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?

The Standard Height From The Floor To The Bull's-eye At Which A Standard Dartboard Is Hung Is 5 Feet

Answers

Answer 1

Answer:

Yes, Samuel dart does land on the dart board

Step-by-step explanation:

The given parameters are;

The height from the floor to the bulls eye = 5 feet 8 inches

The size of the standard board = 18 inches diameter

The distance of the bulls eye from the wall to the left = 11 feet

The distance the dart Samuel throws land from the left wall = 11.5 feet

The distance above the ground, the dart Samuel throws land = 5.5 feet

Whereby Samuel throws the dart directly at the dartboard, we have;

The location of the bulls eye = (11, 5.67)

The equation of the circle representing the dart board = (x - 11)² + (y - 5.67)² = 0.75² = 0.5625

The unit of the radius is in feet

The position of Samuel's dart is represented by the coordinate, (11.5, 5.5)

Plugging in the coordinates of the position of Samuel's dart into the equation of the circle of the dart board gives;

(11.5 - 11)² + (5.5 - 5.67)² = 0.2789 ≈ 0.528²

Therefore, given that the square of the distance of the position of Samuel's dart is less than the square of the radius of the dart board, we have;

Yes, Samuel dart does land on the dart board.

Answer 2

From the parameters given to find out if Samuel's dart landed on the dartboard, we can say that;

Samuel's dart does not land on the dartboard.

We are given;

Height from the floor to the bulls eye = 5 ft 8 in = 5.67 ft

Diameter of the standard dartboard = 18 in = 1.5 ft

Thus, radius; r = 1.5/2 = 0.75 ft

Distance of the bulls eye from the wall to the left = 11 ft

Distance of dart thrown by Samuel from the left wall = 11.5 ft

Height of dart thrown by Samuel above the ground = 5.5 ft

We know that general equation of a circle is;

(x - a)² + (y - b)² = r²

Since Height from the floor to the bulls eye is 5.67ft,then a = 5.67 ft

And also since Distance of the bulls eye from the wall to the left = 11 ft, then b = 11 ft

Thus;

(x - 11)² + (y - 5.67)² = 0.75²

(x - 11)² + (y - 5.67)² = 0.5625

Now, since he 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. Thus;

r² = (11.5 - 11)² + (5.5 - 5.67)²

r² = 0.2789

r² of 0.2789 gotten here is lesser than 0.5625 gotten earlier, we can conclude that Samuel's dart does not land on the dart board.

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Related Questions

Use the model to solve for x.

A) x = 2

B) x = 4

C) x = 8

D) x = 12

Answers

9514 1404 393

Answer:

  B)  x = 4

Step-by-step explanation:

You observe that the smaller number of (+1) tokens is 2 of them, found on the right side. Remove 2 (+1) tokens from each side to get ...

  x + 4 = 2x

The smaller number of (x) tokens is 1, found on the left side. Remove 1 (x) token from each side to get ...

  4 = x . . . . . matches choice B

_____

Comment on this approach

In general, this is a decent approach to use for solving any linear equation. You may find that x and number tokens end up on the same side of the equal sign (with 0 on the other side). Then you need to add some number of (-1) tokens to both sides to cancel the ones on the side with x.

At the end, you may need to split the problem evenly into equal parts according to the number of times x appears. (If this had been x+6 = 3x+2, then you would end with 4=2x. Splitting that into two equal parts, each would be 2=x.)

A bus and a truck leave a gas station at the same time and are headed to the same destination. If the bus traveled 110 miles in 2 hours, and the truck traveled 180 miles in 3 hours, who is on pace to reach the destination first?

Answers

Answer:

The truck is on pace.

Step-by-step explanation:

To find which truck will arrive first, you need to find each vehicle's mph. To get the mph of each vehicle you just need to divide the distance by time.

Bus: 110 (miles) ÷ 2 (hours) = 55 (miles per hour)

Truck: 180 (miles) ÷ 3 (hours) = 60 (miles per hour)

When you do this you can see the mph of the bus is < the mph of the truck.

If you have any questions please leave them in the comments.

A tv costs $150. You have a coupon for 12% off.
1) How much money will be taken off of the price of the tv?
2) How much will you pay for the tv?

Answers

Answer:$18 taken away and the total will be 132

Step-by-step explanation:

what is $3 as a decimal​

Answers

Answer:

3.00

Step-by-step explanation:

Answer:

3.00

Step-by-step explanation:

Since three is a whole number, that means it would be in front of the decimal.

The graph of an equation intersects the y-axis at some point. What do the coordinates of the intersection indicate?

A. the input when the output is zero

B. the output when the input is zero

C. the input when the output is 1

D. the output when the input is 1

Answers

Answer:

B

Step-by-step explanation:

got stuck on it too lol

The graph of an equation intersects the y-axis at some point. Therefore, the coordinates of the intersection indicate is B. the output when the input is zero.

What is perimeter?

Its the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Since sum of side lengths of the triangle of vertices: 3

Area: ½ × base × height

Number of edges: 3

Internal angle: 60° (for equilateral)

The Sum of interior angles is 180°

Therefore, the coordinates of the intersection indicate will be;

B. the output when the input is zero.

Learn more about perimeter here:

https://brainly.com/question/10466285

#SPJ2

a and b are positive integers and a+b=2009!

what is the amount of ordered pairs of (a, b)?

Answers

Answer:

[tex]2000 \: and \: 9.[/tex]

[tex]it \: could \: be \: the \: sum \: of \: any \: two \: \\ positive \: integers \: so \: they \: are : \\ 2000 \: and \: 9[/tex]

Let's consider a much smaller value and work our way up to the factorial 2009!

Start with a+b = 2. The value 2 is the smallest right hand side possible since a > 0 and b > 0, so a = b = 1 is the smallest a,b possible.

The only solution to a+b = 2 is a = b = 1 as mentioned.

----------

Now move onto a+b = 3. We have two solutions:

a = 1, b = 2

a = 2, b = 1

-----------

Now move onto a+b = 4. We have three solutions

a = 1, b = 3

a = 2, b = 2

a = 3, b = 1

Note how 'a' counts up while b counts down. I have 'a' starting at the smallest value, and b is set to add with 'a', getting to the right hand side.

So 'a' counts up to 3, while b counts down from 3.

We cannot reach 4 since 0 is not allowed for a or b.

-------------

The conjecture is that a+b = k has k-1 positive integer solutions. A simple proof of this is to list out all solutions like so

a = 1, b = k-1

a = 2, b = k-2

a = 3, b = k-3

....

a = k-3, b = 3

a = k-2, b = 2

a = k-1, b = 1

Where k > 2

Going from 1 to k-1 is exactly k-1 items. It's similar to how {1,2,3,..,m} has m different integers in it. Replace m with k-1 and you have the same idea.

This confirms there are k-1 solutions listed above.

The last step is to simply replace k with 2009! and we have 2009! - 1 different ordered pair solutions

Since the factorial 2009! is so massive, it's best to not expand this out using a calculator. Many calculators would produce "overflow", or similar, if you tried to compute the factorial 2009!

Please help with this problem

Answers

Step-by-step explanation:

the answer is because AP is not congruent to PB

Ashley is preparing for a horse riding competition. She has trained her horse for 6 hours and has completed 240 rounds. At what rate has Ashley ridden her horse in rounds per hour?

Answers

Answer:

40

Step-by-step explanation:

x - 13 = 22 linear equations

Answers

Answer:

x = 35

Step-by-step explanation:

x - 13 = 22

Add 13 to each side

x - 13+13 = 22+13

x = 35

See attachment for math work and answer.

PLEASE HELP ME with this equation I’m struggling

Answers

Answer:

describe this

Step-by-step explanation:

the first one is the one that is closest to horizontal.

Identify the exponent in the following number: 2^5
A. 2
B. 5
C. 16
D. 32

Answers

Answer: 5

Explanation: This type of algebraic expression is called a power.

Here, 2 represents the base and the  represents the exponent.

Every quotitent of two integers is an integer

Answers

That’s true in some cases but mostly it’s true so yes the quotient of two integers is sometimes an integer

y = -5x– 1
y = -5x + 7

Answers

Answer:

see below

Step-by-step explanation:

y = -5x– 1

y = -5x + 7

Since they are both equal to y, we can set them equal to each other

-5x-1 = -5x+7

Add 5x to each side

-5x-1+5x= -5x+7+5x

-1 = 7

This is not true so there is no solution

The lines are parallel with different y intercepts

The answer is “There is on solution “:)

7) Compare the ratios of the corresponding sides to prove or disprove that the polygons are similar.

Answers

Answer:um thers no picture

Step-by-step explanation:

What is a point.? endless flat surface,line that cross, an exact location a, straight path

Answers

Answer:

an exact location should be the right answer

Help me please this is a function questions need asap

Answers

Answer:

y hfaczdg eek Robocop teardrop outbound liquidz

Which of the following equations could represent the points in the table? Select all that apply.

Answers

Answer:

Options (A) and (C)

Step-by-step explanation:

From table attached,

Let the equation of a linear equation that represents the input-output values in the table is,

y - y' = m(x - x')

Where (x', y') is a point lying on the graph.

And m = slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope of the line passing through (0, 11) and (1, 5) will be,

m = [tex]\frac{11-5}{0-1}[/tex]

m = -6

Therefore, equation of the line passing through (0, 11) and slope = -6 will be,

y - 11 = -6(x - 0)

Equation of a line passing through (1, 5) and slope = -6 will be,

y - 5 = -6(x - 1)

Equation of a line passing through (2, -1) and slope = -6 will be,

y + 1 = -6(x - 2)

Equation of a line passing through (3, -7) and slope = -6 will be,

y + 7 = -6(x - 3)

Therefore, Options (A) and (C) are the correct options.

31 SPORTS Sixteen students in Mr. Prank's gym class each
participate in one or more sports as shown in the
table. Examples 2 and 3
Mr. Frank's Gym Class
Basketball Soccer Volleyball
Ayanna Lisa Pam
Ayanna Lisa
Sue
Pion
Shin
Lisa Tyron Mex
Ron
Max
Alda
Max
Aida
Juan
Ito
Evita
Juan
Nela
Percy
Tino
Kai
Percy
Nella
a. Let B represent the set of basketball players, S
represent the set of soccer players, and V represent the
set of volleyball players. Draw a Venn diagram of this
situation.
b. Find Sn V. What does this set represent?
c. Find S. What does this set represent?
d. Find BUV. What does this set represent?

Answers

A. Correct answer...................

Juan is debating whether or not to continue the recent lunch special promotion at his restaurant. The following graph shows the profit earned, y, from the number of lunch specials ordered per hour, x.

Answers

Answer:

Max profit is 115. The resturant will break even after 10 lunch specials. The interval on which the restaurant makes a profit is (0,10).

Step-by-step explanation:

A bakery sold a total of 500 cupcakes in a day, and 93% of them were vanilla flavored. How many of the cupcakes sold that day were vanilla flavored?

Answers

I also got 465 lol. What grade are you all in?

These ordered pairs represent a proportional relationship. Use the interactive and the constant of proportionality to find the missing coordinates for the ordered pairs.

(3, 9), (A, 12), (5, 15), (6, B)

A =
B =

Answers

3,A,5,6 = A
9,12,15,B= B

Answer:

A=4 B=18

Step-by-step explanation:

PLEASE ANSWER BOTH QUICK

Answers

Answer:

1.C

2.A

Step-by-step explanation:

dude trust me

The wood framing cost $4.82 per foot. How much the framing cost for a rectangular picture that measures 3 f t by 5 f t?​

Answers

I think the answer is 77.12

What is a ratio equal to 56:64​

Answers

Answer:

A ratio equal to 56:64 would be 7:8.

Step-by-step explanation:

7:8 is the simplest form

Answer:

Simplify it to get an equivalent ratio, i.e 7:8!

Hope this helps :))

HURRY!!!!
The value of a baseball card can be represented by the equation y = 3 x + 39, where x represents the number of years that Robert has owned the card and y represents the total value, in dollars, of the card. What was the value of the card when Robert originally purchased it?
$3
$13
$36
$39

Answers

The value of the card was $13 when he originally purchased it.

Answer:

mark as brainliest plz...        it is $39

Step-by-step explanation:

ayeeeeeeeeeeeeeee

16+4|5x-4(x+2)|=7-2x

Answers

there are no solutions

There are no solutions like kathy0315 said

8. A sequence can be generated by using 2n - 11. What are the first four terms in
the sequence?

Answers

Answer:

              [tex]\bold{a_1=-9\,,\quad a_2=-7\,,\quad a_2=-5\,,\quad a_4=-3}[/tex]

Step-by-step explanation:

[tex]a_n=2n-11\\\\a_1=2(1)-11=2-11=-9\\\\a_2=2(2)-11=4-11=-7\\\\a_3=2(3)-11=6-11=-5\\\\a_4=2(4)-11=8-11=-3[/tex]

What is the Sum of Roots of x^2+9x+14=0?

Answers

Answer:

x=-2,x=-7

Step-by-step explanation:

quadratic equation form ax^2+bx+c=0

Answer:

- 9

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then

the sum of the roots = [tex]\frac{-b}{a}[/tex]

x² + 9x + 14 = 0 ← is in standard form

with a = 1 and b = 9 , thus

sum of roots = [tex]\frac{-9}{1}[/tex] = - 9

what is the value of the power a if 5a = 1/125?

Answers

Answer:

If

5

a

=

1

125

, find the value of a?

Step-by-step explanation:

There is a base f

5

on the left side, so write the denominator on the right as a base of

5

as well.

5

a

=

1

125

5

a

=

1

5

3

Move the base to the numerator.

5

a

=

5

3

If the bases are equal, the indices are equal:

a

=

3

help please!!!!!!!!!!!!!!!

Answers

Answer:

A

Step-by-step explanation:

HI

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