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4 years ago

What is y-2={-3}(x-7)

Mathematics

1 answer:

Leno4ka [110]4 years ago

5 0

Answer:

The given expression is a line equation with slope - 3 and y-intercept 9 .

Step-by-step explanation:

Given expression as

y - 2 = ( - 3) (x - 7)

Now, Rearranging the equation

i,e y - 2 = - 3 x + 7

Or, y = - 3 x + 7 + 2

Or, y = - 3 x + 9

Now, The equation is similar to the equation of any line

∵ <u>The standard equation of any line is written as</u>

y = m x + c

where m is the slope of line and c is the y-intercept

So, while comparing expression with line equation, we get

The equation of line as y = - 3 x + 9

Where - 3 is the slope of line and 9 is the y-intercept

So,The given expression is line equation

Hence, The given expression is a line equation with slope - 3 and y-intercept 9 . Answer

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DIscrete Math

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Answer:

Step-by-step explanation:

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

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

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Step-by-step explanation:

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