A dartboard has a diameter of 30 inches. What are its radius and circumference?

Answer:

AB=8cm⇒AE=4cmCD=6m⇒CF=3cmIn△AEDAE=4cm,AO=5cmOE=(AO)2−(AE)2=52−42=3cmIn△OFCCF=3cm,CO=5cmOF=OC2−CF2=52−32=4cm

∴ Distance between the chords=4cm−3cm=1cm

Answer:

I) 1 cm

II) 7 cm

Step-by-step explanation:

We are given a circle with a radius of 5 cm. AB and CD are two parallel chords of length 8cm and 6cm respectively. And we want to calculate the length of the chords if they are:

I) On the same side of the center.

Please refer to the first figure.

In it, O is the center, AB measures 8 and CD measures 6.

To find the distance between the two chords, we essentially need to find KJ, which is OJ - OK.

We will construct a segment from O to K and from K to J. This is perpendicular to the chords. Therefore, by the Perpendicular Bisector Theorem, it also bisects the chords.

ΔAOK is a right triangle. Therefore:

[tex]AO^2=OK^2+KA^2[/tex]

AO is simply the radius.

KA is half the length of AB since OK perpendicularly bisects the chord.

Therefore:

[tex](5)^2=OK^2+(4)^2[/tex]

So:

[tex]25=OK^2+16\Rightarrow OK^2=9\Rightarrow OK=3[/tex]

Likewise, ΔCOJ is also a right triangle. Therefore:

[tex]CO^2=OJ^2+JC^2[/tex]

CO is the radius, and JC will be half the length of CD. Thus:

[tex](5)^2=OJ^2+(3)^2\Rightarrow OJ^2=16\Rightarrow OJ=4[/tex]

Therefore, the distance KJ between the two chords are:

[tex]KJ= OJ-OK=4-3=1\text{ cm}[/tex]

II) On opposite sides of the center.

Please refer to the second figure.

Again, O is the center, AB measures 8, and CD measures 6.

Likewise, segments OK and OJ are perpendicular bisectors of AB and CD, respectively.

And to find the distance, we essentially need to find JK or OJ + OK.

ΔKOB is a right triangle. Thus:

[tex]OB^2=OK^2+KB^2[/tex]

OB is the radius, and KB is half of AB:

[tex](5)^2=OK^2+(4)^2\Rightarrow OK=3[/tex]

ΔJOD is also a right triangle. Thus:

[tex]OD^2=OJ^2+JD^2[/tex]

OD is the radius and JD is half of CD:

[tex](5)^2=OJ^2+(3)^2\Rightarrow OJ=4[/tex]

Therefore, the distance between the two chords are:

[tex]JK=OJ+OK=4+3=7\text{ cm}[/tex]

Step-by-step explanation:

there are 7 decimal places from between 2 and 3 to the very end. so the answer is 7

Answer: 2.36x^10

Step-by-step explanation:

Answer:

[tex]n = \frac{1}{6} [/tex]

Step-by-step explanation:

[tex] \frac{1}{2n} + 3 = 6[/tex]

[tex] \frac{1}{2n} = 6 - 3[/tex]

[tex] \frac{1}{2n} = 3[/tex]

[tex]1 = 6n[/tex]

[tex]n = \frac{1}{6} [/tex]

Answer:

x= - 3

Step-by-step explanation:

2x - 3= 4x + 3

2x = - 6

x = - 3

Answer:

Solution given:

radius [r]=40ft

length of arc=70/360×2πr=70/360×2×π×40

=48.86=49ft is your answer

Answer:

49ft is the answer. hope it helps

Answer:

[tex]6n + 3 + 2n = 8n + 3[/tex]

[tex]99-9-9 = 81[/tex]

[tex]2p + 3p+ 6-p-3 = 4p + 3[/tex]

[tex]2.25(14.3m + 6 + 2.7m) = 38.25m + 15.5[/tex]

Answer:

ZWXY

Step-by-step explanation:

The other shape is the same but you want to name it the same way that they named the first one

Answer:

KitKat

Step-by-step explanationKitKat

Answer:

The home is worth $424,528 today

Step-by-step explanation:

To get the worth of the home today, we are going to use the exponential formula

We have this as follows;

A = P(1 + r)^t

where A is the value of the house after some time t

P is the initial value the home was worth which is $160,000

r is the rate of increase in the price of the home which is 5% = 5/100 = 0.05

t is the number of years which is 20

substituting these values;

A = 160,000(1 + 0.05)^20

A = $424,528

Answer:

y= -3x + 10

Step-by-step explanation:

we can answer this question thanks to this formula:

y-y1 = m(x-x1) where y1 and x1 indicate the coordinates of the given point and m indicates the slope

y-4 = -3(x-2)

y = -3x+6+4

y= -3x + 10

Answer:

360° 2π rad 6.283185 rad

Answer:

Area is 124.8999

Answer:

v = 87

Step-by-step explanation:

the angle v+39 lies on a straight line. so substract v+39 from 180 to get the interior angle for that side.

afterwards, knowing that the sum of interior angles of a triangle = 180, form an equation with all the angles and solve for v

Answer:

D

Step-by-step explanation:

Remark

First characters:  6 choices

Second two characters: 25 * 26

Third set of 2: 10 * 10 = 100

6 * 25 * 26 * 100 = 390000

Answer:

Your answer will be A. positive correlation

Step-by-step explanation:

hope this helps :)

Answer:

Let E denote the event of choosing a jury with 10 men and 2 women.

The sample space for selecting 12 members from the pool contains 55C12 elements.

The number of ways of selecting 10 men and 2 women is 26C10  29C2.

The probability of event E =  

The probability of selecting a jury with 10 men and 2 women is 0.005 (0.5%).

Step-by-step explanation:

see the image :

Answer:

The probability of selecting a jury with 10 men and 2 women out of out of 29 men and 26 women  is 0.005 (0.5%)

Step-by-step explanation:

Let P(E) denote the probability of choosing a jury with 10 men and 2 women out of 29 men and 26 women.

The sample space for selecting 12 members from the total no of member will be 55c12

The number of ways of selecting 10 men and 2 women is 26c10  29c2.

The probability of event E =  [tex]$=P(E)=\frac{{ }_{20} C_{10} \times{ }_{20} C_{2}}{-C_{12}}$[/tex]

                                                [tex]$=\frac{5,311,735 \times 406}{438,729,741,450}$[/tex] [tex]$=0.005$.[/tex]

The probability of selecting a jury with 10 men and 2 women is 0.005 (0.5%).

Click here to know more about the probability .

https://brainly.com/question/24756209

#SPJ2

Answer:

first box is 24

second is -5

third is -6

Step-by-step explanation:

Answer:

(x - 3)² + (y - 2)² = 16

Step-by-step explanation:

The center of the circle is (3, 2).

The radius of the circle is 4.

(x - 3)² + (y - 2)² = 4²

Answer: (x - 3)² + (y - 2)² = 16

The complete equation of this circle​ with center (3, 2) and radius 4 units is

(x - 3)² + (y - 2)² = 4²

Used the concept of the equation of the circle which stated that,

The standard form of the equation of a circle is,

(x - h)² + (y - k)² = r²

Where, (h, k) is the center of the circle and 'r' is the radius of the circle.

Given that,

The center of the circle is (3, 2).

And, The radius of the circle is 4.

Here, (h, k) = (3, 2)

And, r = 4

Substitute all the values in the standard form of the equation of a circle,

(x - 3)² + (y - 2)² = 4²

Therefore, the equation of a circle,

(x - 3)² + (y - 2)² = 16

To learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ6

Answer:

Step-by-step explanation:

Find the worth of B and E and add them

Answer:

for the first photo the answer is 5x + 6(-x + 4) = 13

Step-by-step explanation:

if y equals to -x +4

then replace the y in this equation: 5x + 6y = 13  with this ( -x +4 ) its simple.

I cannot answer the other 2 photos at the moment but ill see if I can whenever else I have time.

Answer:

80 Degrees

Step-by-step explanation:

just flip and overlap the figure (in your mind)

Answer:

positive slope is shown by the graph

Answer:

There was a %5 increase

Step-by-step explanation:

You just have to substract 65-60 and you get 5

Answer:

i got 15.1

Step-by-step explanation:

Answer:

5.6

Step-by-step explanation:

Given :

Quality rating for 8 movies :

5.6, 7.9, 7.0, 5.9, 7.8, 6.2, 6.4, 5.2

Let rating for the 9th movie = x

Average quality rating olfor the 9 movies = 6.4

To find x :

Sum of all ratings / number of ratings = 6.4

(5.6 + 7.9 + 7.0 + 5.9 + 7.8 + 6.2 + 6.4 + 5.2 + x) / 9 = 6.4

(52 + x) / 9 = 6.4

52 + x = 57.6

x = 57.6 - 52

x = 5.6

Answer:

Reduced fee for each additional round will be $5.

Step-by-step explanation:

Let the reduced fee for each additional round played = $x

Charges for one round = $13

If Tom played for 6 rounds, total charges for the 6 rounds = 13 + 6x

Since, Tom paid $43 for 6 rounds,

13 + 6x = 43

6x = 43 - 13

6x = 30

x = 5

Therefore, reduced fee for each round will be $5.