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2 years ago

Which system of equations can be used to find the roots of the equation4x^5-12x^4+6x=5x^3-2x?

Mathematics

1 answer:

goblinko [34]2 years ago

5 0

Answer:

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

Step-by-step explanation:

The system of equations that can be used to find the roots of the equation 4x^5-12x^4+6x=5x^3-2x are;

y = 4x^5 - 12x^4 + 6x and

y = 5x^3 - 2x

We simply formulate two equations by splitting the left and the right hand sides of the given equation.

The next step is to graph these two system of equations on the same graph in order to determine the solution(s) to the given original equation.

The roots of the given equation will be given by the points where these two equations will intersect.

The graph of these two equations is as shown in the attachment below;

The roots are thus;

x = 0 and x = 0.813

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Answer:

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3 years ago

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Step-by-step explanation:

The mid point can be found with the formula

$P_{m}=(\frac{x_{1}+x_{2} }{2},\frac{y_{1} +y_{2} }{2} ,\frac{z_{1}+z_{2} }{2} )$

The given coordinates are $P(5,10,8)$ and $Q(7,11,10)$ .

Replacing coordinates in the formula, we have

$P_{m}=(\frac{5+7}{2},\frac{10+11 }{2} ,\frac{8+10}{2} )=(\frac{12}{2},\frac{21 }{2} ,\frac{18}{2} )\\P_{m}=(6,10.5,9)$

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natali 33 [55]

Answer: By the slope formula.

Step-by-step explanation:

Given: ABC is a triangle (shown below),

In which A≡(6,8), B≡(2,2) and C≡(8,4)

And, D and E are the mid points of the line segments AB and BC respectively.

Prove: DE║AC and DE = AC/2

Proof:

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By the distance formula,

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By the slope formula,

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Statement Reason

1. The coordinate of D are (4,5) and 1. By the midpoint formula

the coordinate of E are (5,3)

2. The length of DE = √5 2. By the Distance formula

The length AC = 2√5 ⇒ Segment DE

is half the length of segment AC

3. The slope of DE = -2 and the 3. By the slope formula

slope of AC = -2

4. DE║AC 4. Slopes of parallel lines are equal

7 0

3 years ago

Read 2 more answers