In the diagram below, BC−→− bisects ∠FBE If m∠ABF=(7x+20)°, m∠FBC=(2x−5)° and m∠ABC=159°, find the value of x.

X=16

Step-by-step explanation:

m<ABF + m<FBC = m<ABC

7x + 20 + 2x - 5=159     by substitution

9x + 15=159     by combining like terms

9x=144      by subtracting 15 from 159

x=16               by division

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743

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: