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2 years ago

14

Help me if you can please

1 answer:

Luden [163]2 years ago

8 0

Answer:

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Let Ebe the set of all even positive integers in the universe Zof integers, and XE : Z R be the characteristic function of E.

AnnZ [28]

Answer:

$\mathbf{X_E (2) = 1}$

$\mathbf{X_E (-2) = 0 }$

$\mathbf{\{ x \in Z: X_E(x) = 1\} = E}$

Step-by-step explanation:

Let E be the set of all even positive integers in the universe Z of integers,

i.e

E = {2,4,6,8,10 ....∞}

$X_E : Z \to R$ be the characteristic function of E.

∴

$X_E(x) = \left \{ {{1 \ if \ x \ \ is \ an \ element \ of \ E} \atop {0 \ if \ x \ \ is \ not \ an \ element \ of \ E}} \right.$

For XE(2)

$\mathbf{X_E (2) = 1}$ since x is an element of E (i.e the set of all even numbers)

For XE(-2)

$\mathbf{X_E (-2) = 0 }$ since - 2 is less than 0 , and -2 is not an element of E

For { x ∈ Z: XE(x) = 1}

This can be read as:

x which is and element of Z such that X is also an element of x which is equal to 1.

∴

$\{ x \in Z: X_E(x) = 1\} = \{ x \in Z | x \in E\} \\ \\ \mathbf{\{ x \in Z: X_E(x) = 1\} = E}$

E = {2,4,6,8,10 ....∞}

5 0

3 years ago

dlinn [17]

Answer:

V = pi * R^2 * h

R = (V / (pi * h))^1/2 = (141.3 / (3.14 * 5))^1/2 = 3 cm

8 0

3 years ago

Which is larger a millimeter or a millimeter

maksim [4K]

They are exactly the same thing

3 0

3 years ago

5 miles to 35 miles in a fraction ?

LenKa [72]

5/35
Simplify by dividing both sides by 5
1/7
Final Answer: 1/7

4 0

2 years ago

Can someone help me with these and show the work also?

Snezhnost [94]

QUESTION:

Simplify each expression

ANSWER:

1.) $\green{{- 8n}}$

2.) $\green{{- 2b - 60}}$

3.) $\green{{- 10x - 14}}$

4.) for number 4 study my step-by-step explanation so you can answer that

STEP-BY-STEP EXPLANATION:

1.) First, If the term doesn't have a coefficients, it is considered that the coefficients is 1

WHY?

Learn why:

Why is it considered that the coefficient is 1?

Remember that any term multiplied by $\blue{{1}}$ remains the same :

$\blue{{1}}$ ${× x = x}$

Step 1:

The equality can be read in the other way as a well, so any term can be written as a product of $\blue{{1}}$ and itself:

${x = }$ $\blue{{1}}$ ${× x}$

Step 2:

Usually, we don't need to write multiplacation sign between the coefficient and variable, so the simple form is:

${x = 1x}$

This is why we can write the term without the coefficient as a term with coefficient ${1}$

Now let's go back to solving as what i said if a term doesn't have a coefficient, it is considered that the coefficient is 1

${n - 9n}$

$\red{{1}}$ ${n -9n}$

Second, Collect like terms by subtracting their coefficients

$\red{{1n - 9n}}$

$\red{{( 1 - 9)n}}$

Third, Calculate the difference

how?

Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from larger

$\red{{1 - 9}}$

$\red{{- (9 - 1)}}$

Subtract the numbers

- ( $\red{{9 - 1}}$ )n

- $\red{{8}}$ n

$\green{\boxed{- 8n}}$

2.) First, Distribute - 6 through the parentheses

how?

Multiply each term in the parentheses by - 6

$\red{{- 6(b + 10)}}$

$\red{{- 6b - 6 × 10}}$

Multiply the numbers

- ${6b}$ - $\red{{6 × 10}}$

- ${6b}$ - $\red{{60}}$

Second, Collect like term

how?

Collect like terms by calculating the sum or difference of their coefficient

$\red{{- 6b + 4b}}$

$\red{{(- 6 + 4)b}}$

Calculate the sum

$\red{{(- 6 + 4)}}$ b

$\red{{-2}}$ b

$\green{\boxed{- 2b - 60}}$

3.) First, Distribute 2 through parentheses

how?

Multiply each term in the parentheses by 2

$\red{{2(x - 5)}}$

$\red{{2x - 2 × 5}}$

Multiply the numbers

${2x -}$ $\red{{2 × 5}}$

${2x -}$ $\red{{10}}$

Second, Distribute - 4 through the parentheses

how?

Multiply each term in the parentheses by - 4

$\red{{- 4(3x + 1)}}$

$\red{{- 4 × 3x - 4}}$

Calculate the product

- $\red{{4 × 3}}$ x - 4

- $\red{{12}}$ x - 4

Third, Collect like terms

how?

Collect like terms by subtracting their coefficient

$\red{{2x - 12x}}$

$\red{{(2 - 12)x}}$

Calculate the difference

$\red{{(2 - 12)}}$ x

$\red{{- 10}}$ x

Fourth, Calculate the difference

how?

Factor out the negative sign from the expression

$\red{{- 10 - 4}}$

$\red{{- (10 + 4)}}$

Add the numbers

- ( $\red{{10 + 4}}$ )

- $\red{{14}}$

$\green{\boxed{- 10x - 14}}$

That's all I know sorry but I hope it helps :)

6 0

2 years ago