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3 years ago

14

Explain how you would graph the point (2,-6) and which quadrant it would be in. Nour answer

1 answer:

Gwar [14]3 years ago

5 0

Answer:

It would he in quadrant 4

Step-by-step explanation:

First off you should know 2 represents x and -6 represents y since it is (x,y). To graph this we must find positive 2 on the x line which in the horizontal line. Then we must point -6. Since this term is negative, we move 6 points down since down is negative and up is positive.

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Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.

sergiy2304 [10]

Answer:

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

All the sides of the rhombus are congruent: $|DG|\cong |GF| \cong |EF| \cong |DE|$
The diagonals are perpendicular

Using the distance formula; $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$|DG|=\sqrt{(0-(-a-b))^2+(0-c)^2}$

$\implies |DG|=\sqrt{a^2+b^2+c^2+2ab}$

$|GF|=\sqrt{((a+b)-0)^2+(c-0)^2}$

$\implies |GF|=\sqrt{a^2+b^2+c^2+2ab}$

$|EF|=\sqrt{((a+b)-0)^2+(c-2c)^2}$

$\implies |EF|=\sqrt{a^2+b^2+c^2+2ab}$

$|DE|=\sqrt{(0-(-a-b))^2+(2c-c)^2}$

$\implies |DE|=\sqrt{a^2+b^2+c^2+2ab}$

Using the slope formula; $m=\frac{y_2-y_1}{x_2-x_1}$

The slope of EG is $m_{EG}=\frac{2c-0}{0-0}$

$\implies m_{EG}=\frac{2c}{0}$

The slope of EG is undefined hence it is a vertical line.

The slope of DF is $m_{DF}=\frac{c-c}{a+b-(-a-b)}$

$\implies m_{DF}=\frac{0}{2a+2b)}=0$

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since $|DG|\cong |GF| \cong |EF| \cong |DE|$ and $DF \perp FG$ , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is $m_{DE}=\frac{2c-c}{0-(-a-b)}$

$m_{DE}=\frac{c}{a+b)}$

The slope of FG is $m_{FG}=\frac{c-0}{a+b-0}$

$\implies m_{FG}=\frac{c}{a+b}$

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3 years ago

Is 12n2+12n+1 prime over the set of polynomials with rational coefficients? Need help ASAP

professor190 [17]

Answer:

No, the given polynomial is not prime.

Step-by-step explanation:

Given: a polynomial $12n^2+12n+1$

To check: whether the given polynomial is prime or not.

Solution:

A prime polynomial is a polynomial that cannot be factored into polynomials of lower degree and has integers as coefficients.

In the given polynomial, coefficients are integers.

Also, the polynomial $12n^2+12n+1$ cannot be factored further into polynomials of lower degree.

So, the given polynomial is not prime.

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