Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 6, 8, 10 and a second triangle labeled D prime with side lengths of 24, 32, 40 Determine the scale factor used. one fourth 4 3 one third

Answers

Answer 1

The scale factor represents the Ratio of the side lengths between the two similar figures. side length in triangle D' is four times larger than the corresponding side length in triangle D.

The scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

Triangle D has side lengths of 6, 8, and 10 units, while triangle D' has side lengths of 24, 32, and 40 units.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

For the first side, D' has a length of 24 units, while D has a length of 6 units.

24/6 = 4

For the second side, D' has a length of 32 units, while D has a length of 8 units.

32/8 = 4

For the third side, D' has a length of 40 units, while D has a length of 10 units.

40/10 = 4

Since all the ratios are equal to 4, we can conclude that the scale factor used to dilate triangle D to create triangle D' is 4.

The scale factor represents the ratio of the corresponding side lengths between the two similar figures. In this case, every side length in triangle D' is four times larger than the corresponding side length in triangle D.

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Answer 2

Answer: it is 4

Step-by-step explanation:

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Related Questions

Will give brainliss if correct
Siplify this Step 1: −4(x − 15y) + 5(−4x − 6y)
And also please have it like this and
Step 1:
Step 2:
Step3:
Step4:
Etc
depending on how many steps it takes to simplify it
Please need it quick

Answers

Answer:

-24x + 30y

Step-by-step explanation:

Step 1:

−4(x − 15y) + 5(−4x − 6y)

Step 2:

−4x + 60y + (−20x − 30y)

Step 3:

Combine like terms within each set of parentheses:

−4x + 60y − 20x − 30y

Step 4:

Combine like terms:

(-4x - 20x) + (60y - 30y)

Step 5:

Simplify:

-24x + 30y

Final result:

-24x + 30y

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The sum of the first n whole numbers is given by the
expression (n²+ n). Expand the
equation by multiplying, then find the sum of the first 12 whole numbers.

Answers

The sum of the first 12 whole numbers of the sequence is 156.

Given that, the sum of the first n whole numbers is given by the expression (n²+ n).

Here, n=12

Substitute n=12 in the expression n²+ n, we get

12²+ 12

= 144+12

= 156

Therefore, the sum of the first 12 whole numbers of the sequence is 156.

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A group of twelve people is going to take a ride on a roller coaster at the same time in two different trains. One train cannot fit more than 8 passengers, and the other cannot fit more than 7. In how many ways can the group take a ride?

Answers

There are 1287 ways in which the group of twelve people can take a ride on the roller coaster.

To determine the number of ways the group of twelve people can take a ride on the roller coaster, we need to consider the different combinations of people that can fit in each train.

Let's analyze the possibilities:

If the train that can fit 8 passengers is chosen:

There are 12 people to choose from, and we need to select 8 of them to ride in this train.

The number of ways to choose 8 people out of 12 can be calculated using the combination formula, denoted as C(12, 8) or 12C8, which is equal to 12! / (8! × (12-8)!).

Simplifying this expression, we find that C(12, 8) = 12! / (8! × 4!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495.

If the train that can fit 7 passengers is chosen:

There are 12 people to choose from, and we need to select 7 of them to ride in this train.

The number of ways to choose 7 people out of 12 can be calculated using the combination formula as well, denoted as C(12, 7) or 12C7, which is equal to 12! / (7! × (12-7)!).

Simplifying this expression, we find that C(12, 7) = 12! / (7! × 5!) = (12 × 11 × 10 × 9 × 8) / (5 × 4 × 3 × 2 × 1) = 792.

Therefore, the total number of ways the group can take a ride on the roller coaster is the sum of the possibilities from both scenarios:

495 (for the train fitting 8 passengers) + 792 (for the train fitting 7 passengers) = 1287.

Hence, there are 1287 ways in which the group of twelve people can take a ride on the roller coaster.

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