Points X and Z are on a number line, and point Y partitions line XZ into two parts so that the ratio of the length of line segment XY to the length of line segment YZ is 1:4. The coordinate of X is 1.3, and the coordinate of Y is 3.8. What is the coordinate of Z?

Step-by-step explanation:

if Points X and Z are on a number line and point Y partition line XZ into two parts where XY: YZ = 1:4, this can be expressed as;

XY/YZ = 1/4

cross multiply;

YZ = 4XY

Also, if The coordinate of X is 1.3, and the coordinate of Y is 3.8, then the distance XY will be expressed as XY = 3.8 - 1.3

XY = 2.5

YZ = 4(2.5)

YZ = 10

Since Y is at 3.8 and YZ is 10, then coordinate Z will be YZ + Y

coordinate of Z = 10+3.8

coordinate of Z = 13.8

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step-by-step explanation:

just for that im not answering

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)