Joseph louis lagrange (1736-1813) conjectured that every odd natural number greater than 5 can be written as a sum a plus 2 b, where a and b are both primes. (a) verify this for the odd natural number 11. (b) verify that the odd natural number 17 can be written in this form in four different ways.

Step-by-step explanation:

(a) 11 can be written as (5+2*3), being 5 and 3 prime numbers

(b) 17 can be written as:

3 + 2*7 = 17

7 * 2*5 = 17

11 + 2*3 = 17

13 + 2*2 = 17

CHECK!!

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)