How do you find the x and y intercepts of the equation 3x-6y=18 ?

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:

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

7 0

3 years ago

tom rides the bus part of the way to school and then he walks the rest pf the way. he walks five minutes longer than he rides. t

ruslelena [56]

Answer:

16 minutes

Step-by-step explanation:

Tom walks for 5 minutes longer than he rides. To figure out the answer, start by subtracting 5:

27 - 5 = 22

Now that you have done this, divide 22 by 2:

22/2 = 11

Now you know that he rode the bus for 11 minutes, and you can add five to the other 11 minutes to know how long he walked:

11 + 5 = 16.

7 0

3 years ago

Read 2 more answers

HELP PLS ILL GIVE BRAINLIEST ANSWER HELP ASAP!!

AlexFokin [52]

The answer is C

Hope this helped:)

5 0

3 years ago

So the question on the pic

gtnhenbr [62]

Explanation + answers

Because there are lengths going from 0 to 1, the lines must mean either decimals or fractions (we'll use fractions for this.)

1. There are twelve lines from 0 and 1, which we can use as the denominator for our fraction. This means the length of each line is 1/12.

2. In order to find where K's point is at, we simply need to count until we get to it. After counting, I see that K is on point 8/12, which we can simplify to get a smaller number. If we simplify once, we get 4/6, which we can again simplify to get 2/3. This gives us the answer K is on point 8/12 or 2/3.

4 0

3 years ago

Hello !!!!!!Please help me ASAP

andriy [413]

Answer:

A

Step-by-step explanation:

I hope this helped you out

5 0

3 years ago