Choose all of the expressions that are equal to 61. |−61| the opposite of −61 the opposite of 61 the distance from zero to −61 −|61| −|−61| −(−61)

Step-by-step explanation:

We need to choose all the expressions that are equal to 61.

(i) |−61| : It is true. Modulus of any negative number gives positive number. |-61|=61.

(ii) The opposite of −61 ; It is true. Opposite of negative is positive.

(iii) The opposite of 61 : It is false. The opposite of 61 gives -61.

(iv) distance from zero to −61 : It is true. Distance is positive always.

(v) −|61| : False. It remains negative.

(vi) −|−61| : False. It remains negative.

(vii) -(-61) : True. Double negative makes positive .

Hence, the correct options are : (i), (ii), (iv), (vii).

We need to choose all the expressions that are equal to 61.

(i) |−61| : It is true. Modulus of any negative number gives positive number. |-61|=61.

(ii) The opposite of −61 ; It is true. Opposite of negative is positive.

(iii) The opposite of 61 : It is false. The opposite of 61 gives -61.

(iv) distance from zero to −61 : It is true. Distance is positive always.

(v) −|61| : False. It remains negative.

(vi) −|−61| : False. It remains negative.

(vii) -(-61) : True. Double negative makes positive .

Hence, the correct options are : (i), (ii), (iv), (vii).

Step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: