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kicyunya [14]
3 years ago
14

Tony plans to run a 5,000-meter fun run at a constant rate of 250 meters per minute. He uses function f to model his distance fr

om the finish line x minutes after the start of the race.
x f(x)
0 5,000
1 4,750
2 4,500
3 4,250
4 4,000
5 3,750
6 3,500


A.
Tony's function is always decreasing.
B.
Tony's function is always negative.
C.
Tony's function is exponential.
D.
The domain of Tony's function is [0 , 5,000].

Mathematics
2 answers:
kramer3 years ago
8 0

Answer:

Option A.

Step-by-step explanation:

Based on the information provided on the question

the function used to model Tony's run is:

f(x) = -250*x  + 5000

This means that after x = 20 minutes, Tony will arrive to the finish line

f(20) = -250*(20)  + 5000 = -5000 + 5000 = 0

The function is always decreasing, because we are dealing with a line with negative slope.

Option A.

Elden [556K]3 years ago
5 0

Answer:

Step-by-step explanation:

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DIscrete Math
Daniel [21]

Answer:

Step-by-step explanation:

As the statement is ‘‘if and only if’’ we need to prove two implications

  1. f : X \rightarrow Y is surjective implies there exists a function h : Y \rightarrow X such that  f\circ h = 1_Y.
  2. If there exists a function h : Y \rightarrow X such that  f\circ h = 1_Y, then f : X \rightarrow Y is surjective

Let us start by the first implication.

Our hypothesis is that the function f : X \rightarrow Y is surjective. From this we know that for every y\in Y there exist, at least, one x\in X such that y=f(x).

Now, define the sets X_y = \{x\in X: y=f(x)\}. Notice that the set X_y is the pre-image of the element y. Also, from the fact that f is a function we deduce that X_{y_1}\cap X_{y_2}=\emptyset, and because  f the sets X_y are no empty.

From each set X_y  choose only one element x_y, and notice that f(x_y)=y.

So, we can define the function h:Y\rightarrow X as h(y)=x_y. It is no difficult to conclude that f\circ h(y) = f(x_y)=y. With this we have that f\circ h=1_Y, and the prove is complete.

Now, let us prove the second implication.

We have that there exists a function  h:Y\rightarrow X  such that f\circ h=1_Y.

Take an element y\in Y, then f\circ h(y)=y. Now, write x=h(y) and notice that x\in X. Also, with this we have that f(x)=y.

So, for every element y\in Y we have found that an element x\in X (recall that x=h(y)) such that y=f(x), which is equivalent to the fact that f is surjective. Therefore, the prove is complete.

3 0
2 years ago
If f(x) 3 x-1+ 4 and g(x) 4x-7 what is (f-g)(x)?
andre [41]
Hello : 
<span>If f(x)=  3 ^x-1+ 4 and g(x) = 4x-7
 (f-g)(x) = f(x) - g(x)= </span>3 ^x-1+ 4  - (4x - 7) 
(f-g)(x) =3 ^x-1-4x +11.....( answer : a)

5 0
3 years ago
Read 2 more answers
How would you solve 3x^2-12=0?
Gennadij [26K]

                                                                                 3x^2 - 12  =  0

Personally, I would divide each side by 3                x^2 - 4  =  0

Then I would add 4 to each side                              x^2        =  4

Then I would take the square root of each side:     x  =  +4
                                                                                     x  =  -4 .

Having found both solutions, I would relax with a cup of tea.

3 0
3 years ago
Please help meeee …………..
ycow [4]

Answer:

3 or 6/2

Step-by-step explanation:

when there are two subtraction signs it can be taken as a plus sign

1/2 + 5/2

1/2 + 5/2 = 6/2

6 / 2 = 3

3 is your answer

4 0
2 years ago
The buyer of a car pays Php 169,000 cash and Php 12, 000 every month for 5 years. If money is 10% compounded monthly, how much i
Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

3 0
2 years ago
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