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'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
I need help with number 1 I don’t understand I’ll give BRAINLIEST to whoever helps me the best
Answers
Answer:
The answer is B.200
Step-by-step explanation:
145.93×1.37=199.9
We need to multiply because the second team takes the times as longer than the first team. The answer is 200 because we need to roundup 199.9 into 200
Hope it helps :)
Tyson and his friends go to ice skating. Tyson must pay an initial fee of $18.30 plus $4.80 per hour. Which equation can be used to find h, the number of
hours he can skate, if he pays a total of $37.50?
37.50 -4.80 + 18.30h
37.50 - 18.30 + 4.80 +h
37.50 - (18.30 + 4.80)
37.50 - 18.30 + 4.80h
Answers
Answer: 37.50-18.30+4.80h
Angie has to fill in a reading log for her English class. She is required to read a total of 10 and 5 over six hours a week. On Monday she read 1 and 1 over 3 hours, Tuesday she read 3 over 4 of an hour and Thursday she read 3 hours. How many total hours does she still need to read in order to get full credit?
Answers
Given:
She is required to read a total = [tex]10\dfrac{5}{6}[/tex] hours a week.
Monday she read [tex]1\dfrac{1}{3}[/tex] hours.
Tuesday she read [tex]\dfrac{3}{4}[/tex] of an hour.
Thursday she read 3 hours.
To find:
The total hours does she still need to read in order to get full credit.
Solution:
Total time = [tex]10\dfrac{5}{6}[/tex] hours a week.
Total time she already read [tex]=1\dfrac{1}{3}+\dfrac{3}{4}+3[/tex] hours
[tex]=\dfrac{1\times 3+1}{3}+\dfrac{3}{4}+3[/tex] hours
[tex]=\dfrac{4}{3}+\dfrac{3}{4}+3[/tex] hours
[tex]=\dfrac{16+9+36}{12}[/tex] hours
[tex]=\dfrac{61}{12}[/tex] hours
Now,
Remaining time = Total time - Total time she already read
[tex]=10\dfrac{5}{6}-\dfrac{61}{12}[/tex]
[tex]=\dfrac{65}{6}-\dfrac{61}{12}[/tex]
[tex]=\dfrac{130-61}{12}[/tex]
[tex]=\dfrac{69}{12}[/tex]
[tex]=\dfrac{23}{4}[/tex]
[tex]=5\dfrac{3}{4}[/tex]
Therefore, the required time is [tex]5\dfrac{3}{4}[/tex] hours.
-2 (3x - 6) + 4 (5x - 8) = 92
Answers
Answer: x=7
Step-by-step explanation:
Please answerrr!!! (don’t answer if you don’t know it) will give brainliest
Answers
Is √3,600 rational? Or a perfect square
Answers
Answer:
Yes to both
Step-by-step explanation:
The polynomial p(x)=3x^3-5x^2-4x+4 has a known factor of (x-2)
Answers
Answer:
3x^2-x-2 or (x+1) (3x-2) (x-2)
Step-by-step explanation:
I'm assuming you have to divide:
(x-2)[tex]\sqrt{3x^3-5x^2-4x+4}[/tex]
Hope this helps.
Answer:
p(x)=(x+1)(3x-2)(x-2)
Step-by-step explanation:
Tristan bought 23 chicken wings for $57.50. What's the unit cost of one wing?
Answers
Answer:
$2.50
Step-by-step explanation:
to find the unit price you would divide it by 23
so 57.50/23=2.50
hope this helps
brainliest?
En la figura, la suma de las medidas p + q + r + s =/In the figure, the sum of the measures p + q + r + s =
And if someone know the explanation please write it
Answers
Answer:
I think its 300
Step-by-step explanation
This is from my understanding, so I may be a bit wrong.
1. First observe the amount of triangles that form, you have two main triangles and one isosceles triangle that forms in the middle by how these are joined together.
2. Using this idea we will come up with the equations of each triangle that has been formed.
3. We can observe that almost all angles are named with a variable except the one in the middle, being an isosceles we will name the missing variable y.
4. Triangle 1(left side) or T1 equals 180 degrees but what angles form this triangle, these would be p+q+y = 180, T2(right side) = r+s+y = 180
5. After creating these two triangles we notice that we have not taken into account the triangle in the middle, we are given 1 angle of this isosceles. There is a mathematical property which I don't remember the name, but essentially the angle below is the same as the angle above, this being 120 degrees. This will result in T3 = 2y + 120 = 180
6. Solve for y, which gives us y=30, *simple triangle math you know*
7. Finally we fix our equations for p+q+r+s, essentially T1 and T2 will transform into p+q = 180-y and r+s = 180-y, we add them up forming p+q+r+s = 2(180-y)
8. Solve the equation p+q+r+s = 360 - 2y which when adding y becomes p+q+r+s = 360-60 = 300
Notes: when doing these exercises it is important to take into account every triangle, the isosceles triangle is very vital for solving it, as it gives us a way for making an equation that is single handedly dependent on y a constant we can find and use. A good approach for these issues would be writing every piece of information as separate sets and then trying to join them using algebra.
The figure shown is reflected over the x-axis, then reflected
over the y-axis, and then translated 3 units right.
Which graph best represents the new position of the figure
after the three transformations?
Select one:
Answers
Answer:
grapgh?????
Step-by-step explanation:
I need some help with (−3f−5f+9)−(−6f+2)
Answers
Answer:
the correct answer would be -2f+7
HELP PLEASE PLEASEEEEEEE
Answers
Answer:
about 1854.55 miles (rounded to the hundredth)
Step-by-step explanation:
1.
[tex] \frac{44}{100} = \frac{816}{x} [/tex]
The first fraction represent the percentage of the distance.
The second one represent the number of 816 miles out of x
2. 100 × 816 = 44 × x
3. You'll get 81,600 = 44x
4. and then you divided both side by 44 to solve for x
Can someone please help this is math? ill give BRAINLIEST
Answers
Answer:
27
Step-by-step explanation:
To solve this problem, let us follow it step by step;
Let Peter's number = P;
So;
⇒ P - 17
⇒ -2 (P - 17 )
⇒ -2 (P - 17 ) = -20
Solve the problem for P;
-2 (P - 17 ) = -20
-2P + 34 = -20
-2P = -20 -34
-2P = -54
P = 27
Answer:
Answer:
27
Step-by-step explanation:
To solve this problem, let us follow it step by step;
Let Peter's number = P;
So;
⇒ P - 17
⇒ -2 (P - 17 )
⇒ -2 (P - 17 ) = -20
Solve the problem for P;
-2 (P - 17 ) = -20
-2P + 34 = -20
-2P = -20 -34
-2P = -54
P = 27
Step-by-step explanation:
Given f(x)=3x+7 and g(x)=5x-4 answer the following g(2)
Answers
Answer:
6
Step-by-step explanation:
They are asking you to plug in 2 for the g(x) equation
5(2)-4=6
WILL GIVE 100 POINTS AFTER YOU ANSWER
What is the median of this data set: 17, 13, 18, 20, 17, 15, 12
20
17
19
16
Answers
Answer:
b
Step-by-step explanation:
Solve for x please help me
Answers
0.4 (3d - 5) =4 hi :)))))
Answers
Answer:
d=5
Step-by-step explanation:
0.4 times 3= 1.2
0.4 times -5= -2
4+5= 6
6/1.2=5
READ THE END! PLEASE HELP! OK, will mark best straight answer with brainiest (with explanation) URGENT! Justin's sand castle is 180 cm tall but the wind is blowing away sand at a rate of 8 cm per minute. Taylor's sand castle is 160 cm tall and she is adding sand to it at a rate of 6 cm per minute. After how many minutes will their sand castles be at an equal height? [ Also, if its 17.5 please explain what happened to 180 & 160!!! ]
Answers
Answer:
Both castles will have the same height at 3.33 minutes
Step-by-step explanation:
This problem will be solved with linear modeling, that is, expressing both people's sand castle's height as a function of time.
Justin built a sandcastle 180 cm tall, and its height is losing at 8 cm/min by the effect of wind. Thus, the height of Justin's sandcastle is:
[tex]H_J=180-8t[/tex]
Where t is the time expressed in minutes.
Taylor's sandcastle is initially 160 cm tall. The wind blows away sand at 8 cm/min but she adds sand at 6 cm/min, thus the real loss of sand is 8 cm/min - 6 cm/min= 2 cm/min. Thus, the height of Taylor's sandcastle is:
[tex]H_T=160-2t[/tex]
To find when both castles have the same height, we set:
[tex]180-8t=160-2t[/tex]
Simplifying:
6t=20
Solving:
t=20/6=3.33\ minutes
Both castles will have the same height at 3.33 minutes
Is this right? I need help pls, I'm failing
Answers
Answer:
its right
Step-by-step explanation:
you are insine or what ever you know what i mine alright im not smart or dum
A company makes two sizes of dog toys. The regular size works for most dogs, and the jumbo size is for really big dogs! Last week, the company made 1,740 dog toys. They made 11 times as many regular size toys as jumbo size toys. How many jumbo size dog toys did they make?
Answers
Answer: 1595 jumbo size
Step-by-step explanation:
From the question, let regular size toys be represented by a.
We are informed that the company made 11 times as many regular size toys as jumbo size toys. This means that:
Jumbo side toys = 11 × a = 11a
To calculate the number of jumbo size dog toys they make goes thus:
11a + a = 1740
12a = 1740
a = 1740/12
a = 145
Jumbo size toys = 11a
= 11 × 145
= 1595
A bag weighing 80 N rests on a horizontal surface. The coefficient of static friction between the bag and the surface is 0.4, and the coefficient of kinetic friction is 0.2. What minimum horizontal force must be applied to keep the bag moving at constant velocity once it has started to move?
Answers
Answer:
The minimum horizontal force that must be applied to keep the bag moving at constant velocity once it has started to move is 16 newtons.
Step-by-step explanation:
According to the First and Second Newton's Laws, an object has net force of zero when it is at rest or moves at constant velocity. Given that bag rests on a horizontal surface, the equation of equilibrium is:
[tex]\Sigma F = P - f = 0[/tex] (Eq. 1)
Where:
[tex]P[/tex] - Horizontal force exerted on the bag, measured in newtons.
[tex]f[/tex] - Kinetic friction force, mesured in newtons.
From (Eq. 1), we get that horizontal force is:
[tex]P = f[/tex]
On the case of a horizontal surface, normal force exerted from ground on the bag and kinetic friction force is:
[tex]f = \mu_{k}\cdot W[/tex] (Eq. 2)
Where:
[tex]\mu_{k}[/tex] - Kinetic coefficient of friction, dimensionless.
[tex]W[/tex] - Weight of the bag, measured in newtons.
Then we eliminate kinetic friction force by equalizing (Eqs. 1, 2):
[tex]P = \mu_{k}\cdot W[/tex]
If we know that [tex]\mu_{k} = 0.2[/tex] and [tex]W = 80\,N[/tex], then the horizontal force that must be applied to is:
[tex]P =0.2\cdot (80\,N)[/tex]
[tex]P = 16\,N[/tex]
The minimum horizontal force that must be applied to keep the bag moving at constant velocity once it has started to move is 16 newtons.
What is the factored form of 8x^3 - 27y^3?
A. (2x + 3y)(4x^2 - 6xy + 9y^2)
B. (2x – 3y)(4x^2 + 9xy + 6y^2)
C. (2x – 3y)(4x^2 + 6xy + 9y^2)
D. (2x + 3y)(4x^2 - 9xy + 6y^2)
Answers
For your birthday, you had a party at The Main Event. Your parents paid for you and 9 friends to play one game of bowling and one game of laser tag. It costs $8 for each combo ticket (covers both bowling and laser tag). Your parents also paid for a meal ticket ($6) for all of you to have pizza and a drink, but only you and 6 of your friends wanted a meal ticket.
6. Write an expression and solve it to find how much money your parents spent for the games and food/drink at The Main Event. Show all work
Answers
Answer:
$140
Step-by-step explanation:
8x+6x
solve for b d=3a+3b
Answers
[tex]b = - a + \frac{1}{3} d[/tex]
3 7/10 x 7 what is the answer in fraction form or decimal form. Perhaps both
Answers
Answer:
Step-by-step explanation:
3 7/10 *7
37/10 *7
259/10
25.9 or 25 9/10
What’s the greatest common factor of 156 and 260 show your work
Answers
Answer:
52
Step-by-step explanation:
156: 22 313
260: 22 513
GCF: 22 13
The Greatest Common Factor (GCF) is: 2 x 2 x 13 = 52
Which of the following describes a square root of 41?
A.between 5 and 6
B.between 6 and 7
C.between 20 and 21
D.between 40 and 42
Answers
Answer:
the answer is b between 6 and 7
Step-by-step explanation:
i say this because the square root of 41 is 6.4031.
6.4031 is in between 6 and 7.
hope this helps :)
Provide reasons for the proof.
Given: ∠2≅∠4 and ∠2 and ∠3 are supplementary
Prove: ∠1 ≅∠3
Answers
Answer:
See picture below.
Explanation
I took the test and got a 100% on it, so this should be right for any future students.
At the beginning of the week, Tideland Manufacturing had an inventory of 60,000 screws. This week they received a shipment of 30,000 more screws. Then they used 50,000 screws to make their Tideland mowers. How many screws do they have left in inventory?
Answers
Answer:
40,000
Step-by-step explanation:
You just add 60,000 and 30,000 which makes 90,000 and subtract it with the 50,000 then which equals to 40,000. you don't need to rate me.
A farmer has 1000 feet of fencing and wants to enclose a rectangular yard, and divide it into four pens as shown.
a. Find a function A(x) modeling the total area as a function of x, Hint: write the amount of fencing needed
in terms of x and y and set that equal to 1000, then you can solve for y. This should allow you to write
down the area in terms of x alone. Your function should be a quadratic function.
Answers
9514 1404 393
Answer:
A(x) = -2/5x^2 +200x
Step-by-step explanation:
There are 5 lengths of fence that are y long, and 2 lengths of fence that are x long. So, the perimeter is ...
5y +2x = 1000
Then the value of y is ...
y = (1000 -2x)/5
The area is the product of x and y:
A(x) = xy
A(x) = x(1000 -2x)/5
A(x) = (2/5)(x)(500-x) . . . a convenient form for finding the maximum area
In standard form, the equation is ...
A(x) = -2/5x^2 +200x