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2 years ago

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

1 answer:

vladimir2022 [97]2 years ago

6 0

The option second "A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right" is correct.

<h3>What is inequality?</h3>

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The options are attached in a picture please refer to the attached picture.

We have an inequality:

3(8 – 4x) < 6(x – 5)

After solving:

8 - 4x < 2(x - 5)

8 - 4x < 2x - 10

8 + 10 < 2x + 4x

18 < 6x

3 < x or

x > 3

x ∈ (3, ∞)

Thus, the option second "A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right" is correct.

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ1

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Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

8 0

3 years ago

WHAT ARE THE SPECIFIC RULES FOR PROVING SIMILARITY IN TRIANGLES? EXPLAIN.

weeeeeb [17]

Answer:

AAA (Or even just two angles work too, since the last has to be the same no matter what) ASA and SSS

Step-by-step explanation:

I believe this is the same as before? As far as I know these are the main rules for proving similarity. (AAS and A** do not exist (Brainly won't let me say the two Ss), make sure no trick questions get you ;p)

I'm not sure if what you needed earlier was the relationships between angles to find them? Like to find Exterior Angles subtract <C from 180 = <EA?

4 0

3 years ago

A pure substance is a liquid homogeneous mixture in which the solute is distributed evenly within the solvent

Licemer1 [7]

That would be False
.....

4 0

3 years ago

Turn 5/7 into its smallest form

DiKsa [7]

Answer:

5/7

Step-by-step explanation:

5 0

3 years ago

Gcf of 9 46 7 21 18 12 15 25 55

Taya2010 [7]

1 because the only factors of 7 are 1, 7. Numbers like 9 and 46 and 18 and 12 and 15 and 25 and 55 do not have a factor of 7.

4 0

3 years ago