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Marina86 [1]
3 years ago
9

The ratio of the number of students to the number of teachers in a school is 17:5. If there are 35 teachers in a school, how man

y students are there in the school.
Mathematics
1 answer:
kompoz [17]3 years ago
4 0

Answer:

75 students

Step-by-step explanation:

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Answer:

A 180° rotation of then a dilation by a scale factor of one-third

Step-by-step explanation:

The coordinates of the vertices of ΔABC are;

A(-9, 3), B(-9, 6), and C(0, 3)

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A'(3, -1), B'(3, -2), and C'(0, -1)

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D_{O, \, k} (x, \, y) = (k\cdot x, \, k\cdot y)

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k =The scale factor = 1/3, (one-third) we have;

A dilation of ΔA''B''C'', by a scale factor of 1/3, we get ΔA'B'C' as follows;

D_{O, \, \frac{1}{3} } A''(9, \, -3) = A'(\frac{1}{3} \times 9, \, \frac{1}{3} \times -3) = A'(3, -1)

D_{O, \, \frac{1}{3} } B''(9, \, -6) = B'(\frac{1}{3} \times 9, \, \frac{1}{3} \times -6) = A'(3, -2)

D_{O, \, \frac{1}{3} } C''(0, \, -3) = C'(\frac{1}{3} \times 0, \, \frac{1}{3} \times -3) = C'(0, -1)

The coordinates of the vertices of ΔA'B'C' are A'(3, -1), B'(3, -2), and C'(0, -1), which is the same as the required coordinates of the image;

Therefore, the transformation that can be performed to show that ΔABC and ΔA'B'C' are similar are rotating ΔABC by 180°  then a dilating the image derived after rotation by a scale factor of one-third (1/3) we get ΔA'B'C'.

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