On a school field trip, the school requires that there are 3 teachers for every 75 students. If 125 students attend the trip how many teachers are needed? Write and solve a proportion.
Triangle CAT is located at C (-5, 2), A (-4, 4), T (-1, 2). Find the coordinates of its image after a dilation with a scale factor of 4. (3 points)
Square ABCD was dilated to form square A’B’C’D’. What scale factor was used?
The answer to that one is two just come up with an explanation.
Tell whether the pair of polygons is similar. Explain why or why not.
The top and bottom of the two are 11 and 9.4 for the other one. The right and left are 10 and 8.4 for the other
class: 3/75 = x/125
CAT: just multiply all the coordinates by the scale value
ABCD: no idea, as there is no picture and no information
They are similar only if the ratio of the sides is the same. So, check whether
11/10 = 9.4/8.4
@Steve thank you!
1)3/75 = x/125;x=5
2)(-20,8 or -20,20)(-16,16)(-4,8)
3)2
4)111*8.4=10*9.4=92.4;94
so does 4 mean that it's similar?
To find the number of teachers needed for a school field trip, we can set up a proportion using the given ratio.
Let's say the number of teachers needed for 75 students is x. We can write the proportion as:
3 teachers / 75 students = x teachers / 125 students
To solve the proportion, we can cross-multiply:
3 * 125 = 75 * x
375 = 75x
Dividing both sides of the equation by 75 will give us the value of x:
375 / 75 = x
x = 5
Therefore, 5 teachers are needed for 125 students on the field trip.
Now, let's find the coordinates of the image of triangle CAT after a dilation with a scale factor of 4.
To perform a dilation, we multiply the x and y coordinates of each point by the scale factor.
For point C (-5, 2):
New x-coordinate = -5 * 4 = -20
New y-coordinate = 2 * 4 = 8
So, the new coordinates of point C would be (-20, 8).
Similarly, we can find the new coordinates for points A and T:
Point A (-4, 4) -> New coordinates: (-4 * 4, 4 * 4) = (-16, 16)
Point T (-1, 2) -> New coordinates: (-1 * 4, 2 * 4) = (-4, 8)
Therefore, the image of triangle CAT after a dilation with a scale factor of 4 has the coordinates C'(-20, 8), A'(-16, 16), and T'(-4, 8).
Now, moving on to the square ABCD and its image A’B’C’D’.
For a dilation, the scale factor is determined by comparing the side lengths of the original and the image.
If the length of AB = a, and the length of A'B' = b, then the scale factor can be found using the formula:
Scale factor = b / a
Without the side lengths of the original and the image square provided, it is not possible to determine the exact scale factor. Therefore, we cannot conclude that the scale factor used was two based on the information given.
Lastly, let's determine if the pair of polygons with sides 11 and 9.4 for the top and bottom, and 10 and 8.4 for the right and left, are similar.
Two polygons are considered similar if their corresponding sides are proportional.
To check for similarity, we can compare the ratios of the corresponding side lengths:
Ratio of top/bottom sides = 11 / 9.4
Ratio of right/left sides = 10 / 8.4
If the two ratios are equal, then the polygons are similar.
To check, we can simplify both ratios:
11 / 9.4 ≈ 1.17
10 / 8.4 ≈ 1.19
Since the two ratios are not equal, the polygons are not similar.
In summary:
- 5 teachers are needed for 125 students on the field trip.
- The image of triangle CAT after a dilation with a scale factor of 4 has the coordinates C'(-20, 8), A'(-16, 16), and T'(-4, 8).
- The scale factor used for square ABCD and its image A’B’C’D’ cannot be determined based on the given information.
- The polygons with sides 11 and 9.4 for the top and bottom, and 10 and 8.4 for the right and left are not similar.