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3 years ago

How to get everything to one side of the inequality for 3+4/x>=(x+2)/x

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

6 0

Answer:

$2x+2\geq 0$

Step-by-step explanation:

Given:

The given inequality is.

$3+\frac{4}{x} \geq \frac{x+2}{x}$

Solution:

Simplify the given expression.

$3+\frac{4}{x} \geq \frac{x+2}{x}$

Multiply by x both side of the equation.

$x(3+\frac{4}{x}) \geq x(\frac{x+2}{x})$

Simplify.

$3x+\frac{4x}{x} \geq x(\frac{x+2}{x})$

$3x+4\geq x+2$

Rewrite the equation as.

$3x+4-x-2\geq 0$

$2x+2\geq 0$

Therefore, $2x+2\geq 0$ is the simplest form of the given expression.

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postnew [5]

The correct answer is A.-1050

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3 years ago

Read 2 more answers

Find the standard equation of a sphere that has diameter with the end points given below. (3,-2,4) (7,12,4)

DiKsa [7]

Answer:

The standard equation of the sphere is $(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

Step-by-step explanation:

From the question, the end point are (3,-2,4) and (7,12,4)

Since we know the end points of the diameter, we can determine the center (midpoint of the two end points) of the sphere.

The midpoint can be calculated thus

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Let the first endpoint be represented as $(x_{1}, y_{1}, z_{1})$ and the second endpoint be $(x_{2}, y_{2}, z_{2})$ .

Hence,

Midpoint = $(\frac{x_{1} + x_{2} }{2}, \frac{y_{1} + y_{2} }{2}, \frac{z_{1} + z_{2} }{2})$

Midpoint = $(\frac{3 + 7 }{2}, \frac{-2+12 }{2}, \frac{4 + 4 }{2})$

Midpoint = $(\frac{10 }{2}, \frac{10}{2}, \frac{8 }{2})\\$

Midpoint = $(5, 5, 4)$

This is the center of the sphere.

Now, we will determine the distance (diameter) of the sphere

The distance is given by

$d = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} - y_{1})^{2} + (z_{2}- z_{1})^{2} }$

$d = \sqrt{(7 - 3)^{2} +(12 - -2)^{2} + (4- 4)^{2}$

$d = \sqrt{(4)^{2} +(14)^{2} + (0)^{2}$

$d = \sqrt{16 +196 + 0$

$d =\sqrt{212}$

$d = 2\sqrt{53}$

This is the diameter

To find the radius, r

From $Radius = \frac{Diameter}{2}$

$Radius = \frac{2\sqrt{53} }{2}$

∴ $Radius = \sqrt{53}$

r = $\sqrt{53}$

Now, we can write the standard equation of the sphere since we know the center and the radius

Center of the sphere is $(5, 5, 4)$

Radius of the sphere is $\sqrt{53}$

The equation of a sphere of radius r and center $(h,k,l)$ is given by

$(x-h)^{2} + (y-k)^{2} + (z-l)^{2} = r^{2}$

Hence, the equation of the sphere of radius $\sqrt{53}$ and center $(5, 5, 4)$ is

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = \sqrt{(53} )^{2}$

$(x-5)^{2} + (y-5)^{2} + (z-4)^{2} = 53$

This is the standard equation of the sphere

6 0

3 years ago

Need heeeelp please

statuscvo [17]

Answer:

1) log7 (5*8)= log7(40)

2) log2(11) -log2(9)=log2(11/9)

3)2log9 2=log9(2^2)

7 0

2 years ago

Surface area of a cube or a rectangular prism

suter [353]

Answer:

96 cm^2

Step-by-step explanation:

All faces of a cube are equal in area.

Therefore the Formula for SA of a cube is 6*s^2

SA = 6*4*4 = 96

5 0

2 years ago

29.

Elis [28]

Answer:

Sum of their present ages = 20 years

Step-by-step explanation:

Present age :

Neha's age = x years

Reemas' age = x - 4

After 5 years:

Neha's age = (x +5) years

Reemas' age = (x - 4 + 5 ) = x + 1

Sum of the ages of Reema and Neha will be 30

Therefore,

x + 5 + x + 1 = 30

x + x + 5 + 1 = 30

2x + 6 = 30

2x = 30 - 6

2x = 24

x = 24/2

x = 12

Neha's age = 12 years

Reema's age = 12 - 4 = 8 years

Sum of their present ages = 12 + 8 = 20 years

4 0

3 years ago