10. The distance of the point (a, b) from the origin is twice its

Let A be a set of numbers.

LUCKY_DIMON [66]

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

a.

Let A be a set of all integers divisible by 5.

Let $x,y$ ∈A such that $x=5m\,,\,y=5n$

Find $x+y,xy$

$x+y=5m+5n=5(m+n)$

So, $x+y$ is divisible by 5.

$xy=(5m)(5n)=25mn=5(5mn)$

So,

$xy$ is divisible by 5.

Therefore, A is closed under addition and multiplication.

b.

Let A = { 2n +1 | n ∈ Z}

Let $x,y$ ∈A such that $x=2m+1\,,\,y=2n+1$ where m, n ∈ Z.

Find $x+y,xy$

$x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)$

So,

$x+y$ ∉ A

$xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1$

So,

$xy$ ∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

c.

$Let A=\{2,5,8,11,14,...\}$

Let $x=2,y=5$ but $x+y=2+5=7$ ∉A

Also,

$xy=2(5)=10$ ∉A

Therefore, A is not closed under addition and multiplication.

d.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

Find x + y and xy

$x+y=17n+17m=17(n+m)$

$xy=(17m)(17n)=289mn=17(17mn)$

So,

$x+y,xy$ ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let $x,y$ ∈ A such that $x=-1,y=1$

Find x + y

$x+y=-1+1=0$

So,

$x+y$ ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

4 0

3 years ago

Determine which value best represents each point on the number line below?

DaniilM [7]

A= 0.5 B=1 C=2.5 D=3.5

5 0

3 years ago

Please help me pleaseee

jekas [21]

Answer: A - sin 63

Step-by-step explanation:

3 0

2 years ago

Solve the equation<br> -2(2x - 4) = 4x <br> Write it step by step. I really need help

Artist 52 [7]

Answer:

x = 1

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−2(2x−4)=4x

(−2)(2x)+(−2)(−4)=4x(Distribute)

−4x+8=4x

Step 2: Subtract 4x from both sides.

−4x+8−4x=4x−4x

−8x+8=0

Step 3: Subtract 8 from both sides.

−8x+8−8=0−8

−8x=−8

Step 4: Divide both sides by -8.

3 0

3 years ago

Read 2 more answers

Miguel invests money in an account paying simple interest. He invests $170 and no money is added or removed from the investment.

stiv31 [10]

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$185.30\\ P=\textit{original amount deposited}\dotfill & \$170\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &1 \end{cases} \\\\\\ 185.30=170[1+(\frac{r}{100})(1)]\implies \cfrac{185.30}{170}=1+\cfrac{r}{100}\implies \cfrac{109}{100}=\cfrac{100+r}{100} \\\\\\ 109=100+r\implies \stackrel{\%}{9}=r$

7 0

2 years ago