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3 years ago

Ln (x-2) +ln (2x-3)=2ln x

1 answer:

4 0

$D:x-2\ \textgreater \ 0 \wedge 2x-3\ \textgreater \ 0 \wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2 \wedge x\ \textgreater \ \dfrac{3}{2}\wedge x\ \textgreater \ 0\\
D:x\ \textgreater \ 2\\\\
\ln (x-2) +\ln (2x-3)=2\ln x \\
\ln (x-2)(2x-3)=\ln x^2\\
(x-2)(2x-3)=x^2\\
2x^2-3x-4x+6=x^2\\
x^2-7x+6=0\\
x^2-x-6x+6=0\\
x(x-1)-6(x-1)=0\\
(x-6)(x-1)=0\\
x=6 \vee x=1\\
1\not \in D\\
\boxed{x=6}$

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tyreee bought a collection comic book for 49.62 last year.this year he would sold it for 52.10 find the percent of change.

wlad13 [49]

Answer:

The percentage increased by approximately 5%.

Step-by-step explanation:

52.10 - 49.62 = 2.48

2.48/49.62 x 100 = 4.998%

The percentage increase in the price is approximately 5%. Hope this helps! :)

3 0

3 years ago

Find the value of x. (Type an integer or decimal.)

SOVA2 [1]

Answer:

Step-by-step explanation:

An angle formed by 2 tangent lines is equal to one half the measure of the major arc minus the measure of the minor arc.

we are given the minor arc ( 110 ) however we are not given the major arc.

Because circles make a 360 degree rotation we can find the major arc by subtracting the measure of the minor arc from 360

Thus, major arc = 360 - 110 = 250

Now that we have identified the major and minor arc we can find x

Recall that x = 1/2 ( major arc - minor arc )

Thus, x = 1/2 ( 250 - 110 )

250 - 110 = 140

140 / 2 = 70

Hence, x = 70

6 0

3 years ago

a cone with a radius of 3” has a total area of 24pie square inches. Find the volume of the cone. 12pie, 24 pie or 15 pie

Ratling [72]

Answer:

$12\pi (inches)^{2}$

Step-by-step explanation:

Given:

radius of cone = 3 inch

Total area of cone = $24\pi (inch)^{2}$

Find the volume of the cone?

We know the area of cone = $\pi r(r+s)$ -------(1)

Where r = radius

Ans s = side of the cone

Put the area value in equation 1

$24\pi=\pi r(r+s)$ -------(1)

$\frac{24\pi }{\pi r} =r+s$

$\frac{24}{ r}-r =s$

Put r value in above equation.

$s =\frac{24}{ 3}-3$

$s=8-3$

$s=5$

The side s = 5 inches

We know the side of the cone formula

$s^{2}=r^{2}+ h^{2}$

$h^{2}=s^{2}- r^{2}$

Put r and s value in above equation.

$h^{2}=5^{2}- 3^{2}$

$r^{2} = 25-9$

$r^{2} = 16$

$r = 4$

The volume of cone is

$V = \frac{1}{3} \pi r^{2} h$

Put r and h value in above equation.

$V = \frac{1}{3} \pi (3)^{2}\times 4$

$V = 12\pi (inches)^{2}$

The Volume of the cone is $12\pi (inches)^{2}$

7 0

3 years ago

(x*y=1210)=(-55=x+y)

Romashka [77]

Evaluate
x⋅y, then set it equal to x+y.

X = y / y-1

8 0

3 years ago

An office has 150 employees, and 30 of the employees work the night shift. What percentage of the employees work the night shift

Zanzabum

<h2>Answer:</h2>

The percent of employees who work in the night shift are:

20%

<h2>Step-by-step explanation:</h2>

Total number of employee in the office are: 150

Number of employee who work in the night shift are: 30

The percent of the employee who work in the night shift is calculated as follows:

$\dfrac{\text{Number\ of\ people\ working\ in\ the\ night\ shift}}{\text{Total\ number\ of\ employees}}\times 100$

Hence, on putting the value in the above formula we get:

$=\dfrac{30}{150}\times 100\\\\\\=\dfrac{1}{5}\times 100\\\\\\=20\%$

Hence, the answer is:

20%

4 0

3 years ago

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