Acarpenter has two lengths of wood; one is 108cm long and the other is 72cm long. he wants to cut them up to produce smaller pieces of wood to build a shelving unit so they all need to be the same length, with no wood left over. what is the greatest length, in cm, that he can make the shelves?

36 centimeters.

Step-by-step explanation:

1. To solve this problem you must find the Greatest common factor.

2. List the prime factor of 108 and 72:

3. Now, you must choose the common prime numbers with the lowest exponents and multiply them:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

explanation:

step-by-step explanation: