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3 years ago

Pls help! (don't give wrong answer pls)

Mathematics

1 answer:

myrzilka [38]3 years ago

3 0

Check arithmetic

t4-t3 t3-t2

25-16 16-9

=9 =7

sequence is not arithmetic bcoz t4-t3 is unequal to t4-t3

check geometric

t4÷t3 t3÷t2

25÷16 16÷9

=1.6 1.7

sequence is not geometric bcoz t4÷t3 is unequal to t3÷t2

neither

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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

$f : X \rightarrow Y$ 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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3 years ago

Write the direct variation: The total cost C of gasoline is $3.00 times the number of gallons g

Zielflug [23.3K]

Is it 3g? idk sorry i need points

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4 years ago

10=Z+6 can u please solve it in evaluate the expression

Eva8 [605]

Answer: z=4

Step-by-step explanation:

Subtract 6 on both sides and 10-6=4 and then plug 4 into z and the equation is true