A car rental agency charges $75 per week plus $0.25 per mile to rent a car.

Triangle QRS is dilated according to the rule DO,2 (x,y).

Gemiola [76]

The correct options about the dilation are; Options A, B and E

<h3>How to interpret Dilated Objects?</h3>

From the given information, find attached a dilated image.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2(x, y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

A) DO, 2 (x, y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

Thus Option A is correct.

B) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

m = 4/(-6+2) = 4/-4

m = -1

Option B is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

Option C is false

d) The vertices of the image are closer to the origin than those of the pre-image.

From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.

Option D is False

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

Option E is correct.

Read more about Dilated Objects at; brainly.com/question/10253650

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8 0

2 years ago

Find (f^-1)(a). F(x)=cosx- sin x + pi/2 a=pi/2, 0

Novosadov [1.4K]

Answer:

pi/4

Step-by-step explanation:

my answer is in the image above

7 0

2 years ago

Select the correct answer.

Sonja [21]

I believe the answer is c

3 0

3 years ago

A rectangular prism has a length of 14 cm, width of 2 cm, and height of 3 cm. What is the volume?

Cloud [144]

Answer: 84 cubic cm

Step-by-step explanation: You just do 14 times 2 and the answer times 3 which is 84 cubic cm.

4 0

3 years ago

Read 2 more answers

A freight company has shipping orders for two products. The first product has a unit volume of 10 cu ft and weighs 50 lb. The se

nydimaria [60]

Answer:

Number of units of first product = 112

Number of units of second product = 400

Step-by-step explanation:

Given that there are two products which are to be shipped.

<em>First product details:</em>

Unit volume = 10 cu ft

Weight of one unit = 50 lb

<em>Second product details:</em>

Unit volume = 3 cu ft

Weight of one unit = 40 lb

Total volume that can be carried by a truck = 2320 cu ft

Total weight that can be carried by a truck = 21600 cu ft

To find:

The number of units of each product that can be transported in one shipment in the truck?

Solution:

Let number of units of first product = $x$

Let number of units of second product = $y$

We can write down two linear equations in two variables here and solving them will give us the answer we are required to find.

As per question statement, the equations can be written as:

$10x+3y = 2320 ...... (1)\\50x+40y = 21600\\\Rightarrow 5x+4y = 2160...... (2)$

Multiplying equation (2) with 2 and subtracting equation (1) from it:

$8y - 3y = 4320-2320\\\Rightarrow 5y = 2000\\\Rightarrow \bold{ y = 400}$

By equation (1):

$10x+1200 = 2320\\\Rightarrow 10x = 1120\\\Rightarrow \bold{x = 112}$

Answer is:

Number of units of first product = 112

Number of units of second product = 400

6 0

2 years ago