Find each indicated measure and show steps please

m∠N = 72°

mNQ = 94°

Step-by-step explanation:

An inscribed angle is equal to half the measure of its intercepted arc

∠N is an inscribed angle and arc MP is it's intercepted arc

Thus, ∠N = 1/2 arc MP

if arc MP = 144

Then ∠N = 144/2

144/2 = 72

Hence, ∠N = 72°

For ∠P and arc NQ we are given the measure of the inscribed angle and need to find the measure of the intercepted arc.

If the measure of an inscribed angle equals half the measure of its intercepted arc, then the measure of the intercepted arc equals twice the measure of the inscribed angle.

Thus, arc mNQ = 2(∠P)

If ∠P = 47, then mNQ = 2(47)

2 * 47 = 94

Hence, mNQ = 94

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: