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3 years ago

Solve the compound inequality. 5 < 2x - 1 < 9 Show your work

Mathematics

1 answer:

ASHA 777 [7]3 years ago

4 0

Answer:

3<x<5

Step-by-step explanation:

5<2x-1<9

Add 1 on all the sides because of the inverse operation.

Which is 6<2x<10

The divide 2 on all sides to isolate x.

Which is 3<x<5.

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Answer:

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Step-by-step explanation:

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4 years ago

Which of the following lists has a mode of 213? / 111, 108, 213, 198, 205/ /212, 215, 213, 211, 220/ /213, 278, 108, 213, 157/ /

Fed [463]

The mode is the most frequent one
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3 years ago

Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic

Andrei [34K]

Answer:

$\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

$(x-a)^2+(y-b)^2+(z-c)^2=r^2$

Where ( $x,y,z$ ) are the points on sphere.

$(a, b, c)$ is the center of the sphere and

$r$ is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

$D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$

Here,

$x_1 =0 \\y_1 =0 \\z_1 =0 \\x_2 =-2 \\y_2 =2 \\z_2 =3$

So, Radius is:

$r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}$

Therefore the equation of the sphere is:

$(x-(-2))^2+(y-2)^2+(z-2)^2=(\sqrt{17})^2\\\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}$

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Step-by-step explanation:

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