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2 years ago

How many natural numbers between 45 and 46.

Mathematics

2 answers:

frosja888 [35]2 years ago

4 0

Answer:

Step-by-step explanation:

91 natural numbers are there between the square of 45 and 46.

Anna35 [415]2 years ago

3 0

91 is the correct answer for this problem

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Solve 2x2 + 20x = −38.

cestrela7 [59]

2x^2+20x=-38 divide both sides by 2

x^2+10x=-19, halve the linear coefficient, square it, than add that value to both sides of the equation, in this case add (10/2)^2=25...

x^2+10x+25=6 now the left side is a perfect square

(x+5)^2=6 take the square root of both sides

x+5=±√6 subtract 5 from both sides

x=-5±√6 (so answer c.)

4 0

2 years ago

DIscrete Math

Daniel [21]

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.

3 0

2 years ago

What is the distance between the points (-4,2) and (3,-5)

34kurt

Answer:

7√2 units

Step-by-step explanation:

The distance between two points having coordinates (x1, y1) and (x2, y2) is given by,

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$