There are 120 different combinations.

There are 5 to use for the first bead; then after it is used, 4 for the second; 3 for the third; 2 for the fourth; and 1 for the fifth and last bead:

5*4*3*2*1 = 120.

8 0

2 years ago

Help !! Please I can’t find the answer

SVETLANKA909090 [29]

Answer:

$\large\boxed{r^2=(x+5)^2+(y-4)^2}$

Step-by-step explanation:

The equation of a circle:

$(x-h)^2+(y-k)^2=r^2$

(h, k) - center

r - radius

We have diameter endpoints.

Half the length of the diameter is the length of the radius.

The center of the diameter is the center of the circle.

The formula of a distance between two points:

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

Substitute the coordinates of the given points (-8, 2) and (-2, 6):

$d=\sqrt{(6-2)^2+(-2-(-8))^2}=\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}$

The radius:

$r=\dfrac{d}{2}\to r=\dfrac{\sqrt{52}}{2}$

The formula of a midpoint:

$\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$

Substitute:

$x=\dfrac{-8+(-2)}{2}=\dfrac{-10}{2}=-5\\\\y=\dfrac{2+6}{2}=\dfrac{8}{2}=4$

$(-5,\ 4)\to h=-5,\ k=4$

Finally:

$(x-(-5))^2+(y-4)^2=\left(\dfrac{\sqrt{52}}{2}\right)^2\\\\(x+5)^2+(y-4)^2=\dfrac{52}{4}\\\\(x+5)^2+(y-4)^2=13$

5 0

3 years ago