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2 years ago

Which graph shows the solution set for |x - 3| < 4?

Mathematics

2 answers:

ikadub [295]2 years ago

4 0

Answer:

see below

Step-by-step explanation:

|x - 3| < 4

To remove the absolute values, we need to make two inequalities, one positive and one negative

x-3 < 4 and x-3 > -4

Add 3 to each side

x-3+3<4+3 and x-3+3 > -4+3

x<7 and x >-1

-1 <x <7

lawyer [7]2 years ago

4 0

Answer:

Step-by-step explanation:

One way to do this is to interpret |x - 3| < 4 is to say: "the distance of variable x from the center 3 is less than 4."

On the left side: measuring 4 units to the left from 3, mark an open circle (since x does not actually touch -1).

On the right side: measuring 4 units to the right from 3, mark an open circle at 7.

So the correct graph consists of the line segment connecting x = -1 and x = 7 but not touching or including these two numerical values.

Next time, please share the four possible answers.

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2/21 * 7/8

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divide top and bottom by 14

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2 years ago

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Answer:

Step-by-step explanation:

<u>Angles and Lines</u>

We must recall:

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Note from the triangle, angle R is what it takes to get to 180°:

$m\angle R=180-25x-(57+x)$

From the line SQ, angle R what it takes to get to 180°. Thus:

$m\angle R=180-45x$

Equating:

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1 year ago

A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the

creativ13 [48]

Answer:

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

$2r+s=18$

$s=r \theta$

$2r+r \theta=18$

solve for r

$r=\frac{18}{2+\theta}$

step 2

Find the value of s

$s=r \theta$

substitute the value of r

$s=\frac{18}{2+\theta}\theta$

step 3

we know that

The area of complete circle is equal to

$A=\pi r^{2}$

The complete circle subtends a central angle of 2π radians

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

$\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}$

substitute the value of r

$A=\frac{(\frac{18}{2+\theta})^2\theta}{2}$

$A=\frac{162 \theta}{(\theta+2)^2}$

Convert to function notation

$A(\theta)=\frac{162 \theta}{(\theta+2)^2}$

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Answer:

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Step-by-step explanation:

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