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2 years ago

Which expression best represents the product of two consecutive integers? CLEAR CHECK x?(2+x) x?(x+1) 2?(x+1) 2x+2

Mathematics

1 answer:

Stella [2.4K]2 years ago

4 0

Answer:

<h2>The product of two consecutive integers:</h2><h2>x · (x+1) = x(x + 1)</h2>

Step-by-step explanation:

Consecutive integer:

... -2, -1, 0, 1, 2, 3, ...

Difference between two consecutive integers is equal to 1.

Therefore two consecutive integers is x and x + 1.

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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.

3 0

2 years ago

16x+4(x-5) how do I solve this.?

Nadusha1986 [10]

Answer:20x-20

16x+4(x-5)

4(x-5)=4x-20

16x+4x

20x-20

8 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!

BabaBlast [244]

Answer:

The first term of the sequence is -120.

Step-by-step explanation:

The formula for the "nth" term of a geometric sequence is shown below:

an = a0*r^(n-1)

Where an is the nth term, r is the ratio and n is the position of the term on the sequence. For this problem we want to find what is the initial term, a0, so we will isolate it in the formula as shown below:

a0*r^(n-1) = an

a0 = an/[r^(n-1)]

We then apply the data given to us

a0 = 31.45728/[-0.8^(7-1)]

a0 = 31.45728/[-0.8^6] =31.45728 /-0.262144= -120

The first term of the sequence is -120.

4 0

3 years ago

19 Sasha drinks 2.5 liters of water during the weekdays. She drinks a total of 3 liters of water on the weekend. What is the tot

12345 [234]

13.5
Hope this helps. Anymore questions?

6 0

3 years ago

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What is the answer to this<br> -11 - (-3)

BaLLatris [955]

Answer:

<u>-</u><u>8</u>

Step-by-step explanation:

-11 - (-3) =

(-11) + 3

<u>-</u><u>8</u>

5 0

2 years ago

Read 2 more answers