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Serggg [28]
3 years ago
15

Can u plz help me answer question 30

Mathematics
1 answer:
slamgirl [31]3 years ago
3 0

We are given:

3x^3-2x^2

There seems to be nothing I can do to simplify this equation. However, I can factor out an x^2 since they both have at least an x^2. Here is what we get:

x^2(3x-2)

This is in the simplest form I can get into. I cannot do anything more to simplify this expression. This is your final answer.

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The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
daser333 [38]

Answer: The correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

Explanation:

It is given that  coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .

The distance formula for two points is given below,

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

DE=\sqrt{(2+2)^2+(4-5)^2}=\sqrt{17}

EF=\sqrt{(0-2)^2+(0-4)^2}=\sqrt{20}

FG=\sqrt{(-4-0)^2+(1-0)^2}=\sqrt{17}

DG=\sqrt{(-4+2)^2+(1-5)^2}=\sqrt{20}

Slope formula,

m=\frac{y_2-y_1}{x_2-x_1}

Slope of DE,

m_1=\frac{4-5}{2+2}= \frac{-1}{4}

Slope of EF,

m_2=\frac{0-4}{0-2}= 2

Slope of FG,

m_3=\frac{1-0}{-4-0}= \frac{-1}{4}

Slope of DG,

m_4=\frac{1-5}{-4+2}= 2

The slope of opposite sides are equal, it means the opposite sides are parallel.

All four sides do not have the same length. It means it is not a rhombus.

From the figure it is noticed that the opposite sides are parallel.

Therefore, the correct option is a.Quadrilateral DEFG is a rhombus because opposite sides are parallel and all four sides have the same length.

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