Which of the following expressions are equivalent to

Step-by-step explanation:

Some facts to establish before we try to solve: and another way of writing is . Also order of operations: PEMDAS

For the first option:

We solve what is in the parenthesis: 2*2=4*2=8*2=16*2=32*2=64 so , which is another way to write

For the second option: If the square root of 64 is 8, the there is no way we can multiply another value by it.

The third option: When dealing with square roots, we can solve the inside first and then take the square root:

definitely not 64 (though if you're curious it's 4096)

The fourth: Another way to write the square root is to raise the value to the 1/2 power so

Which is the same as

Fifth: Like the third, we solve the inside of the square root first

16*4= 64 and then

Sixth: We need a nice whole number (8), and has no clean roots, so its result will have decimals. It can't be our answer

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: