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3 years ago

What is the value of x? Enter your answer in the box.

Mathematics

1 answer:

Tamiku [17]3 years ago

3 0

It's a hexagon.

The formula of the sum of internal angles in the polygon:

$S=(n-2)\cdot180^o$

Therefore

$112^o+133^o+128^o+100^o+120^o+x^o=(6-2)\cdot180^o\\\\593^o+x^o=720^o\ \ \ \ |-593^o\\\\x^o=127^o$

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A circle has the order pairs (-1, 2) (0, 1) (-2, -1) what is the equation . Show your work.

olga55 [171]

We know that:

$(x-a)^2+(y-b)^2=r^2$

is an equation of a circle.

When we substitute x and y (from the pairs we have), we'll get a system of equations:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}$

and all we have to do is solve it for a, b and r.

There will be:

$\begin{cases}(-1-a)^2+(2-b)^2=r^2\\(0-a)^2+(1-b)^2=r^2\\(-2-a)^2+(-1-b)^2=r^2\end{cases}\\\\\\
\begin{cases}1+2a+a^2+4-4b+b^2=r^2\\a^2+1-2b+b^2=r^2\\4+4a+a^2+1+2b+b^2=r^2\end{cases}\\\\\\
\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\\\\\
$

From equations (II) and (III) we have:

$\begin{cases}a^2+b^2-2b+1=r^2\\a^2+b^2+4a+2b+5=r^2\end{cases}\\--------------(-)\\\\a^2+b^2-2b+1-a^2-b^2-4a-2b-5=r^2-r^2\\\\-4a-4b-4=0\qquad|:(-4)\\\\\boxed{-a-b-1=0}$

and from (I) and (II):

$\begin{cases}a^2+b^2+2a-4b+5=r^2\\a^2+b^2-2b+1=r^2\end{cases}\\--------------(-)\\\\a^2+b^2+2a-4b+5-a^2-b^2+2b-1=r^2-r^2\\\\2a-2b+4=0\qquad|:2\\\\\boxed{a-b+2=0}$

Now we can easly calculate a and b:

$\begin{cases}-a-b-1=0\\a-b+2=0\end{cases}\\--------(+)\\\\-a-b-1+a-b+2=0+0\\\\-2b+1=0\\\\-2b=-1\qquad|:(-2)\\\\\boxed{b=\frac{1}{2}}\\\\\\\\a-b+2=0\\\\\\a-\dfrac{1}{2}+2=0\\\\\\a+\dfrac{3}{2}=0\\\\\\\boxed{a=-\frac{3}{2}}$

Finally we calculate $r^2$ :

$a^2+b^2-2b+1=r^2\\\\\\\left(-\dfrac{3}{2}\right)^2+\left(\dfrac{1}{2}\right)^2-2\cdot\dfrac{1}{2}+1=r^2\\\\\\\dfrac{9}{4}+\dfrac{1}{4}-1+1=r^2\\\\\\\dfrac{10}{4}=r^2\\\\\\\boxed{r^2=\frac{5}{2}}$

And the equation of the circle is:

$(x-a)^2+(y-b)^2=r^2\\\\\\\left(x-\left(-\dfrac{3}{2}\right)\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}\\\\\\\boxed{\left(x+\dfrac{3}{2}\right)^2+\left(y-\dfrac{1}{2}\right)^2=\dfrac{5}{2}}$

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3 years ago

Melanie is 2 years older than Bill. Bill is 27 years old. After correctly carrying out the Solve step of the five-step problem-s

slava [35]

it should just be 2 + 27 in order to find her age!

8 0

3 years ago

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Find the measure of the missing angles! Pls help thank you

Inga [223]

Answer:

a=61°

Step-by-step explanation:

a= 180° - 90° - 29°

a = 61°

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2 years ago

Find the value of n. 4 × 62 = (4 x n) + (4 × 2)

tino4ka555 [31]

The answer is 1000 because 62x4= 248 and then you take 248 and multiply it by 4 and you get 992 then you have to multiply 4x2 which is 8 and then when you add 992+8, you would get 100 ;)

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2 years ago

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Elspeth knows that . What would she need to do to find the circumference?

Alika [10]

It looks like the options are missing something, but based on what I can see it looks like
<span>D.She could divide 9.42 by to find the radius, then multiply 9.42 by the radius.</span>

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3 years ago