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2 years ago

15

Which number line represents the solution set for the inequality -1/2x>4?

1 answer:

jasenka [17]2 years ago

8 0

Answer:

2nd Option

Step-by-step explanation:

Hello!

First, let's solve the inequality for x.

<h3>Solve for x</h3>

$-\frac12x \ge 4$
$x \le-8$

Since the symbol is less than or equal to, it will be a closed circle on Point -8 going in the left direction (all values less than -8).

The answer is the Second Number Line.

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3 years ago

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3 years ago

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed

N76 [4]

Answer:

the length of his shadow on the building is decreasing at the rate of 0.525 m/s

Step-by-step explanation:

From the diagram attached below;

the man is standing at point D with his head at point E

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ΔABC and Δ ADE are similar in nature; thus their corresponding sides have equal ratios; i.e

$\dfrac{AD}{AB} = \dfrac{DE}{BC}$

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8y = 24

y = 24/8

y = 3 meters

Let take an integral look at the distance of the man from the building as x, therefore the distance from the spotlight to the man is 12 - x

∴

$\dfrac{12-x}{12}=\dfrac{2}{y}$

$1- \dfrac{1}{12}x = 2* \dfrac{1}{y}$

To find the derivatives of both sides ;we have:

$- \dfrac{1}{12}dx = 2* \dfrac{1}{y^2}dy$

$- \dfrac{1}{12} \dfrac{dx}{dt} = 2* \dfrac{1}{y^2} \dfrac{dy}{dt}$

During that time ;

$\dfrac{dx}{dt }= 1.4 \ m/s$ and y = 3

So; replacing the value into above ; we have:

$-\dfrac{1}{12}(1.4) = - \dfrac{2}{9} \dfrac{dy}{dt}$

$\dfrac{dy}{dt} = \dfrac{\dfrac{ 1.4} {12 } }{ \dfrac{2}{9}}$

$\dfrac{dy}{dt} = {\dfrac{ 1.4} {12 } }*{ \dfrac{9}{2}}$

$\dfrac{dy}{dt} =0.525 \ m/s$

Thus; the length of his shadow on the building is decreasing at the rate of 0.525 m/s

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3 years ago

What is the solution to the system of linear equations?

galina1969 [7]

Answer:

(6, -5) (Answer C)

Step-by-step explanation:

Multiply the first equation by 2. We get the following equivalent system:

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------------------

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