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21 day ago

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What is true about the solution of StartFraction x squared Over 2 x minus 6 EndFraction = StartFraction 9 Over 6 x minus 18 EndF

raction?
x = plus-or-minus StartRoot 3 EndRoot, and they are actual solutions.
x = plus-or-minus StartRoot 3 EndRoot, but they are extraneous solutions.
x = 3, and it is an actual solution.
x = 3, but it is an extraneous solution.

2 answers:

tester [8.8K]21 day ago

3 0

Answer:

Option A is correct!

Step-by-step explanation:

PIT_PIT [9.1K]21 day ago

3 0

Answer:

$x=\pm\sqrt{3}$ and these represent genuine solutions.

Step-by-step explanation:

We have

$\frac{x^2}{2x-6}=\frac{9}{6x-18}$

Factor both sides' denominators.

$\frac{x^2}{2(x-3)}=\frac{9}{6(x-3)}$

Simplify.

$\frac{x^2}{2}=\frac{9}{6}$

$x^2=\frac{18}{6}$

$x=\pm\sqrt{3}$

Verify

1) For $x=\sqrt{3}$

$\frac{\sqrt{3}^2}{2(\sqrt{3}-3)}=\frac{9}{6(\sqrt{3}-3)}$

$\frac{3}{2(\sqrt{3}-3)}=\frac{9}{6(\sqrt{3}-3)}$

$18=18$ ---> is valid.

Thus,

$x=\sqrt{3}$ -----> is a legitimate solution.

2) For $x=-\sqrt{3}$

$\frac{-\sqrt{3}^2}{2(-\sqrt{3}-3)}=\frac{9}{6(-\sqrt{3}-3)}$

$\frac{3}{2(-\sqrt{3}-3)}=\frac{9}{6(-\sqrt{3}-3)}$

$18=18$ ---> is valid.

Therefore,

$x=-\sqrt{3}$ -----> is a legitimate solution.

Thus,

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Svet_ta [9518]

Answer:

Base Charge = $7

Additional Fees = $7

Step-by-step explanation:

Let x represent the base charge and y for the additional fees.

For a job that lasts 5 hours, we obtain:

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For the 3-hour task

$28 = x + 3y$

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Deduct the second equation from the first

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1 month ago

Solve for y 4.2x - 1.4y = 2.1

tester [8842]

4.2x - 1.4y = 2.1
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1 month ago

Read 2 more answers

If ef bisects angle ceb,angle cef=7x+31 and angle feb=10x-3

lawyer [9240]

Given: The angle < CEB is divided by EF.

< CEF = 7x +31.

< FEB = 10x -3.

We will find the values of x and the measures of < FEB, < CEF, and < CEB.

Solution: The angle < CEB is divided into two angles < FEB and < CEF.

Therefore, < FEB is equal to < CEF.

By substituting the values of < FEB and < CEF, we obtain:

10x -3 = 7x +31

By adding 3 to both sides, we have:

10x -3 +3 = 7x +31 +3.

Thus, 10x = 7x + 34

After subtracting 7x from both sides, we conclude:

10x -7x = 0 + 34.

This simplifies to 3x = 34.

Dividing both sides by 3 yields:

x = 11.33.

Substituting x=11.33 into < CEF = 7x +31 gives us:

< CEF = 7(11.33) +31 = 79.33 +31 = 110.33.

< FEB = < CEF = 110.33 (approximately)

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1 month ago

A building casts a shadow 25 m long. At the same time, the shadow cast by a 44-cm tall pole is 59 cm long. Find the height of th

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Once everything is expressed in meters, we can set up the proportions accordingly. Our proportion becomes $\frac{x}{25} =\frac{0.44}{0.59}$

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Svet_ta [9518]

Result:

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Detailed steps:

Initially, calculate the exponents, perform the foil, combine like terms, and the resulting figure will be 0.884.

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