Mathematics, 06.11.2020 06:50 zionAboss

1/x+x/2=11/6 transformable to quadratic equations

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Answer from: freddymoskali

Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).

Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

We are given the algebraic equation: 1/x+x/2=11/6

Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.

LCD(x,2,6) = 6x

Multiply all through the fractions by 6x

(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)

6 + 3x² = 11x

Rewriting the equation:

3x² - 11x + 6 = 0

Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

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Answer from: math10030

Note: Consider we need to find the solution of given equation.

Given:

The equation is

$\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}$

To find:

The solution of the equation.

Solution:

We have,

$\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}$

$\dfrac{2+x^2}{2x}=\dfrac{11}{6}$

By cross multiplication, we get

6(2+x^2)=11(2x)

12+6x^2=22x

6x^2-22x+12=0

2(3x^2-11x+6)=0

Divide both sides by 2.

3x^2-11x+6=0

Splitting the middle term, we get

3x^2-9x-2x+6=0

3x(x-3)-2(x-3)=0

(x-3)(3x-2)=0

Using zero product property, we get

x-3=0 and 3x-2=0

x=3 and $x=\dfrac{2}{3}$

Therefore, the solutions of the given equation are x=3 and $x=\dfrac{2}{3}$ .

Answer from: Quest

he will have 300 because he is really broke and 300 is in his imangine

step-by-step explanation: he ehe heh step by the thy

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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1/x+x/2=11/6 transformable to quadratic equations...