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2 years ago

Prove that if every two of them have a vertex in common, then "they all have a vertex in common"

Mathematics

1 answer:

USPshnik [31]2 years ago

6 0

Adjacent angles.............

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Is the given point interior , exterior, or on the circle k (x+2)2 + (y-3)2 =18 P (8,4)

Mnenie [13.5K]

One way would be to find the distance from the point to the center of the circle and compare it to the radius

for
$(x-h)^2+(y-k)^2=r^2$
the center is (h,k) and the radius is r

and the distance formula is
distance between $(x_1,y_1)$ and $(x_2,y_2)$ is
$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

r=radius
D=distance form (8,4) to center

if r>D, then (8,4) is inside the circle
if r=D, then (8,4) is on the circle
if r<D, then (8,4) is outside the circle

so
$(x+2)^2+(y-3)^2=18$
$(x-(-2))^2+(y-3)^2=(\sqrt{18})^2$
$(x-(-2))^2+(y-3)^2=(3\sqrt{2})^2$

the radius is $3\sqrt{2}$
center is (-2,3)

find distance between (8,4) and (-2,3)

$D=\sqrt{(8-(-2))^2+(4-3)^2}$
$D=\sqrt{(8+2)^2+(1)^2}$
$D=\sqrt{10^2+1}$
$D=\sqrt{100+1}$
$D=\sqrt{101}$

$r=3\sqrt{2}$ ≈4.2
$D=\sqrt{101}$ ≈10.04

do r<D

(8,4) is outside the circle

6 0

3 years ago

If the area of a circle below is 18ft, what is the area of the shaded sector?

erik [133]

The Shaded area is .25 of the circle, so:

Area/4 = Shaded

18/4 = Shaded

4.5 = Shaded

Hope this helps!

8 0

3 years ago

7 pounds of plums make 8 rolls of fruit leather. If every batch of fruit leather requires the

serg [7]

Answer: 17.5 lbs of plums are required to make 20 rolls of fruit leather.

Step-by-step explanation:

Since 7 lbs of plums yield 8 rolls of fruit leather, 1 lb will yield 1 1/7 rolls of fruit leather.

To find how many pounds of fruit will yield 20 rolls of fruit leather, divide how many rolls of leather you want to get by how many rolls of leather one pound will yield.

20 divided by 8/7 equals 17 1/2.

4 0

2 years ago

64, –48, 36, –27, ... Which formula can be used to describe the sequence? f(x + 1) = 3/4 f(x) f(x + 1) = -3/4 f(x) f(x) = 3/4 f(

marysya [2.9K]

Answer:

the formulae given do not make sense.

Step-by-step explanation:

5 0

3 years ago

Jenna bought 6 pounds of apples for $7.38. What is the unit price per pound of apples?

Leto [7]

6 pounds of apples cost $7.38

1 pound of apples would cost $7.38 / 6 = $1.23

So the unit price of apples = $1.23 per pound

I hope this helps.

7 0

3 years ago