The image of an eraser in a magnifying glass is three times the eraser’s actual size and has a width of 14.4 cm. What is the actual width of the eraser in cm?
a) 14.4 cm.
b) 3 cm.
c) 43.2 cm.
d) 4.8 cm.
is it C?
A square has 16-cm sides. What is the perimeter of the image of this square after a dilation of 0.8?
a) 12.8 cm.
b) 51.2 cm.
c) 20 cm.
d) 80 cm.
is it A?
A dilation maps triangle LMN to triangle L’M’N’. MN = 14 in. and M’N’ = 9.8 in. If LN = 13 in., what is L’N’?
a) 18.6 in.
b) 9.1 in.
c) 9.8 in.
d) 0.7 in.
is it B?
The first is wrong.
I don't know the other two answers.
For the first question, we are given that the image of an eraser in a magnifying glass is three times the eraser's actual size and has a width of 14.4 cm. We need to find the actual width of the eraser in cm.
To solve this, we can set up a proportion. Let's say the actual width of the eraser is 'x' cm. We can set up the proportion as follows:
(actual width of eraser) / (width of image) = (actual size ratio) / (image size ratio)
x / 14.4 = 1 / 3
To solve for 'x', we can cross-multiply and divide:
3x = 14.4
x = 14.4 / 3
x ≈ 4.8 cm
So, the actual width of the eraser is approximately 4.8 cm.
Therefore, the correct answer is d) 4.8 cm.
Moving on to the second question, we are asked to find the perimeter of the image of a square after a dilation of 0.8. We are given that the square has 16 cm sides.
To find the perimeter of the image, we need to multiply the length of each side by the dilation factor (0.8) and then add up the lengths of the four sides.
Perimeter of the image = (dilation factor) x (length of each side) x 4
Perimeter of the image = 0.8 x 16 x 4
Perimeter of the image = 51.2 cm
Therefore, the correct answer is b) 51.2 cm.
Now, let's move on to the third question. We are given that a dilation maps triangle LMN to triangle L’M’N’. MN = 14 in. and M’N’ = 9.8 in. We need to find the length of L’N’.
Since dilation preserves the ratio of corresponding sides, we can set up the proportion:
(M'N') / (MN) = (L'N') / (LN)
Substituting the given values, we have:
9.8 / 14 = L'N' / 13
To solve for L'N', we can cross-multiply and divide:
(9.8 * 13) / 14 = L'N'
L'N' ≈ 9.1 in.
Therefore, the correct answer is b) 9.1 in.