Find value of a and b if 2root3+root5/2root3-root5=aroot15+b

No intro-

First rationalize: root 5 + root 3 divided by root 5 - root 3,

we get, (root 5 + root 3)2 / (root 5 - root 3)( root 5 + root 3)

= (8+2 root 15)/2

now compare LHS and RHS,

(given), (8+2root15) / 2 = a+root 15b

=> 2(4+ root 15) / 2 = a+root15 b [here we removed the common factor and cancelled]

=> 4+ root 15 = a+ root 15 b

therefore, the value of 'a' can be 4 and the value of 'b' can be 1 ( as any no. multiplied with one will be the no. itself)

oof bai

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: