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sveta [45]
3 years ago
11

Which does not show a direct variation between x and y?  

Mathematics
1 answer:
Dmitry [639]3 years ago
3 0
(1)\\direct\ variation\ between\ x\ and\ y:\ \ \ y=k\cdot x\ \ \ and\ \ \  k\in\ R\\\\Ans.\ NOT\ direct\ is\ D\\\\(2)\\f(x) = m\cdot x\ \ \ and\ \ \ f(6)=8\\\\ \Rightarrow\ \ \ m\cdot 6=8\ \ \ \Rightarrow\ \ \ m= \frac{8}{6} = \frac{4}{3} \ \ \ \ \Rightarrow\ \ \ \ Ans.\ D\\\\(3)\\f(x)=30x\ \ \ \Leftrightarrow\ \ \  \frac{f(x)}{x} =30\ \ \ \ \ \ \Rightarrow\ \ \ \ constans=30\ \ \ \ Ans.\ B.

\\\\(4)\\f(x)=m\cdot x\ \ and\ \ f(8)=56\\\\m\cdot8=56\ \ \Leftrightarrow\ \ m= \frac{56}{8} =7\ \ \Rightarrow\ \ \ f(x)=7x\ \ \ \Rightarrow\ \ \ f(2)=7\cdot2=14\\\\Ans.\ D.
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Answer:

<em>a) 3<x<8</em>

<em>b) -4<x<-2</em>

<em>c) -6<x<5</em>

<em>d) -21/4 < x-8/3</em>

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Step-by-step explanation:

Given the following inequalities

a)  x > 3, 2x - 3 < 15

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3<x<8

b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7

25 > 1 - 6x

25-1>-6x

24>-6x

Divide through by -6:

24/-6 > -6x/-6

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For the inequality 1 > 3x + 7

1-7>3x

-6>3x

-6/3 > 3x/3

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x < -2

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-4<x<-2

c) For the inequalities 2x - 7<3< 27 + 4x

On splitting:

2x - 7<3 and 3< 27 + 4x

2x < 3+7

2x<10

x<5

Also for 3< 27 + 4x

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-24/4 < 4x/4

-6<x

Combining both solutions i.e x<5 and -6<x will give;

<em>-6<x<5</em>

d) For the inequalities 3x + 8 <0 < 21 + 4x

3x + 8 <0

3x < -8

x < -8/3

Also for 0 < 21 + 4x

0-21<4x

-21<4x

-21/4 < 4x/4

-21/4 < x

Combining -21/4 < x and x < -8/3 will give;

<em>-21/4 < x-8/3</em>

<em></em>

e) For the inequalities 5x - 36 < -1 < 2x – 1​

Split:

5x - 36 < -1

5x < -1+36

5x<35

5x/5 < 35/5

x < 7

For the expression -1 < 2x – 1​

-1+1 < 2x

0 < 2x

0<x

Combining both inequalities 0<x and x < 7 will give:

<em>0<x<7</em>

7 0
3 years ago
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