an island has three towns located at points with the coordinates a (15,3) b (25,10) and c (0,20) where the coordinates have units of Km the government wants to locate a toxic waste dump at a position as far as possible away from each town you may assume that this location is not on the edge of the island find the coordinates at the point where the toxic waste dump should be located
Answers
9514 1404 393
Answer:
(13.06, 16.41)
Step-by-step explanation:
Any point not on a perpendicular bisector of the line between towns will be closer to one town than the other. So, the intersection of perpendicular bisectors will be the equidistant from all towns. That point is the circumcenter of the circle circumscribing the triangle with the towns as its vertices. This can be found as the intersection of two perpendicular bisectors of the segments between the towns.
The midpoint of AB is ...
(A +B)/2 = ((15, 3) +(25, 10))/2 = (40, 13)/2 = (20, 6.5)
The midpoint of AC is ...
(A +C)/2 = ((15, 3) +(0, 20))/2 = (15, 23)/2 = (7.5, 11.5)
__
The differences between points are ...
B -A = (25, 10) -(15, 3) = (10, 7)
C -A = (0, 20) -(15, 3) = (-15, 17)
Then the perpendicular bisector equations can be written as ...
bisector of AB ⇒ 10(x -20) +7(y -6.5) = 0
10x +7x -245.5 = 0
bisector of AC ⇒ -15(x -7.5) +17(y -11.5) = 0
-15x +17y -83 = 0
These have coefficients that aren't particularly nice, so a method similar to Cramer's Rule is suitable for solving this pair of equations. Using the "cross multiplication method", we have ...
x = (7(-83) -17(-245.5))/(10(17) -(-15)(7)) = 3592.5/275 = 13 7/110 ≈ 13.06
y = (-245.5(-15) -(-83)(10))/275 = 4512.5/275 = 16 9/22 ≈ 16.41
The point as far as possible from each town within the boundary of the island has coordinates (13.06, 16.41).
_____
Further detail regarding the solution
Here, we have written the equation for the perpendicular bisector this way. The difference in coordinates between points R and S can be called ...
R -S = (∆x, ∆y)
The midpoint of segment RS can be called ...
(R +S)/2 = (h, k)
Then the line that is a perpendicular bisector of RS can be written as ...
∆x(x -h) +∆y(y -k) = 0
This is the form that is used above.
__
The "cross multiplication method" for solving a pair of general-form linear equations ...
ax +by +c = 0
dx +ey +g = 0
will give the solution as ...
1/(ae -db) = x/(bg -ec) = y/(cd -ga)
If you write the coefficients in two rows of four, the pattern of products and differences is easy to see.
[tex]\left[\begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}\right][/tex]
Related Questions
Answe please, which choice
Answers
Answer:
Both Reflectional and Rotational
Step-by-step explanation:
5x - 7 + 2x = 21 solve the linear and state the property that justifies your first step
Answers
Answer:
x = 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Step-by-step explanation:
Step 1: Define equation
5x - 7 + 2x = 21
Step 2: Solve for x
Combine like terms: 7x - 7 = 21Add 7 on both sides: 7x = 28Divide 7 on both sides: x = 4which point is on the graph of f(x) = 6x?
answer: (1,6)
Answers
Explanation
Which of the following is the proper name for the figure below?
s
E
A. ADSK
B. ADKM
C. ADME
D. ADOM
Answers
Answer:
ADOM IS THE ANSWER OF THIS QUESTIONS
Identify the best method for solving the given
system of equations. DO NOT SOLVE. Justify your
choice using academic vocabulary.
3x + 2y = 0
x - 5y = 17
Answers
a tree of 14 m height is broken so that its top touches ground and makes an a 60 degeree.find the length of broken part of tree
Answers
Answer:
98 - 24√3 is your answer dear.
Step-by-step explanation:
Let the length of broken part of the tree = 14 - x
For finding x
sin60° = √3/2 = x /14-x
14√3 - √3x = 2x
14√3 = 2x + √3x
14√3 = (2 + √3)x
x = 14√3/(2 + √3)x
after rationalisation
x = 24√3 - 84
substract it 14 - (24√3 - 84)
YOU'LL GET 98 - 24√3 WHICH IS YOUR ANSWER.
holaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
HIIIIIIIIIIII
Step-by-step explanation:
SOMEONE PLEASE HELP ME OUT WITH THIS PLEASE PLEASE PLEASEE I WANT TO PASS AND I DONT KNOW THAT ANSWER
Answers
Answer:
A and D
Step-by-step explanation:
C
i gotta add words so i meat the 20 character limit :)
Dany has a business selling bracelets for 7.50 each. She only has enough material to make 5 bracelets. If x represents the number of bracelets sold and y represents the total cost, what is the range for this situation.
Answers
Answer:
The range is [0,37.5]
Step-by-step explanation:
We start by writing the equation that links x and y
From the question;
y = 7.5x
Now, she has enough material to make 5 only
When we talk of range, we are referring to the values on the y-axis
So the lowest y value is 0
and since the highest number of bracelets is 5;
The total cost of the 5 is 7.5(5) = 37.5
So the range is [0,37.5]
plz help asap i'll give brainlest
Answers
Answer:
X=11
Step-by-step explanation
[tex]5^{3+8} =5^{11}[/tex]=11
8. Sheila buys two concert tickets from her friend.
She pays $90 for the two tickets. She looks at the
tickets and sees that each ticket has a face value
of $52.50.
B.What was the percent markdown, rounded to the nearest whole percent
Answers
Cost of two tickets that Sheila paid to her friend = $ 90
Actual price of 1 ticket = $ 52.50
So, actual price of 2 tickets = 52 x 2 = 105
Hence, markdown or discount Sheila's friend gave her is =
105 - 90 = 15
The answer is $15.
Answer:
15
Step-by-step explanation:
105 - 90 = 15
Whats the answer please explain your answer giving brainliest:D..
Answers
Answer:
It is the first one
Step-by-step explanation:
PLEASE HURRY!!
Juan's cell phone company charges $35 a month for phone service plus $0.50 for each
text message. How many text messages does Juan send in a month if his bill was $52?
1.
Define the variable:
2.
Determine the constant:
3
What is the rate:
4
Write the equation and solve:
Answers
Juan sent 34 text messages.
First, you have to subtract 35 from 52. The answer you should get is 17. If you divide 17 by $.50 you should get 34.
Please Help! I'll give Brainliest!
Eshaal is creating a model of a pyramid. The model created will need to be scaled up from the blueprint.
If segments DE and AB are parallel, which of the following expressions will help Eshaal determine the length of segment BC?
BC = CE
BC equals AC times CE all over CD
BC equals AC times DE all over CE
BC = AC
Answers
Answer:
See attachment
PS:
Can I have Brainliest?
The correct statement is BC equals to AC times CE all over CD.
We have, If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. this is known as the triangle proportionality theorem.
Given, DE and AB are parallel
So, [tex]\frac{BC}{CE} =\frac{AC}{CD}[/tex]
[tex]BC = \frac{AC\times CE}{CD}[/tex]
Therefore in statement form we say that BC equals to AC times CE all over CD.
For more details on proportionality theorem follow the link:
https://brainly.com/question/2078223
When loaded with bricks, a lorry has a mass of 11600kg. If the mass of the bricks is three times that the mass of the empty lorry, find the mass of the bricks.
Answers
Answer:
8700kg
Step-by-step explanation:
lorry + bricks = 11600kg
bricks = 3(mass of empty lorry)
lorry mass is x
there for bricks = 3x
x+3x = 11600
4x =11600
x= 2900kg
mass of bricks = 3(2900)
=8700kg
What is the slope of the line on the graph?
Enter your answer in the box
I will brainlist thing to who ever answers this correctly
Answers
(-1-5)/(0-1) = -6/-1 = 6
The slope is 6
Answer:
none.
Step-by-step explanation:
if you examine the dots and solve, they are not equivalent
also it doesn't pass through the orgin
Write the slope intercept form of the equation of each line given the slope and y intercept
Answers
Answer:
11) y= -1x-2
12) y= 3/2x+3
13) y= 3x-2
14) y= 3/4x+1
15) y= 1/2x+1
16) y= -2/5x+0
17) y=7x+2
18) y= 4/3x-4
Step-by-step explanation:
y=mx+b
m is slope and b is y intercept
A side of the triangle below has been extended to form an exterior angle of 156°. Find
the value of x
Answers
Answer:
x=24
Step-by-step explanation:
again 180-156=24
super easy remember exterior +interior angles add up to 180
Brainliest please
First angle = 105
Second angle = x
Third angle = 156 - 105
= 51
_________________________________________
Three angles of the triangle:
[tex]105[/tex]
[tex]x[/tex]
[tex]51[/tex]
___________________________________________
Angle sum of triangle = 180°
[tex]105 + 51 + x = 180[/tex]
[tex]156 + x = 180[/tex]
[tex]x = 180 - 156[/tex]
[tex]x = 24[/tex]
Pizza Hut charges $10 per large pizza plus a $4 delivery fee. If you spent a total of $34, how many pizzas did you order
Answers
Answer:
3 pizzas
Step-by-step explanation:
34-4=30
30/10=3
Answer:
3 pizzas
Step-by-step explanation:
34-4=30 since we already know the delivery fee
30/10=3 since we have 30 dollars left without the delivery fee we are just left to divide 30 by 10 to get the total number of pizzas
What is the value of x in the solution to this system of equations?
3x−6y=45
y=−2x+5
Answers
3x + 12x - 30 = 45
15x - 30 = 45
15x = 15
x = 1
HELP PLEASE. what is the solution to this as an ordered pair. (algebra 1)
Answers
Answer:
(2 , 0)
I solved this using the comparison method ;)
Answer:
y=4×+6=56
56×65
45×34=
2×-4=67
8x – 12y = 48
Find the x-intercept and y-intercept
Answers
Answer:
my answer came out to x = 6 + 1.5y
Step-by-step explanation:
The school that Stefan goes to is selling tickets to a choral performance. On the first day of ticket sales the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets.
Part A: Write a system of equations to represent the given scenario. Use the variables "s" for senior citizen tickets and "c" for child.
Part B: Solve the system of equations from Part A algebraically. Show your work.
Part C: Explain what the solution to the system of equations represents in context of the problem. Hint: You will need to put words here, not an equation.
Answers
Answer:
The school took in $52 on there second day by selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior citizen
Step-by-step explanation:
may someone plz answer this
Answers
Answer:
At least 2 weeks
Step-by-step explanation: You divide until you reach 200
Solve the following system of equations:
x − 2y = 14
x + 3y = 9
Answers
EXPLANATION:
you set both equations equal to each other by subtracting the sum and adding it to the equation. once you set them equal to eachother (x-2y-14=x+3y-9)
you can solve by moving everything to one side by subtracting. once you get it all to one side you can start adding common numbers and variables and solve
Answer:
(12, - 1)
Step-by-step explanation:
x - 2y = 14 ......... (1)
x + 3y = 9 ......... (2)
(2) - (1)
(x - x) + (3y - ( - 2y)) = 9 - 14
5y = - 5 ⇒ y = - 1
x + 3( - 1) = 9 ⇒ x = 12
(12, - 1)
A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
Answers
Answer:
6
Step-by-step explanation:
brainest plz
twice the difference of a number and 3 is 5.
Answers
Answer:
2(3-n)=5
Step-by-step explanation:
what is the answer?
Answers
Answer: that’s super easy
Step-by-step explanation:
What is (6×5-6) +56
Answers
Answer:
(6x5 -6) +56
(30-6) +56
24+56
80
Step-by-step explanation:
On Wednesday mornings, admission to the park swimming pool is $3.00 per adult and $2.00 per child. Which expression can be used to find the cost of admission to the pool for a group of adults (a) and children (c)?
A. 3ac
B.5+ac
C. 3a+2c
D. 2(3)+ac
WILL GIVE BRAINLIEST I NEED THIS FAST
Answers
Answer:
C.) 3a + 2c
Step-by-step explanation:
$3 per adult (a)
$3(a)
+
$2 per child (c)
$2(c)
Answer:
C. 3a+2c
Step-by-step explanation:
It is 3 $ for a adult hence the 3a and 2$ for a child hence 2c