25 points

the figure shows two triangles on a coordinate grid:

what set of transformations is performed on triangle abc to form triangle a’b’c’?

a 180-degree counterclockwise rotation about the origin followed by a translation 5 units down

a translation 5 units down followed by a 180-degree counterclockwise rotation about the origin

a 270-degree counterclockwise rotation about the origin followed by a translation 5 units to the right

a translation 5 units to the right followed by a 270-degree counterclockwise rotation about the origin

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:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: