Which of the following relations has a domain of {−5, 0, 5}? {(−5, 0), (0, 5), (1, 0)} {(−5, 5), (0, 5), (5, 5)} {(0, −5), (0, 0), (0, 5)} {(0, −5), (1, 0), (5, 5)}

It's so easy. Domain is the set made up of the first elements of each ordered pair (x, y). 

Look at the second relation {(-5, 5), (0, 5), (5, 5)}. It has three ordered pairs which arw (-5, 5), (0, 5) and (5, 5). 

First element of the first ordered pair (-5, 5) is -5. First element of the second ordered pair (0, 5) is 0. First element of the third ordered pair (5, 5) is 5. 

So, the set made up of the first elements of the ordered pairs is {-5, 0, 5} and hence it is the domain.

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75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.