Mathematics, 17.10.2019 06:30 Jasonn7787

Which system of equations can be used to find the roots of the equation 12 x 3-5x=2 x 2+x+6

a. y= 12x3-5x
y=2x2+x+6
b. y=12x3-5x+6
y=2x2+x
c. y=12x3+2x2-4x
y=6
d. y=12x3+2x2-4x+6
y=0

Answers: 3

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Answers

Answer from: IkarosSakurai

Option (a) is correct.

The system of equation becomes

$y=12x^3-5x\\\\ y=2x^2+x+6$

Step-by-step explanation:

Given : Equation 12x^3-5x=2x^2+x+6

We have to construct a system of equations that can be used to find the roots of the equation 12x^3-5x=2x^2+x+6

Consider the given equation 12x^3-5x=2x^2+x+6

To construct a system of equation put both sides of the given equation equal to a same variable.

Let the variable be "y", Then the equation 12x^3-5x=2x^2+x+6

becomes,

12x^3-5x=y=2x^2+x+6

Thus, The system of equation becomes

$y=12x^3-5x\\\\ y=2x^2+x+6$

Option (a) is correct.

Answer from: michaellangley

The system of equations are $\boxed{y = 12{x^3} - 5x}{\text{ and }}\boxed{y = 2{x^2} + x + 6}$ that can be used to find the roots of the equation $12{x^3} - 5x = 2{x^2} + x + 6.$ Option (a) is correct.

Further explanation:

Given:

The equation is $12{x^3} - 5x = 2{x^2} + x + 6.$

The options are as follows,

(a). $y = 12{x^3} - 5x{\text{ and }}y = 2{x^2} + x + 6$

(b). $y = 12{x^3} - 5x + 6{\text{ and }}y = 2{x^2} + x$

(c). $y = 12{x^3} + 2{x^2} - 4x{\text{ and }}y = 6$

(d). $y = 12{x^3} + 2{x^2} - 4x + 6{\text{ and }}y = 0$

Explanation:

The given equation is $12{x^3} - 5x = 2{x^2} + x + 6.$

Consider the left hand side of the equation $12{x^3} - 5x = 2{x^2} + x + 6$ as y and the right hand side of the equation $12{x^3} - 5x = 2{x^2} + x + 6$ as y.

$\begin{aligned}y&= 12{x^3} - 5x\\y &= 2{x^2} + x + 6 \\ \end{aligned}$

The equation matches with option (a). Hence, option (a) is correct.

The system of equations are $\boxed{y = 12{x^3} - 5x}{\text{ and }}\boxed{y = 2{x^2} + x + 6}$ that can be used to find the roots of the equation $12{x^3} - 5x = 2{x^2} + x + 6$ . Option (a) is correct.

Learn more:

Learn more about inverse of the functionhttps://. Learn more about equation of circle . Learn more about range and domain of the function

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Polynomials

Keywords: polynomial, solution, linear equation, quadratic equation, system of equations, solution of the equations.

Answer from: Quest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

$\frac{ab}{bc} =\frac{ad}{ab}$

now, we can cross multiply

and we get

$ab\timesab=ad\times bc$

$ab^2=ad\times bc$

so, this could be step to prove it

Seth is using the figure shown below to prove pythagorean theorem using triangle similarity: in the

Answer from: Quest

step-by-step explanation:

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Which system of equations can be used to find the roots of the equation 12 x 3-5x=2 x 2+x+6

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