The length, breadth ND height of box are 32 cm 16cm, 8cm. wht is the maxim length of the string that can be used to measure the sides of the box exactly

8 cm

Step-by-step explanation:

The maximum length of the string will be the greatest common divisor of  32 , 16 , 8

32 = 2 * 2 * 2 * 2 * 2

16 = 2 * 2 * 2 * 2

8 = 2 * 2 * 2

GCD = 2* 2 * 2 = 8

The maximum length of the string = 8 cm

$30.32

step-by-step explanation:

65.00*.12=2.80

65.00-2.80=57.20

57.20*1.06=60.632

60.632/2=30.316

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)