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Anit [1.1K]
3 years ago
12

Work out the missing numbera) __ ÷ (-3)=27b) __x(-2)=70Hlep pls ​

Mathematics
1 answer:
AlekseyPX3 years ago
5 0

Hi,

x/-3 = 27

x = 27 * - 3

x = -81

-2x = 70

x = 70/-2 = -35

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PLEASE HELP!!!!! Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which
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Answer:

The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile

Step-by-step explanation:

This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.

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Roman is born in the year 123 BC and dies at the age of 74 years. Use a negative number to express the year in which he dies
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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).

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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.

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