Which identifies the transformation that occurred after the dilation?

Stanley is reading a 224-page book. There are illustrations on 14 pages. If Stanley opens the book at random, what is the probab

likoan [24]

It will be 0.0625 because you can use a calculator and do 14/224

5 0

3 years ago

Prove the following DeMorgan's laws: if LaTeX: XX, LaTeX: AA and LaTeX: BB are sets and LaTeX: \{A_i: i\in I\} {Ai:i∈I} is a fam

MariettaO [177]

$X-(A\cup B)=(X-A)\cap(X-B)$

I'll assume the usual definition of set difference, $X-A=\{x\in X,x\not\in A\}$ .

Let $x\in X-(A\cup B)$ . Then $x\in X$ and $x\not\in(A\cup B)$ . If $x\not\in(A\cup B)$ , then $x\not\in A$ and $x\not\in B$ . This means $x\in X,x\not\in A$ and $x\in X,x\not\in B$ , so it follows that $x\in(X-A)\cap(X-B)$ . Hence $X-(A\cup B)\subset(X-A)\cap(X-B)$ .

Now let $x\in(X-A)\cap(X-B)$ . Then $x\in X-A$ and $x\in X-B$ . By definition of set difference, $x\in X,x\not\in A$ and $x\in X,x\not\in B$ . Since $x\not A,x\not\in B$ , we have $x\not\in(A\cup B)$ , and so $x\in X-(A\cup B)$ . Hence $(X-A)\cap(X-B)\subset X-(A\cup B)$ .

The two sets are subsets of one another, so they must be equal.

$X-\left(\bigcup\limits_{i\in I}A_i\right)=\bigcap\limits_{i\in I}(X-A_i)$

The proof of this is the same as above, you just have to indicate that membership, of lack thereof, holds for all indices $i\in I$ .

Proof of one direction for example:

Let $x\in X-\left(\bigcup\limits_{i\in I}A_i\right)$ . Then $x\in X$ and $x\not\in\bigcup\limits_{i\in I}A_i$ , which in turn means $x\not\in A_i$ for all $i\in I$ . This means $x\in X,x\not\in A_{i_1}$ , and $x\in X,x\not\in A_{i_2}$ , and so on, where $\{i_1,i_2,\ldots\}\subset I$ , for all $i\in I$ . This means $x\in X-A_{i_1}$ , and $x\in X-A_{i_2}$ , and so on, so $x\in\bigcap\limits_{i\in I}(X-A_i)$ . Hence $X-\left(\bigcup\limits_{i\in I}A_i\right)\subset\bigcap\limits_{i\in I}(X-A_i)$ .

4 0

3 years ago

When fractions share the same number on the bottom they have a?

Snezhnost [94]

Fractions that have the same number on the bottom have a "common denominator."

6 0

3 years ago

A formula for a function y=f(x) is f(x)=x^2-10x,xless than or equal 5. Find f^-1(x) and indentify the domain and range of f^-1(x

evablogger [386]

F(x) =x² - 10x, f⁻¹(x) =?

1st find the missing square of x²-10x, ==> (x-5)² - 25

y= (x-5)² - 25; replace x by y and v0ce versa: x= (y-5)² -25
or
(y-5)² = x+25
y-5 = √(x+25) and y = √(x+25) -5

Domain = {x∈R: X>= 25} AND Range ={y∈R: y>= 5}

6 0

3 years ago

Which of the following is the graph of y=sqr root -x-3

Elan Coil [88]

Answer:

The graph in the attached figure

see the explanation

Step-by-step explanation:

we have

$y=\sqrt{-x-3}$