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2 years ago

Solve 4/x-4=x/x-4-4/3 for x and determine if the solution is extraneous or not

Mathematics

1 answer:

4vir4ik [10]2 years ago

7 0

Answer:

x = 4 (extraneous solution)

Step-by-step explanation:

$\frac { 4 } { x - 4 } = \frac { x } { x - 4 } - \frac { 4 } { 3 } \\ \frac { 4 } { x - 4 } - \frac { x } { x - 4 } = - \frac { 4 } { 3 } \\ \frac { 4 - x } { x - 4 } = - \frac { 4 } { 3 } \\ 3 ( 4 - x ) = - 4 ( x - 4 ) \\ 1 2 - 3 x = - 4 x + 1 6 \\ 4 x - 3 x = 1 6 - 1 2 \\ x = 4 \\$

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back $x=4$ , we will get two fractions with zero denominator which would be undefined.

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Can some please answer! There is a picture! Thank you!!!!

Cerrena [4.2K]

We know that the measure of arc AC = 92 degrees, and x and y are both inscribed angles of this arc, which means that they will have 1/2 of its measure.

Therefore, x = 1/2 (92) = 46 degrees and y = 1/2 (92) = 46 degrees

x = 46, y = 46 is your answer, or the first option

3 0

2 years ago

AB = 3 + x

ICE Princess25 [194]

The given quadrilateral ABCD is a parallelogram since the opposite sides are of same length AB and DC is 4 and AD and BC is 2.

Step-by-step explanation:

ABCD is a quadrilateral with their opposite sides are congruent (equal).

The both pairs of opposite sides are given as AB = 3 + x , DC = 4x , AD = y + 1 , BC = 2y.

AB and DC are opposite sides and have same measure of length.
AD and BC are opposite sides and have same measure of length.

To find the length of AB and DC :

AB = DC

3 + x = 4x

Keep x terms on one side and constant on other side.

3 = 4x - x

3 = 3x

x = 1

Substiute x=1 in AB and DC,

AB = 3+1 = 4

DC = 4(1) = 4

To find the length of AD and BC :

AD = BC

y + 1 = 2y

Keep y terms on one side and constant on other side.

2y-y = 1

y = 1

Substiute y=1 in AD and BC,

AD = 1+1 = 2

BC = 2(1) = 2

Therefore, the opposite sides are of same length AB and DC is 4 and AD and BC is 2. The given quadrilateral ABCD is a parallelogram.

6 0

2 years ago

Calculate the income needed based on the following budgeted expenses.

Lynna [10]

Hope this helped you :)

5 0

3 years ago

Elevii clasei a IV-a au fost la patinoar. Stiind ca numarul baietilor reprezinta jumatate plus 3 din numarul copiilor si ca numa

Shalnov [3]

Step-by-step explanation:

Fie x numărul de copii

$f = 10$ $=\:fete$

$b\:=\:\frac{x}{2}\:+\:3$

$f\:+\:b\:=\:x$

$10\:+\:\frac{x}{2}\:+\:3\:=\:x$

$20\:+\:x\:+\:6\:=\:2x$

$x\:=\:26\:copii\:au\:fost\:la\:patinoar$

$b=\frac{26}{2}+\:3$

$b\:=\:16\:baieti$

7 0

2 years ago

For what values of t on the interval [0, 21 ]is the instantaneous velocity positive (the projectile moves upward)?

OLEGan [10]

Answer:

0 <=t<=21

Step-by-step explanation:

Projectile is Moving upwards on an interval of (0 to 21), if we plot Velocity vs Time and denote positive y-axis above 0 and negative y-axis below 0(for velocity), then from 0 to 21 t projectile is moving upwards and has positive velocity, when the projectile reaches the top of it's motion and returns back down to ground it's velocity is negative and is plotted below the y =0 (note that is for t > 21).

hence for the interval 0 <=t <=21 the instantaneous velocity is positive (Note, instantaneous velocity is also the derivative of the velocity or the slope ).

8 0

2 years ago