Which of the following expressions has a coefficient of 10 and a constant of 5?
10 – 5 , 10 + 5r , 10r + 5 , 10+5


  1. Answer:
    Step-by-step explanation:
    Below, we’ll examine definitions of “coefficients” and “constants” in the context of the correct answer “10r+5”
    Coefficients are numbers that are multiplied to letters.  When a number is multiplied to a letter, the multiplication symbol is often not explicitly written in.
    In this case, the 10r means there are ten r’s, similar to how if one had ten cars, one could say 10 cars (without needing to write in a multiplication symbol).
    Constants are numbers that are not multiplied to a number.  They are a number on their own that may (or may not) be connected to something else by addition (note: it may also be connected to something by “subtraction”, but the subtraction should instead be thought of as “plus a negative”).
    In this case, the 5 is by itself (not multiplied to anything), and is added to other things.
    Ruling out the other answers
    In the first choice, 10-5, there is subtraction, so we envision it as 10+(-5).  the neither the 10 nor the -5 are multiplied to anything, so they are both constants.
    In the second choice, the 10 is not multiplied to anything, but the 5 is multiplied to “r”.  So, the 10 is a constant, and the 5 is a coefficient, but that is not what was requested.
    In the last choice, again, the 10 and the 5 are not multiplied to anything, so they are both constants.


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