A dilation with a scale factor of 2 is applied to
the three line segments shown. The resulting
images are P'Q , A'B' , and M'N'

The lengths of the three line segments after dilation is , and

Explanation:

Given that the length of three line segments are PQ = 2 cm, AB = 1.5 cm and MN = 3 cm

Also, given that the dilation with a scale factor of 2 is applied to the three line segments.

We need to determine the length of line segments P'Q', A'B' and M'N'

Dilation means the transformation of the same shape with different size.

Since, it is given that the dilation with a scale factor of 2, we shall multiply each of the line segments with 2.

Thus, we have,

Thus, the lengths of the three line segments after dilation is , and

6e14 is the answer.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)