All categories

2 years ago

Solve for x: x/2x+3 + 2x+3/x = 184/65

Mathematics

2 answers:

Marat540 [252]2 years ago

6 0

Answer:

x/2x+3 + 2x +3/x = 184 /65

x(2x + 3)–1 + (2x+3)x-1 = 184/65

(2x + 3)x / (2x +3)x = 184/65

2x² + 3x / 2x² + 3x = 184/65

1x= 184/64

x = 184/64

tatuchka [14]2 years ago

6 0

Step-by-step explanation:

Given that: {x/(2x+3)} + {(2x+3)/x} = 184/65

⇛[{(x*x) + (2x+3)(2x+3)}/{(x)(2x+3)}] = 184/65

⇛[{x² + 2x(2x+3) + 3(2x+3)}/(2x²+3x)] = 184/65

⇛[{x² + 4x² + 6x + 6x + 9}/(2x²+3x)] = 184/65

⇛[{x² + 4x² + 12x + 9}/(2x² + 3x)] = 184/65

⇛{(5x² + 12x + 9)/(2x² + 3x)} = 184/65

On applying cross multiplication then

⇛184(2x² + 3x) = 65(5x² + 12x + 9)

Multiply the number outside of the brackets with numbers and variables in the brackets on LHS and RHS.

⇛388x² + 582x = 325x² + 780x + 584

⇛388x² + 582x -325x² - 780x - 584 = 0

⇛388x²-325x² + 582x-780x - 584 = 0

⇛63x² - 198x - 584 = 0

⇛8(7x² - 22x - 65) = 0

⇛7x² - 22x - 65 = 0

Now,

This is of the form ax² + bx + c = 0, Where, a = 7, b = -22 and c = -65

Using the quadratic formula x = [{-b±√(b²-4ac)}/2a] , we get

x = [{-(-22)±√(-22)² - 4(7)(-65)}/{2(7)]

x = [{-(-22)±√(-22*-22) - 4(7)(-65)}/{2(7)]

x = [{22 ± √(484 + 1820)}/14]

x = [{22 ± √(2304)}/14]

x = {(22 ± 48)/14}

x = {(22 + 48)/14} or {(22 - 48)/14}

x = (70/14) or (-26/14)

x = 5 or x = -13/7

Therefore, x = 5 or -13/7

<u>Answer</u>: Hence, the value of x for the given equation is 5 or -13/7.

Please let me know if you have any other questions.

You might be interested in

Find a third degree polynomial function of the lowest degree that has the zeros below and whose leading coefficient is one.

Tanzania [10]

Answer:

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is $p(x) = x^{3}-5\cdot x^{2}-6\cdot x$ .

Step-by-step explanation:

From Fundamental Theorem of Algebra, we remember that the degree of the polynomials determine the number of roots within. Since we know three roots, then the factorized form of the polynomial function with the lowest degree is:

$p(x) = (x-r_{1})\cdot (x-r_{2})\cdot (x-r_{3}) = 0$ (1)

Where $r_{1}$ , $r_{2}$ and $r_{3}$ are the roots of the polynomial.

If we know that $r_{1} = -1$ , $r_{2} = 0$ and $r_{3} = 6$ , then the polynomial function in factorized form is:

$p(x) = (x+1)\cdot x \cdot (x-6)$ (2)

And by Algebra we get the standard form of the function:

$p(x) = x\cdot (x+1)\cdot (x-6)$

$p(x) = x\cdot (x^{2}-5\cdot x -6)$

$p(x) = x^{3}-5\cdot x^{2}-6\cdot x$ (3)

The polynomial function of the lowest degree that has zeroes at -1, 0 and 6 and with a leading coefficient of one is $p(x) = x^{3}-5\cdot x^{2}-6\cdot x$ .

6 0

3 years ago

Please help me I really need to turn it in I hate khan academy

kow [346]

42.5 units sq
I’m not sure because I did this partly in my head but this should be right.

5 0

3 years ago

The probability that an event will happen is 3/6. What is the probability the event won’t happen

Mnenie [13.5K]

Answer:

3/6

Step-by-step explanation:

If the probability that it will happen is 3/6 or 1/2 the probability is the opposite. which is also 3/6 or 1/2.

7 0

3 years ago

Read 2 more answers

Find the value of x.

Semenov [28]

Answer:

x= 35.7339234

Step-by-step explanation:

cos(52)= 22/x

x= 22/cos(52)

4 0

3 years ago

what is the measure of a central angle of a circle if the associated minor arc has an angle measure of 65 degrees?

Butoxors [25]

Answer:

65 degrees

Step-by-step explanation:

Ⓗⓘ ⓣⓗⓔⓡⓔ

Well, it would have to also be 65 degrees since the measure of the inner angle is equal to the measure of the arc.

(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥

Please, please give brainliest, it would be greatly appreciated, I only need one more before I advance, thanks!

8 0

3 years ago

Read 2 more answers

Solve for x: x/2x+3 + 2x+3/x = 184/65​

Solve for x: x/2x+3 + 2x+3/x = 184/65