The endpoints of AB are A(9,4) and B(5,-4). The endpoints of its image after a dilation ar A(6,3) and B(3,-3). a. explain how to find te scale factor. b. locate the center of dilation. show your work

Answers

Answer 1

Answer: Look at the picture for the answer.

Answer 2

Answer:

Final answer:

The scale factor of the dilation is calculated by dividing the length of the line after dilation by the length of the initial line. The length of a line is calculated using the distance formula. The center of dilation is the point from which the shape scales, but we can't determine its location without more information.

Explanation:

To find the scale factor of a dilation in a two-dimensional plane, we divide the length of the line after dilation by the length of the initial line. The length of a line can be calculated using the distance formula which is √[(x₂ - x₁)² + (y₂ - y₁)²].

For AB, the distance will be √[(5 - 9)² + (-4 - 4)²] = √[(-4)² + (-8)²] which equals √80. For A'B', the distance will be √(3 - 6)² + (-3 - 3)² = √[(-3)² + (-6)²] which equals √45. The scale factor (k) of the dilation is the ratio of these distances, so k = √45 / √80 which simplifies to √(9/16) or 3/4.

Unfortunately, without more information, such as a fixed point in the original shape, we can't determine the exact location of the center of dilation. But, conceptually, it's the point that the shape is scaling towards or away from during the dilation.

Learn more about Dilation in Mathematics here:

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If takes 5 farmers 10 days to plant a garden. How many days will it take 10 farmers?

Answers

Answer:

Step-by-step explanation:

2days

The answer is 5 days because you are using twice the number of farmers so it should take half the time to plant the garden

Which of these geometric terms best describes railroad tracks?

Answers

Gee, there's nothing to choose from. I'd guess parallel lines.

What is the complement of the angle 178 degrees and 100 degrees

Answers

$Complement - x \n \n 178 + x = 90 \n \n x = 90-178 = -88. \n\n\nComplement-y \n \n 100 + y = 90 \n \n y = 90-100 = -10$

Thus, the complement of 178 is -88 degrees and complement of 100 is -10.

$The\ complement\ of\ an\ angle\ \alpha \ is\ the\ angle\ 90^0- \alpha .\n\n \alpha =178^0\ \ \ \Rightarrow\ \ \ 90^0- \alpha =90^0-178^0=-88^0\n\n\alpha =110^0\ \ \ \Rightarrow\ \ \ 90^0- \alpha =90^0-110^0=-20^0$

A bin contains red balls and purple balls. A ball is selected at random and then placed back in the bin. The results are recorded after 10 trials, 50 trials, and 200 trials. The results are recorded in the table.Outcome| Number of trials
| 10__50___200
Red | 5___36___152
Purple | 5___14___48

Based on the table, how many times can you expect that a purple ball will be selected in 400 tries?

Answers

In total, we have 5+14+48=67 purple balls in 10+50+200=260 trials, so based on our data, purple balls appear with probability 67/260=0.258, so we expect .258*400=103 purple balls to appear in the larger sample.

Hey there

A bin contains red balls and purple balls. A ball is selected at random and then placed back in the bin. The results are recorded after 10 trials, 50trials, and 200 trials. We know that 5+14+48=67 purple balls in 260 trials. , Purple balls appear with probability 67/260 . Now we multiply and get 258*400=103

a rectangular lawn has a perimeter of 36 meters and a circular exercise run has a circumference of 36 meters which shape will give rico´s dog more area to run?

Answers

The shape is a rectangle lawn

Final answer:

The circular exercise run provides more area for Rico's dog to run than the rectangular lawn. This is determined by calculating the maximum possible area for a rectangle with a perimeter of 36 meters and a circle with a circumference of 36 meters.

Explanation:

To answer which shape will give Rico's dog more area to run, we need to calculate the areas of the given shapes - a rectangle and a circle - using their respective perimeters/circumferences.

For a rectangle with a perimeter of 36 meters, one plausible dimension could be a rectangle with a length of 10 meters and a width of 8 meters, giving an area of 80 square meters assuming the shape is a square. (This gives the maximum area for a given perimeter).

The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. If the circumference is 36 meters, then the radius would be 36/(2π) ≈ 5.73 meters. The area of this circle would then be πr², approximately 103.07 square meters.

In conclusion, the circle will offer more area for Rico's dog to run, despite the rectangular lawn and circular exercise run having the same perimeter and circumference lengths respectively.