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a_sh-v [17]
4 years ago
12

Solve the rational equation x divided by 4 equals x squared divided by quantity x plus 2 end quantity, and check for extraneous

solutions.
Mathematics
2 answers:
____ [38]4 years ago
5 0

Answer:

x = 0, x = 2/3

Step-by-step explanation:

x / 4 = x² / (x + 2)

x = 4x² / (x + 2)

x * (x + 2) = 4x²

x² + 2x = 4x²

3x² - 2x = 0

x(3x - 2) = 0

x = 0, x = 2/3

Norma-Jean [14]4 years ago
5 0

Answer:

x=0, 2/3

Step-by-step explanation:

x/4 = x^2 /(x+2)

Using cross products

4x^2 = x(x+2)

Distribute

4x^2 = x^2 +2x

Subtract x^2 from each side

3x^2 = 2x

Subtract 2x from each side

3x^2 -2x =0

Factor out x

x(3x-2) =0

Using the zero product property

x=0   3x-2 =0

x=0   3x=2

x=0   x= 2/3

Check

x=0

0/4 = 0^2 /(0+2)

0 = 0

Check

x=2/3

(2/3)/4 = (2/3)^2 /((2/3)+2)

1/6 = (4/9)/ (8/3)

1/6 = 4/9 * 3/8

1/6 = 4/8 *3/9

1/6 = 1/6

Both solutions are valid

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NEED HELP PLEASE!!!! |3x-3/7|=2 1/3
lyudmila [28]

Answer: x= 58/63 or x= -40/63

Step-by-step explanation: thats your answer.

7 0
3 years ago
The diameter of 0 gauge copper wire is 8.252 mm. Find the resistance (in ω) of a 2.40 km length of such wire used for power tran
VashaNatasha [74]

d = diameter of the copper wire = 8.252 mm

r = radius of the copper wire = d/2 = 8.252 mm /2 = 4.126 mm = 0.004126 m

A = area of cross-section of the copper wire = πr² = (3.14) (0.004126)² = 53.5 x 10⁻⁶

L = length of the copper wire = 2.40 km = 2400 m

ρ = resistivity of copper wire = 1.68 x 10⁻⁸

resistance of copper wire is given as

R = ρL/A

inserting the above values in the formula

R = ( 1.68 x 10⁻⁸)(2400)/(53.5 x 10⁻⁶)

R = 0.753 ohm

8 0
4 years ago
George Kyparisis makes bowling ball in his Miami plant. With recent increases in his cost, he has a newfound interest in efficie
Harlamova29_29 [7]

We compute the productivity percentage change of each category using the formula:

\text{\% Change }=\frac{\text{ Value now - Value last year}}{\text{Value last year}}\cdot100\%.

Productivity percentage change for each category

1) Units produced:

\frac{1,000-1,000}{1,000}\cdot100\%=0\cdot100\%=0\%.

2) Last (hours)

\frac{275-300}{300}\cdot100\%=-\frac{25}{300}\cdot100\%=-8.33\%.

3) Resin (pounded)

\frac{45-50}{50}\cdot100\%=-\frac{5}{50}\cdot100\%=-10\%.

4) Capital invested ($)

\frac{11,000-10,000}{10,000}\cdot100\%=\frac{1,000}{10,000}\cdot100\%=10\%.

5) Energy (BTU)

\frac{2,850-3,000}{3,000}\cdot100\%=\frac{-150}{3,000}\cdot100\%=-5\%.

2) Improvement for labour hours

From the previous computations, we see that the percentage change of the category "Last (hours)" has a negative value of -8.33%, which means that this value decreased by 8.33% with respect to the last year.

Answer

1) Productivity percentage change for each category

0. Units produced: ,0%

,

1. Last (hours): , -8.33%

,

2. Resin (pounded):, -10%

,

3. Capital invested ($): ,10%

,

4. Energy (BTU): ,-5%

2) Improvement for labour hours

The percentage change of the category "Last (hours)" has a negative value of -8.33%, which means that this value decreased by 8.33% with respect to the last year.

4 0
2 years ago
Find the equation of a circle with the same center as the circle in the graph above and that passes through a point 2 units away
Ira Lisetskai [31]
The equation of a circle with center at (a, b) and radius, r, is given by
(x-a)^2+(y-b)^2=r^2

The given circle in the graph has the center at (0, 2) with the radius of 1 units.

<span>A circle with the same center as the circle in the graph and that passes through a point 2 units away from the given circle has its center at (0, 2) and a radius of 3 units.

Thus the equation of the circle is given by
(x-0)^2+(y-2)^2=3^2 \\  \\ x^2+y^2-4y+4=9 \\  \\ x^2+y^2-4y-5=0</span>
5 0
3 years ago
Simplify (sinx + cosx) ^2/ sin2x
Aleksandr [31]

\csc 2x+1

Step-by-step explanation:

  • \frac{(\sin x+\cos x)^2}{\sin2x}

  • We expand (\sin x+\cos x)^2 using algebraic identity (a+b)^2=a^2+b^2+2ab

  • =\frac{\sin^2x+\cos^2x+2\sin x.\cos x}{\sin2x}

  • = \frac{1+\sin2x}{\sin2x}

  • =\frac{1}{\sin2x}+\frac{\sin2x}{\sin2x}

  • =\csc 2x+1
8 0
2 years ago
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