B is the midpoint of line AC. AB=x+6 and AC=3x-31. What is the length of line BC

BC = 49

Step-by-step explanation:

Since B is the midpoint,  AB is half of AC & AB equals to BC

3x-31 = 2(x+6)           >> distribute 2 (AB is doubled here since AB=BC)

3x-31 = 2x+12            >> add 31 to both sides

3x = 2x+43                >> subtract 2x from both sides to get x alone

x = 43

AB=BC so you can use AB's equation

BC = x + 6

BC = (43) + 6

BC = 49

the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

the root or roots of a polynomial are the values of the variable that makes the polynomial equal to 0. we can find the roots of a polynomial making the expression equal to 0 and then, isolating the variable (it it has just one variable).

for example, given the following polynomial:

the root or zero of the polynomial, can be found by making the expression equal to 0, and then, isolating the variable, so, finding the root we have:

therefore, we have that the root of the polynomial is equal to 2.

we must remember that the number of roots that a polynomial can have, will depend on the degree of the polynomial, a first degree polynomial have will have one single root, a second degree polynomial (quadratic expression) may have two roots and so.

hence the correct option is:

b. a value of the variable that makes the polynomial equal to zero.

have a nice day!

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