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3 years ago

Express the following in scientific notation: 10,030,400,000

Mathematics

1 answer:

Stella [2.4K]3 years ago

6 0

Answer:

1.00304 * 10^10

Step-by-step explanation:

The first one dark blue I think

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Check whether the relation R on the set S = {1, 2, 3} is an equivalent

kozerog [31]

Answer:

$R$ isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.

Step-by-step explanation:

Let $S$ denote a set of elements. $S \times S$ would denote the set of all ordered pairs of elements of $S\!$ .

For example, with $S = \lbrace 1,\, 2,\, 3 \rbrace$ , $(3,\, 2)$ and $(2,\, 3)$ are both members of $S \times S$ . However, $(3,\, 2) \ne (2,\, 3)$ because the pairs are ordered.

A relation $R$ on $S\!$ is a subset of $S \times S$ . For any two elements $a,\, b \in S$ , $a \sim b$ if and only if the ordered pair $(a,\, b)$ is in $R\!$ .

A relation $R$ on set $S$ is an equivalence relation if it satisfies the following:

Reflexivity: for any $a \in S$ , the relation $R$ needs to ensure that $a \sim a$ (that is: $(a,\, a) \in R$ .)

Symmetry: for any $a,\, b \in S$ , $a \sim b$ if and only if $b \sim a$ . In other words, either both $(a,\, b)$ and $(b,\, a)$ are in $R$ , or neither is in $R\!$ .

Transitivity: for any $a,\, b,\, c \in S$ , if $a \sim b$ and $b \sim c$ , then $a \sim c$ . In other words, if $(a,\, b)$ and $(b,\, c)$ are both in $R$ , then $(a,\, c)$ also needs to be in $R\!$ .

The relation $R$ (on $S = \lbrace 1,\, 2,\, 3 \rbrace$ ) in this question is indeed reflexive. $(1,\, 1)$ , $(2,\, 2)$ , and $(3,\, 3)$ (one pair for each element of $S$ ) are all elements of $R\!$ .

$R$ isn't symmetric. $(2,\, 3) \in R$ but $(3,\, 2) \not \in R$ (the pairs in $\! R$ are all ordered.) In other words, $3$ isn't equivalent to $2$ under $R\!$ even though $2 \sim 3$ .

Neither is $R$ transitive. $(3,\, 1) \in R$ and $(1,\, 2) \in R$ . However, $(3,\, 2) \not \in R$ . In other words, under relation $R\!$ , $3 \sim 1$ and $1 \sim 2$ does not imply $3 \sim 2$ .

3 0

2 years ago

How does the definition of the prefixes mono-,bi-, and tri- help when naming polynomials

Leviafan [203]

Answer:

They let you know the number of numbers there are/will be.

Step-by-step explanation:

Mono, being one, means there will only be one number is the equation.

Bi, being two, means there will be two numbers in the equation.

and tri, being three, means there are three numbers in the equation.

8 0

2 years ago

Read 2 more answers

Alexis has a steady babysitting job over the summer. She starts out with $50 by the end of the first week and earns $30 each wee

Ket [755]

Yes it is correct because you would multiply 30 by 7 which equals 210 + the extra 20 dollars / 50 dollars (idk).. she will have more than enough though

4 0

2 years ago

Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each eq

Alik [6]

Answer:

see below:

Step-by-step explanation:

2y–6=0

a. slope intercept form using y = mx + b

y = 6/2

y = 3

b. slope: use the slope intercept form: y = mx + b

slope = m = 0

c. y-intercept = (0,3)

7 0

3 years ago

Find the inequality represented by the graph.

iris [78.8K]

Answer:

<h2> $x \geqslant \frac{y + 4}{3}$ </h2>

Explanation;

Associated line with this equation is:

y=mx+c

when,

X=0

y=-4

so, c=-4

X=1

y=-1

$- 1 = m- 4 \\ - m = - 4 + 1 \\ - m = - 3 \\ m =3 \\$

$y = 3x - 4 \\ or \: y + 4 = 3x \\ or \: \frac{y + 4}{3} = x$

Inequality representated by graph:

$x \geqslant \frac{y + 4}{3}$

Hope this helps...

Good luck on your assignment...

7 0

2 years ago