (upper-tail alternative)

We will use the test statistic

$T = \frac{\bar{X}-300}{S/\sqrt{25}}$ and the observed value is

$t_{0} = \frac{315.4 - 300}{43.20/\sqrt{25}} = 1.7824$ .

If $H_{0}$ is true, then T has a t distribution with n-1 = 24 degrees of freedom.

a. The rejection region is given by RR = {t | t > $t_{0.9}$ } where $t_{0.9} = 1.3178$ is the 90th quantile of the t distribution with 24 df, so, RR = {t | t > 1.3178}. Because the observed value satisty 1.7824 > 1.3178, there is evidence that the population mean is above $300.

b. If s = 75, then the observed value is $t_{0} = \frac{315.4 - 300}{75/\sqrt{25}} = 1.0267$ . The rejection region for a 0.05 level of significance is RR = {t | t > $t_{0.95}$ } where $t_{0.95} = 1.7108$ is the 95th quantile of the t distribution with 24 df, so, RR = {t | t > 1.7108}. Because the observed value does not fall inside the rejection region, there is no evidence that the population mean is above $300.

c. If $\bar{x} = 305.11$ and s = 43.20, the observed value is $t_{0} = \frac{305.11 - 300}{43.20/\sqrt{25}} = 0.5914$ . For RR = {t | t > 1.3178} we have that the observed value does not fall inside RR, therefore, there is no evidence that the population mean is above $300.

d. Because the director of admissions is concerned about the high cost of textbooks, and there is evidence that the population mean of costs is above $300, the director could ask for cheaper similar books.

8 0

3 years ago

Which of the following does not represent a function of x?

Vadim26 [7]

Answer:

the third one

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers