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chubhunter [2.5K]
3 years ago
10

What are the solutions to the inequality?

Mathematics
1 answer:
denis23 [38]3 years ago
8 0

(x - 3)(x + 5) \leqslant 0 \\ \begin{cases}x - 3 \geqslant 0 \\x + 5 \leqslant 0 \end{cases} \: \vee \: \begin{cases} x - 3 \leqslant 0\\x - 5 \geqslant 0 \end{cases} \\ \Leftrightarrow \begin{cases}x \geqslant 3 \\ x \leqslant  - 5\end{cases} \: \vee \:  \begin{cases}x \leqslant 3 \\x \geqslant   + 5 \end{cases} \\ \Leftrightarrow x\in\emptyset \: \vee \:  - 5 \leqslant x \leqslant 3 \\ \Leftrightarrow  - 5 \leqslant x \leqslant 3

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What is the value of x?
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HELP ASAP! Which of the following tables represents a linear function?
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Table A, B and D are represents a linear function.

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

There are 4 tables.

Now,

For Table A;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 5 = (2 - 5) / (- 1 - (-2))  (x - (-2))

⇒ y - 5 = - 3/1 (x + 2)

⇒ y - 5 = - 3 (x + 2)

⇒ y - 5 = - 3x - 6

⇒ y = - 3x - 1

For Table B;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 5 = (3 - 5) / (- 1 - (-2))  (x - (-2))

⇒ y - 5 = - 2/1 (x + 2)

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For Table C;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - (-2) = (- 1 - (-2)) / (3 - 3)  (x - 3)

⇒ y + 2 = 1/0 (x + 2)

⇒ y - 5 = ∞

Hence, It is not possible.

For Table D;

The equation of line is,

⇒ y - y₁ = (y₂ - y₁) / (x₂ - x₁) (x - x₁)

⇒ y - 0 = (-1 - 0) / ( 1 - 0)  (x - 0)

⇒ y - 0 = - 1/1 (x)

⇒ y = - x

Thus, Table A, B and D are represents a linear function.

Learn more about the equation of line visit:

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