Mathematics High School

The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is
18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 11 feet from a wall to its left.
Samuel throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5.5 feet above the floor.
Does Samuel's dart land on the dartboard?

Answers

Answer 1

Answer:

Yes, Samuel's Dart does land on the dartboard.

Step-by-step explanation:

The diameter of the dartboard = 18 inches

∴ The radius of the circle = 9 inches = 0.75 feet

The coordinate of the bull's-eye = 11 feet from the left wall, 5 feet 8 inches from the ground

∴ The coordinate of the bull's-eye = (11, 5.67)

The position of the dart Samuel throws = 11.5 feet from the left wall, 5.5 feet from the ground

∴ The coordinates of the position of the dart Samuel throws = (11.5, 5.5)

The equation for the area of a circle is given as follows;

(x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center

r = The radius

Given that the bull's-eye is the center of the circle formed by the dartboard of radius 9 inches, we have;

(h, k) = The coordinates of the center

For the dartboard, we have;

(h, k) = The coordinates of the center = The coordinate of the bull's-eye = (11, 5.67)

h = 11, k = 5.67

∴ The equation of the circle formed by the dartboard = (x - 11)² + (y - 5.67)² = 0.75² = (3/4)² = 9/16

The square of the distance of the dart Michael throws from the bull's eye = (11.5 - 11)² + (5.5 - 5.[tex]\overline 6[/tex]7)² = 5/18

Therefore, given that the square of the distance of the dart Michael throws from the bull's eye < The square of the radius of the circle formed by the dart board and that the center of the, where the length of both the position of Samuel's dart and the radius of the circle formed by the dartboard are measured from the same point, (the center of the circle) we have;

The position of Samuel's dart is on the dart board

Therefore;

Yes, Samuel's Dart does land on the dartboard.

Related Questions

The original blueprint of a concrete patio has a scale ofmath2inches=3feet. Victoria wants to make a new blueprint of the patio with alength of 16.8 inches. PART A What is the scale for the new blueprint? math 1inch= feet PART B What is the width, in inches, of the blueprint with the new scale?

Answers

Complete question :

the original blueprint of a concrete patio has a scale of 2 inches=3 feet. victoria wants to make a new blueprint of the patio with a length of 16.8 inches. original blueprints length is 14 inches and original blueprints width is 12 inches. what is the scale for the new blueprint and what is the width of the blueprint with the new scale?

Answer:

2.5 fts, 14.4 fts

Step-by-step explanation:

Given that:

Scale of original blueprint : 2inches = 3 feets

To make a new blueprint with a length of 16.8 inches, the scale for the new blueprint will be :

Original scale : 2 inches = 3 feets

Original blueprint length = 14 inches

Then,

2 inches = 3 feets

14 inches = d

Cross multiply :

2d = 42

d = 21 feets

Hence, new scale for blueprint :

16.8 inches = 21 feets

2 inches = d

16.8d = 42

d = 2. 5 feets

For the width :

14 inches = 16.8 feets

12 inches = w

14w = 201.6

w = 201.6/14

Width = 14.4feets

What is the midpoint between (2,4) and (10,16)?

Answers

Answer:

the midpoint would be (5,9)

Answer:

(6, 10 )

Step-by-step explanation:

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex], [tex]\frac{y_{1+y_{2} } }{2}[/tex] )

Here (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (10, 16) , thus

midpoint = [tex]\frac{2+10}{2}[/tex], [tex]\frac{4+16}{2}[/tex] ) = ( [tex]\frac{12}{2}[/tex], [tex]\frac{20}{2}[/tex] ) = (6, 10 )

SV bisects angle RST. if m angle RST = 62, what is m angle RSV?

Answers

See attachment for math work and answer.

The measure of ∠RSV is 31°.

Given that, SV bisects ∠RST=62°.

We need to find the value of m∠RSV.

What is an angle bisector?

The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts. For example, an angle bisector of a 60-degree angle will divide it into two angles of 30 degrees each. In other words, it divides an angle into two smaller congruent angles.

Since SV bisects ∠RST into equal parts.

That is, ∠RSV=∠TSV

So, ∠RST=∠RSV+∠TSV

⇒∠RST=2∠RSV

⇒62°=2∠RSV

⇒∠RSV=31°

Therefore, the measure of ∠RSV is 31°.

To learn more about an angle bisector visit:

brainly.com/question/12896755.

#SPJ2

A hairdresser is deciding to open her own studio. If the hair dresser chooses Location A she will pay $1200 in rent and will earn $45 per
haircut. If she chooses Location B, she will pay $1800 in rent and will earn $60 per haircut. How many haircuts would she have to give to make
the same profit in either location?

Answers

Answer: x = Number of haircuts

Location A profit: 45x-1200

Location B profit: 60x-1800

(Lets assume that the profit is the same for each location)

45x-1200=60x-1800

By solving that we found:

x = 40 Haircuts

Hope this helps!

Step-by-step explanation:

At a quiz competition for every question team A answered correctly team B answered 2 questions correctly. The ratio of the number of questions team A answered correctly to the number of questions team B answered correctly is ___ 1 to1 2 to 1 1to2 2to2

Answers

Answer:

1 to 2

Step-by-step explanation:

If A answers 1 question, B will answer 2 questions, making the ratio 1 to 2

Answer:

The answer is 1 to 2 i did the quiz on flvs

Step-by-step explanation:

Susan rides her bicycle 5 miles in 1/2 of an hour. At this rate, how many miles could she ride in 2 hours?

Answers

Answer:

20 miles

Step-by-step explanation:

to find how many miles she travels in one hour, multiply by 2 to get 10, and then multiply it by 2 again to find 2 hours

Answer:

20 miles

Step-by-step explanation:

To find out how many miles can be ridden in 2 hours, multiply 1/2 and 5 by 4 to get both answers like so:

1/2 (4) = 2 HOURS

5 (4) = 20 MILES

Therefore, Susan can ride her bike 20 miles in 2 hours.

10 points
HEELP IMEDIALLTLY

Use linear equation to calculate intercepts.

Answers

Answer:

a=8, b=-4

Step-by-step explanation:

set both equal to zero

a: 0 (-1/2)(8)=-4

-1/2y=-4, multiply both sides by the reciprocal of -1/2, which is -2

y=8 when you multiply both sides by -2

b: 4-(0)(0)=-4

when y is 0, the equation become x-0=-4

or x=-4, meaning x must equal -4

Answer:

a is equal to 8

b=-4

Step-by-step explanation:

Audrey and Addy also went hiking up Mount Olympus. Audrey's distance in June was 2.95 miles and for July 2 5/8 miles. Addy went 2.85 miles in June and 3 3/8 miles in July. How much farther did Addy hike than Audrey in both June and July? *Answer will be in decimal form

Answers

Answer:

Addy hiked 0.65 miles more than Audrey.

Step-by-step explanation:

In June we have the following distance traveled by Audrey (Au) and Addy (Ad):

[tex] Au_{Jun} = 2.95 miles [/tex]

[tex] Ad_{Jun} = 2.85 miles [/tex]

And, in July we have:

[tex] Au_{Jul} = 2 + 5/8 miles = 21/8 miles = 2.625 miles [/tex]

[tex] Ad_{Jul} = 3 + 3/8 miles = 27/8 miles = 3.375 miles [/tex]

Hence in June and July, they traveled:

[tex] Au_{T} = Au_{Jun} + Au_{Jul} = 2.95 miles + 2.625 miles = 5.575 miles [/tex]

[tex] Ad_{T} = Ad_{Jun} + Ad_{Jul} = 2.85 miles + 3.375 miles = 6.225 miles [/tex]

Now, we can find how much farther did Addy hike than Audrey in both June and July:

[tex] d = Ad_{T} - Au_{T} = 6.225 miles - 5.575 miles = 0.65 miles [/tex]

Therefore, Addy hiked 0.65 miles more than Audrey.

I hope it helps you!

In the video game Fantasy Farm, it takes 5 6 6 5 start fraction, 5, divided by, 6, end fraction of a minute to harvest magic flowers, and it takes 5 6 6 5 start fraction, 5, divided by, 6, end fraction of an hour to build a golden barn. Which takes more time?

Answers

Answer:

Building gold barn takes more time

Step-by-step explanation:

Time to harvest magic flowers = 5/6 of a minutes

Time to build a gold barn = 5 / 6 of an hour

1 hour = 60 minutes

Time to build a gold barn = 5 / 6 of 60 minutes

= 5/6 × 60 minutes

= 50 minutes

= 50 minutes × 60 seconds

= 3,000 seconds

Time to harvest magic flowers = 5/6 of a minutes

1 minutes = 60 seconds

= 5/6 × 60 seconds

= 50 seconds

Building gold barn takes more time

9. If one inch represents 14 feet,
what dimensions would you use
to make a scale drawing of a
building 84 feet by 126 feet?

Answers

Answer:

the answer would be 6in. by 9in.

Step-by-step explanation:

you have to divide 84 by 14 and 126 by 14

Help please, I need this done as soon as possible

Answer:

Answer:

Step-by-step explanation:gdndvdsjfehsk

2x + y = 1
what are the x and y intercepts if this was plotted on a line graph

Answers

x=1/2 or 0.5 & y=1

x intercept (value of x when y is 0)
So plug in 0 for y
2x+0=1
2x=1
Divide both sides by 2
x=1/2

Y intercept (value of y, when x is 0)
2(0)+y=1
y=1

PLEASE HELP!!!!!!!!!!!!! I HAVE TO TURN THIS IN 5 MIN!!!!!!!!!!!!!!!!
WHATS THE ANSWER FOR THE QUESTION BELOW????

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The answer is choice C.

You could easily narrow it down by seeing that the y-intercept has decreased. Then the graph went from negative to a positive you have to multiply a negative by a negative to make it a positive.

Hello there! The correct asnwer is C. You can first elimenate the unsuitable answers then solve by doing the ¨equation¨.

Hope I helped! Have an amazing day!

Yours,

fellow brainiac

(ps. if I helped in a time efficient amount of time and answered correctly please mark brainliest, vote, comment, and rate!)

Love you! Byeeeeeee

h(x) = x2 + 1 k(x) = x – 2

(h + k)(2) =
2
⇒ 5
(h – k)(3) =
Evaluate

Answers

Answer:

5, 9, and 17

Step-by-step explanation:

Did it on Edg. 2021 and got it right.

HELP this is on my quartly check!!! If ∠A is supplementary to ∠B, ∠A and ∠C are vertical angles, and m∠C = 45, what is m∠B?

Answers

Answer:

135

Step-by-step explanation:

As, Angle A and angle B are supplementry,

So, A+B=180

Angle A and Angle C are vertically opposite angles then, Angle A= Angle C

So angle C = 45°

So angle A = 45

Now, A + B = 180

45 + B = 180

B= 180 - 45

B= 135°

Hope this helps!

The expression -3m - [2m + (5 - m)] + 7 was simplified as 2 - 4m. Without simplifying, explain how you can show that it has been simplified correctly.

Answers

this is how

Step-by-step explanation:

gusto ko lang magka points

400.34 + 678.397
210

Answers

Answer:

1078.73721

Step-by-step explanation:

complete the pattern. 4,9,14,19,__,__,__,__

Answers

Answer:

24,29,34,39

Step-by-step explanation:

4,9,14,19,24,29,34,39

Add my snaq k1nglean if anyone wants to ttrade you gotta be 16+

Answers

Alright waittt trade picsss omgggg this is a school website I’m just playing with you

7x-3 = 5x+ 15
I have to write an explanation for this problem using the words variable term and constant term... can someone help me?

Answers

Answer:

7x-3 = 5x+ 15

2x-3 = 15 (you will need to subtract the variables to get 2x)

2x = 18 (next, add the constants to result up to 18)

x = 9 (lastly, divide the constant 18 with the coefficient 2 to get 9)

If m3 + m1 =230, find m6

Answers

Answer:

m6 is 65 degrees

Step-by-step explanation:

Since angle 3 and angle 1 are congruent, they are the same degree. The problem said that the sum of their angles is 230, so to find the individual angles of each, divide by two to get 115. Angle 3 and angle 6 add up to 180 degrees since they are adjacent to each other (that's an important rule you need to know). If angle 3 is 115 and you need to find angle 6, subtract 180 from 115 and you will get 65.

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