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:
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.
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.
Read more at; https://brainly.com/question/18430680
Related Questions
if 3n-4=8 then what is the value of 5n-3
Answers
Answer:
17
Step-by-step explanation:
Given
3n - 4 = 8 ( add 4 to both sides )
3n = 12 ( divide both sides by 3 )
n = 4
Thus
5n - 3 = 5(4) - 3 = 20 - 3 = 17
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Answer:
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Answers
Answer:
1147 days
Step-by-step explanation:
3x365= 1095
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1095+49+3=1147
rrange the numbers in decreasing order.
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8.508
8.58
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Answer:
8.58
8.508
7.5
7.058
Step-by-step explanation:
Answer:
8.58, 8.508, 7.5, 7.058
Step-by-step explanation:
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Look at the place values.
which two ratios quantities that are proportional
A. 9/5 and 19/10
B. 25/25 and 20/24
C. 4/6 and 10/16
D. 15/10 and 21/14
Answers
Answer:
A
Step-by-step explanation:
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Answer:
C. 15/10 and 21/14
Explanation:
A P E X
the farm covers an area of 13square miles. The farm is divided into 4 equal sections, as shown in this diagram. What is the area, in square miles, of each section?
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Answer:
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Step-by-step explanation:
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Jay bought a painting on sale for 45% off the original price, for $27. What was the price of the painting before the sale?
Answers
Answer:
0.55x = $27
Step-by-step explanation:
Let the price of the painting = x
x - 45% of x = $27
x - 0.45x = $27
0.55x = $27
Divide both sides by 0.55
0.55x/0.55 = $27/0.55
x = $49.09
help show work
assig 8
(a)solve the inequality
(b)graph the solution on the real number line.
(c)write the solution in interval notation.
29
30
31
32
33
Answers
Answer: see below
Step-by-step explanation:
29) -5x ≥ 30
÷ -5 ↓ ÷ -5
x ≤ -6
Graph: ←--------- ·
-6
Interval Notation: (-∞, 6]
30) -4x < -40
÷ -4 ↓ ÷ -4
x > 10
Graph: o---------→
10
Interval Notation: (10, ∞)
31) 2x - 5 ≥ -11
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2x ≥ -6
÷ 2 ÷ 2
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-3x > 12
÷ -3 ↓ ÷ -3
x < -4
Graph: ←---------o
-4
Interval Notation: (-∞, -4)
33) 4x - 11 < 7x + 4
-7x -7x
-3x - 11 < 4
+ 11 +11
-3x < 15
÷ -3 ↓ ÷ -3
x > -5
Graph: o---------→
-5
Interval Notation: (-5, ∞)
6(x-2=4(x+3) what does x equal
Answers
Hey mate here is your answer.
➛ 6(x-2) = 4(x+3)
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⛬ x = 12
What is the equation of the line that is parallel to the line y = 2x + 6 and goes through point C (8, 1)?
Answers
Answer:
y=2x-15
Step-by-step explanation:
In parallel lines the gradient is always the same. then we sub the coordinates in to find c.
so
1=2(8)+c
c equals to -15 t
then
y=2x-15
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Answers
Answer:
5(m+9) = 5m+25
Answer:
5(m+9) = 5m+25
Step-by-step explanation:
durrrrrrrrrrrrrrr
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Why is it that when comparing a squares area with a rectangles area, with the SAME PERIMETER, that the square has a greater area?
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s = side length of square
4s = perimeter of square
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W = width of rectangle
P = 2L+2W = perimeter of rectangle
4s = 2L+2W .... since we want the perimeters the same
4s = 2(L+W)
s = 0.5(L+W)
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s^2 = 0.25(L+W)^2
The last equation shows the area of the square, s^2, in terms of L and W. This way we can connect the square to the rectangle.
-----------------------------------
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Let's subtract this from the area of the square and see what we get
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B = area of rectangle = LW
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So C is always positive as long as [tex]L \ne W[/tex]
If C > 0, and C = A - B, then
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A-B > 0 .... replace C with A-B
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1.
p: you pass the class
q: you go to the next grade
p -> ~q:_______________________________
~p->~q:_______________________________
Answers
Answer:
P is you pass the class, so it's the hypothesis in the conditional. And Q is the conclusion, which ic you got to the next grade.
Step-by-step explanation:
In order to got to the next grade, you need to pass the class.
or
If you pass the class, you go to the next grade.
PLZ HELP ME
In 2001, gold was priced at (0.5x + 300) dollars per ounce. Its price tripled in 2008 and then doubled in 2011. In 2016, its price dropped to 2 3 of the price in 2011.
• Write an expression for the price of gold per ounce in 2016.
• Explain how you found the expression.
Answers
Answer:
[tex]2x + 1200[/tex]
Step-by-step explanation:
[tex].5x + 300 \\ 3(.5x + 300) = 1.5x + 900\\ 2(1.5x + 900) = 3x + 1800 \\ \frac{2}{3} (3x + 1800) = 2x + 1200[/tex]
Each new line represents the change stated in the question.
Drag numbers to complete the table for missing values of x, x2, and x3.
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Answer:
Values are:
x x²
10 100
5
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Answer:
Slope of a line = rise/run
Your answer:
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Answers
Answer:
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Step-by-step explanation:
-12+2/2= -5
-9+10/2= 0.5
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Answers
Answer:
Part 1:
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Part 2:
R’ = (-3, -4)
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Answers
Answer:
the product of the two integers is -80
Answer:
-80
Explanation:
it was on a mathcounts competition
Are the lines parallel? y = x + 4 and y = x-2
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Answers
Answer:
A
Step-by-step explanation:
Remember that parallel lines have the same slope.
The y-intercept does not matter.
We have the two equations:
[tex]y=x+4[/tex]
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[tex]y=x-2[/tex]
The slope is the coefficient in front of the x.
In the first equation, we can rewrite it as:
[tex]y=(1)x+4[/tex]
Therefore, the slope of the first equation is 1.
Similarly, for the second equation, we can rewrite it as:
[tex]y=(1)x-2[/tex]
The slope of the second equation is also 1.
Therefore, since their slopes are equivalent, they are parallel.
Thus, our correct answer is A.
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B.(0,3)
C.(2,3)
D.(-2,2)
Answers
Answer:
C: (2,3)
Step-by-step explanation:
to solve this algebraically just plug in the x and y values of the points and see if they are true, but here is the graph to juse show you
What Is 2+4? I need to know.
Answers
Answer:
the answer is 6
Step-by-step explanation:
Answer:
6! Hope this helps have a great night!!!!
Step-by-step explanation:
May I plz have brainliest?
What is the average rate of change in height over the entire 5 seconds?
Answers
Answer:“To get the average rate of change between 2 points...” To get the average rate of change between 2 points, plug in their coordinate values into the equation (y2-y1)/(x2-x1). The values come from the points (x1,y1) and (x2,y2).
Step-by-step explanation:
Which of the following equations demonstrate the multiplication property of equality for the equation x = 2? Check al
that apply.
x(3) = 2(4)
x(5) = 10
11.5) = 2(2)
x(0.5) = 2(0.5)
x(12) = 12
Answers
Answer:
the 2nd and 4th i think
Step-by-step explanation:
I’m pretty sure the answer would be
x(5) =10.
Jayvon has 33.6 points in a competition. He loses 5.5 points,
Write and then evaluate an addition expression to determine Jayvon's current points.
Answers
Answer:
33.6+(-5.5)=28.1
Step-by-step explanation:
Since positive times negative is equal to negative, we can multiply -5.5 by an addition symbol, making it an addition problem, and making it the same expression.
To evaluate the expression, we can do 33.6-5.5.
When adding or subtraction decimals, write it stacked like a normal problem, and line up the decimal places, like so.
33.6-
5.5
Then you can subtract normally, getting 28.1
What are the values of x and y?
image attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
We'll have to use trigonometry for this.
First, note that in right triangle ABC, if we look from the perspective of angle A, the opposite side is x, the adjacent side is y, and the hypotenuse is 18.
In order to find x, then, we must use sine, which is opposite/hypotenuse. So:
sin(A) = sin(60) = opposite/hypotenuse = x/18
sin(60) is equal to (√3)/2, so multiplying both sides by 18 gives:
[(√3)/2] * 18 = 9√3
Already, we can tell that the answer is likely C, but let's find y to make sure.
We will use cosine to find y because cos = adjacent/hypotenuse.
cos(A) = cos(60) = adjacent/hypotenuse = y/18
cos(60) = 0.5, so multiplying both sides by 18 gives:
0.5 * 18 = 9
So, y = 9.
Thus, C is our answer.
~ an aesthetics lover
Answer:
C
Step-by-step explanation:
Using the cosine/ sine ratio in the right triangle and the exact values
cos30° = [tex]\frac{\sqrt{3} }{2}[/tex] and sin30° = [tex]\frac{1}{2}[/tex] , then
cos30° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{x}{18}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 18[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 9[tex]\sqrt{3}[/tex]
----------------------------------------------------------
sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{AC}[/tex] = [tex]\frac{y}{18}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2y = 18 ( divide both sides by 2 )
y = 9
Thus
x = 9[tex]\sqrt{3}[/tex] and y = 9 → C
someone help with this ASAP I HAVE FEW MINS !!!
Answers
Answer:
Symmetric
Step-by-step explanation:
What is the location of H' after the image is rotated 180 degrees?
Answers
Answer:
The answer is B
Step-by-step explanation:
If you were to rotate the shape 180* it would turn 2 times leaving the point "H" at (5, -3)
Two pounds of grapes cost $6. How many pounds of grapes can
you get for $1? (hint: write a repeating decimal as a fraction)
Answers
Answer:
1/3 of a pound .333
Step-by-step explanation:
6/2 =3
1/3= .333
Answer:
1/3 to 1 and 1 to 3
Step-by-step explanation: