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2 years ago

suppose y varies directly with x, and y = 8 when x = -6. what direct variation equation relates x and y? what is the value of y

when x = -2?

Mathematics

1 answer:

Kisachek [45]2 years ago

8 0

$\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
y=8\\
x=-6
\end{cases}\implies 8=k(-6)\implies \cfrac{8}{-6}=k
\\\\\\
-\cfrac{4}{3}=k\qquad therefore\qquad \boxed{y=-\cfrac{4}{3}x}
\\\\\\
\textit{when x = -2, what is \underline{y}?}\qquad y=-\cfrac{4}{3}(-2)$

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3 years ago

Let A be a set of numbers.

LUCKY_DIMON [66]

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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:

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

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

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

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$xy$ is divisible by 5.

Therefore, A is closed under addition and multiplication.

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

Find $x+y,xy$

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So,

$x+y$ ∉ A

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

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$xy$ ∈ A

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Therefore, A is not closed under addition and multiplication.

Let A = { 17n: n∈Z}

Let $x,y$ ∈ A such that $x=17n,y=17m$

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

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Let $x,y$ ∈ A such that $x=-1,y=1$

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

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