Susanna added 2 × <br> 1<br> 100<br> to 204.197. What is the sum?

Write an equation for the circle with endpoints of a diameter (9, 4) and (-3, -2)

inysia [295]

If the diameter is at (9,4) and (-3,-2), then the center of the circle is the midpoint of that segment.

and since we know that the radius of a circle is half of the diameter, whatever long that diameter segment is, the radius is half that.

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 9 &,& 4~) 
% (c,d)
&&(~ -3 &,& -2~)
\end{array}\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{-3+9}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \stackrel{center}{(3~,~1)}$

$\bf -------------------------------\\\\
~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ 9 &,& 4~) 
% (c,d)
&&(~ -3 &,& -2~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{(-3-9)^2+(-2-4)^2}\implies d=\sqrt{(-12)^2+(-6)^2}
\\\\\\
d=\sqrt{180}\qquad \qquad \qquad radius=\cfrac{\sqrt{180}}{2}$

$\bf -------------------------------\\\\
\textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{3}{ h},\stackrel{1}{ k})\qquad \qquad 
radius=\stackrel{\frac{\sqrt{180}}{2}}{ r}
\\\\\\
(x-3)^2+(y-1)^2=\left( \frac{\sqrt{180}}{2} \right)^2\implies (x-3)^2+(y-1)^2=\cfrac{(\sqrt{180})^2}{2^2}
\\\\\\
(x-3)^2+(y-1)^2=\cfrac{180}{4}\implies (x-3)^2+(y-1)^2=45$

7 0

3 years ago

Nick has an album that holds 700 compact discs. Each page of the album holds 7 compact discs. If 69% of the album is empty, ho

mel-nik [20]

Answer:

41

Step-by-step explanation:

each page holds 7 discs. the alb holds 700 discs. that means there are 100 pages. 69% of the pages are empty so therefore 41 pages are filled.

4 0

2 years ago

Select the correct answer. What is the difference of the values of the two variables in this system of equations? Y = 2x + 1 x +

zzz [600]

Answer:

Option C. $2$

Step-by-step explanation:

we have

$y=2x+1$ -----> equation A

$x+3y=10$ -----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The intersection point is (1,3)

see the attached figure

therefore

The solution of the system of equations is

$x=1,y=3$

Find the difference

$y-x=3-1=2$

8 0

3 years ago

solve systems of equation. equation number 1: 9 x squared + 4 y squared equals 144. equation 2: x squared plus y squared equals

grigory [225]

$9x^{2} + 4y^{2} =144$
$x^{2} + y^{2}=24$

$9x^{2} + 4y^{2} =144$
$4x^{2} + 4y^{2}=96$
by the difference
5 $x^{2}$ =48
so x= $\sqrt{\frac{48}{5}}$ or x=- $\sqrt{\frac{48}{5}}$
and $y^{2}$ =24- $\frac{48}{5}$
then y= $\sqrt{\frac{72}{5}}$ or - $\sqrt{\frac{48}{5}}$

5 0

3 years ago

9 hundreds equal to how many tens?

Evgen [1.6K]

Ok so you do 900 ÷ 10 which = 90 and 90 x 10 = 900 so the answer is 90

4 0

2 years ago

Susanna added 2 × 1 100 to 204.197. What is the sum?