Find the point, m, that divides segment ab into a ratio of 2: 1 if a is at (-1, 2) and b is at (8, 15). a) (6, 8) b) (6, 26 3 ) c) (5, 32 3 ) d) (5, 26 3 )

(5 , 10.67)

Step-by-step explanation:

Given that a point M divides segment AB into a ratio of 2:1

A = (-1,2)

B = (8,15)

x(M) = x1 + a / (a+b) (x2 - x1)

y(M) = y1 + a / (a+b) (y2 - y1)

where,

x1 = -1

x2 = 8

y1 = 2

y2 = 15

a : b = 2 : 1

a = 2

b = 1

x(M) = -1 + ( 2 / (2 + 1)) (8 + 1)

       = 5

y(M) = 2 + 2 / (2 + 1) (15 - 2)

       = 10.67

c

step-by-step explanation:

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)