What is the best estimate of the distance between the point (-25, 10) and the origin? 8 units , 15 units , 23 units or 27 units

  27 units

Step-by-step explanation:

As an estimate, the distance will be somewhere between the maximum magnitude of the two coordinates (25) and the sum of that and about 4/10 of the minimum of the two (25+.4×10 = 29). The only answer choice in that range is 27.

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The actual distance is found using the Pythagorean theorem (or the distance formula):

  d = √(25² +10²) = √725 ≈ 26.926 ≈ 27 . . . units

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: