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3 years ago

15

-x+4y + z = 10 x+2y + 3z = 4 2x-3y + 2z = -7

1 answer:

Viefleur [7K]3 years ago

3 0

Answer:

x=4y+2-10

x=-2y-32+4

x=3/2-2+-7/2

Step-by-step explanation:

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Solve for the missing length

Fofino [41]

Answer:

2 * sqrt(13)

Step-by-step explanation:

Use pythagoras' theorem.

4^2 + 6^2 = x^2 = 16 + 36 = 52 = 4*13

x = sqrt(4*13)=2 * sqrt(13)

6 0

3 years ago

Calculate the average rate of change for the given function, from x = 2 to x = 7.

Marina86 [1]

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\

\begin{array}{ccll}
x&f(x)\\
\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\
-2&0\\2&15\\7&30
\end{array}
\qquad 
\begin{cases}
x_1=2\\
x_2=7
\end{cases}\implies \cfrac{f(7)-f(2)}{7-2}\implies \cfrac{30-15}{5}
\\\\\\
\cfrac{15}{5}\implies 3$

5 0

3 years ago

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

What is The cube of the product of 3 and x

Anni [7]

Answer: 9

Step-by-step explanation:

5 0

3 years ago

W=1000M-200 rearrange your make M the subject

Anton [14]

Answer:

M = $\frac{w+200}{1000}$

Step-by-step explanation:

Given

w = 1000M - 200 ( isolate 1000M by adding 200 to both sides )

w + 200 = 1000M ( divide both sides by 1000 )

$\frac{w+200}{1000}$ = M

7 0

3 years ago