The Martin family has three children. One is in elementary school, one is in middle school, and one is in high school. They are moving and would like to
live at a location that is the same distance from each of the three schools. They have mapped the schools in a coordinate plane. Determine the
coordinates of the best location that will be equidistant from all three schools.
Answers
Answer:
Answer is 1/2,-1 1/2
Step-by-step explanation:
The coordinates of the best location that will be equidistant from all three schools is; (-0.085, -2.232).
What is circumcenter of a triangle?The circumcenter of a triangle is defined as the point where the perpendicular bisectors of the sides of that particular triangle intersect. In other words, the point of concurrency of the bisector of the sides of a triangle is called the circumcenter.
The coordinates of the 3 points that form a triangle attached in the image are;
A(-4, -2), B(0, 3), C(5, -1)
Since the distances to the circumcenter O from the vertices are all equal.
Then; AO = BO = CO.
From the first equality, we have AO² = BO²
(x + 4)² + (y + 2)² = (x - 0)² + (y - 3)²
⇒ 8x + 16 + 4y + 16 = – 6y + 9
⇒ 8x + 10y = -23 ---(1)
Similarly, from the second equality, we have BO² = CO²
(x - 0)² + (y - 3)² = (x - 5)² + (y + 1)²
⇒ – 6y + 9 = -10x + 25 + 2y + 1
⇒ 10x - 8y = 17 ----(2)
Solving eq 1 and 2 simultaneously gives;
x = -0.085
y = -2.232
Therefore, the coordinates of the best location that will be equidistant from all three schools is; (-0.085, -2.232).
Learn more about the circumcenter of a triangle here:
https://brainly.com/question/16276899.
#SPJ2
Related Questions
Given that ABCD is a parallelogram with diagonals intersecting at M. Segment PQ is drawn such that P lies on AB and Q lies on DC and it passes through M. Prove that PM is congruent to QM.
Answers
Answer:
we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and
PM = QM
Step-by-step explanation:
because it's a parrallelogram, Ad = BC and AB = DC.
P passes through both AB and DC on a diagonal, angles created by P have oppoiste exterior angles of eachother.
the diagonals of AC create congruent angles at DMC and AMB and because P is cutting through them, the angles P cuts at DMQ and QMC are equal to that of AMP and PMB
that being said, we now see that the angles of APM triangle and AMC triangol are equal and because the diagonal of BD is is being cut by AC, which AD is parralel to BC and AB to Dc, we know now that lines AM and MC are congruent
we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and
thus PM = QM
The alternate interior angles formed by the parallel sides and a common
transversal are equal, such that ΔPBM and ΔQDM are congruent.
Correct response;
PM is congruent to QM by CPCTCHow is the congruency of the segments determined?The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
ABCD is a parallelogram [tex]{}[/tex] Given
AC and DB are diagonals of ABCD [tex]{}[/tex] Given[tex]{}[/tex]
M is the point of intersection of the diagonals [tex]{}[/tex] Given
MB ≅ DM, and AM ≅ CM;[tex]{}[/tex] Properties of the diagonals of a parallelogram
∠PMB ≅ ∠DMQ [tex]{}[/tex] Vertical angles theorem
∠PBM ≅ ∠QDM [tex]{}[/tex] Alternate interior angles theorem
ΔPBM ≅ ΔQDM [tex]{}[/tex] Angle-Side-Angle Congruency post.
PM ≅ QM [tex]{}[/tex] CPCTC
ΔPBM is congruent to ΔQDM by Angle-Side-Angle congruency
postulate, given that they have two angles and an included side that are
congruent.
Therefore;
PM is congruent to QM by Corresponding Parts of Congruent Triangles are Congruent, CPCTC.Learn more about congruency postulates here:
https://brainly.com/question/17003791
PLEASE HELP! WILL MARK BRANLIEST
A university has 34,590 students. In a random sample of 165 students, 11 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is____
Answers
165x = 380490
x=2306
The expected number of students at the university who speak three or more languages is 2,306.
Solve this quadratic equation using the quadratic formula.
(3- y)(y + 4) =3y -5
Answers
Answer:
y=-(2±√21)
Step-by-step explanation:
Answer:
y=-6.5
Step-by-step explanation:
pls help it’s 30 points :)
Which mathematical sentence matches the story?
A school is holding a cake sale to raise money. They are selling cakes for $1 each and soft
drinks for $.50 (50 cents) each. How many cakes and drinks do they have to sell to make
at least $100?
Answers
Answer: they will need to sell 1,000 soft drinks and 50 cakes
Step-by-step explanation:
What is the missing length?
y
6 in
area = 18 in?
y
inches
Answers
Answer:
3in
Step-by-step explanation:
18 divded by 6 in is 3 in
A clothing store is having a sale in which everything is 10% off. A shirt’s original price is $27. A customer uses a coupon for $5 off after the sale price. How much did the customer save?
Answers
Answer:
$5.70
Step-by-step explanation:
Y=6-4(2). What is the value of y=6-4x when x=2
Answers
Answer:
y = -2
Step-by-step explanation:
Cost of meal for 3 at Olive Garden Restaurant with the tax is $54.
How much would a 15% tip be for the waiter? (Round your answer to the nearest dollar amount.) PLEASE HELP
Answers
CAN SOMEONE HELP ME PLEASEEE
Answers
Answer:
a. 45 degrees
b. 315 degrees
c. 8π
d. π
e. 7π
f. 16π
g. 2π
please help! (URGENT)
Answers
Solve Using Substitution
-9x + 6y = 18
y = -6
Answers
Answer:
the answer should be x = -6
Step-by-step explanation:
-9x + 6y = 18
-9x + 6(-6) = 18
-9x - 36 = 18
-9x - 36 + 36 = 18 + 36
-9x = 54
-9x ÷ -9 = 54 ÷ -9
x = -6
A bag is filled with green and blue marbles. There are 43 marbles in the bag. If there are 7 more green
marbles than blue marbles, find the number of green marbles and the number of blue marbles in the bag.
Equation (use x as your variable):
The number of blue marbles is:____
The number of green marbles is:____
Answers
Answer:
Blue marbles: 18
Green marbles: 25
Step-by-step explanation:
First off, we have to define our variables.
g = # of green marbles
b = # of blue marbles
We know two equations:
g + b = 43 and g = b + 7
If you're wondering how I got the first equation, it was because the number of green and blue marbles is 43. For the second equation, we know that there are 7 more green marbles than blue marbles.
Now, we have an equation for the number of green marbles. We can plug that equation into the equation g + b = 43.
So, (b + 7) + b = 43.
When we simplify it, we get 2b + 7 = 43.
We subtract 7 from both sides, which gets us 2b = 36.
Now, b = 36/2.
b = 18.
So, we found out the number of blue marbles that we have. We know that g + b = 43. Now, all we have to do is plug in the number of blue marbles into that equation to find out the number of green marbles.
g + 18 = 43.
g = 43 - 18.
g = 25.
Thus, the number of green marbles we have is 25 and the number of blue marbles is 18.
Write 7/50 as a percent.
Answers
Answer:
14 percent
Step-by-step explanation:
Lara eats a bowl of granola for breakfast every morning. She wonders how much granola she eats in a year. If Lara eats about one 48-ounce bag of granola every month, how many pounds of granola does she eat each year?
Answers
Answer:
36 pounds granola in a year
Step-by-step explanation:
Well there are 12 months a year.
She eats 48 ounce every month.
48 ounce = 3 pounds
3 pounds * 12 months = 36 pounds a year
//she sure does like granola o.o
Can someone. Explain why it’s 14/50 will mark brainliest.
Answers
Answer:
14/50
Step-by-step explanation:
it's 14/50 b/c with sin, the equation is [sin(w)=opp/hyp]. In this case, the opposite is 14 and the hypotenuse is 50.
PLEASE HELP ME I WILL GUVE BRAINLIEST I REALLY NEED HELP
Answers
1. 12 more than m
A. m - 12
B. 12 - m
C. m + 12
D. 12 + m
2. g less than 36
A. 36 - g
B. g - 36
C. 36 + g
D. g + 36
3. 17 times s
A. 17 + s
B. s/17
C. 17s
D. 17 - s
4. u tripled
A. 3u
B. 3 - u
C. u/3
D. 3 + u
5. 4 less than k
A. 4 - k
B. k - 4
C. 4 + k
D. k + 4
Answers
if you more like this^^^^^^^^^^
Answer:
1.D
2.A
3.C
4.A
5.B
hope it's helpful ❤❤❤❤
THANK YOU.
#
❤
PLEASE HELP ME ASAP?!?
Find the length of the missing side. Simplify all radicals.
Answers
Answer:
22.47
22.5 (simplified)
Step-by-step explanation:
22.47 = √(8^2 + 21^2)
hello please anyone answer that 9/20=.......%
Answers
Question/Equation:
9/20=__%
Answer/Steps to answer:
1. For the denominator, recognize that 20×5=100.
Multiple = 55
2. Multiply both the numerator and denominator by the multiple 5.
9×5/20×5
3. Simplify.
45/100
4. Simplify.
45% (0.45 Is Decimal Form)
Done by NeighborhoodDealer
answers please, asap!!
Answers
Answer:
x2 = -0.600000
x3 = -0.521600
Step-by-step explanation:
Given the formula;
xn+1 = (xn)³-5/10
x2 = (x1)³-5/10
Given x1 = -1
x2 = (-1)³-5/10
x2 = (-1-5)/10
x2 = -6/10
x2 = -0.600000
x3 = (x3)³-5/10
Given x3 = -0.6
x3 = (-0.6)³-5/10
x3 = (-0.216-5)/10
x3 = -5.216/10
x3 = -0.521600
help me please I am very confused T-T
Answers
Answer:
x=31
Step-by-step explanation:
that is an example of suplementary angles meaning that they will add up to equal 180
180-149=31
x=31
If m
= 36 degrees, then find the
m
Answers
Answer:
probablt m= 0.628
Step-by-step explanation:
pLz, help I really don't understand these problems at all.
Click here to see the screenshot
Answers
Answer:
1. You should use subtraction (20-12.68=7.32)
2. You should use multiplication
3. You need to know 5 boxes and $5.29
4. You need to know 10 packages and 2 cases
Step-by-step explanation:
I hope this helpss!!
Seven pizzas require 3 bags of cheese.How many bags of cheese are needed to make 21 pizzas?
Answers
Answer:
12 Bags of Cheese
Step-by-step explanation:
7 Pizza = 3 Bags
( ) 3 = 21
21 pizza's= 12 Bags
Pls help me out with this will mark brainliest
Answers
If M, N, and O are midpoints of JKL, find LJ.
Answers
Answer:
the answer is 12
Step-by-step explanation:
edg 2021
The length of the side LJ of triangle ΔJKL can be obtained as 12 units. The correct option is (C).
What is a triangle?A triangle is a two dimensional shape bound by three sides. The sum of the interior angles of a triangle is 180°. The longest side of a triangle is always less than the sum of other two sides.
As per the given question, O is the midpoint of LK.
Then, LO = OK.
The equation can be written as,
⇒ 2x = x + 8
⇒ x = 8
Then, NJ = 8 - 2 = 6
Since, N is also the midpoint of LJ.
LJ = 2 × NJ
⇒ LJ = 2 × 6 = 12.
Hence, the length of the side LJ can be found as 12 units.
To know more about triangle click on,
https://brainly.com/question/2773823
#SPJ2
Which expression is equivalent to
(5^-2)(5^-1)
A. -1/125
B. -1/5
C.1/125
D.1/5
Answers
Answer:is 5 ^ -2 ????
Step-by-step explanation:
Jamal drew a picture.
8 cm
4 cm
What is the area of the picture Jamal drew? Enter the answer in the box.
Answers
area of rectangle = l×b
So, area of drawing = l×b = 8cm×4cm = 32cm²
What is the area of this parallelogram?
28 m²
56 m²
84 m²
120 m²
Answers
Answer:
84 m squared
Step-by-step explanation:
Answer:
84 m²
Step-by-step explanation:
Area of parallelogram = (4 + 8)* 7 = 12*7 = 84 Sq m
Round 576.558 to the nearest tenths place
Answers
Answer:
576.6
(look at the number by the 10th place and round)
The value of 576.558 after rounding to the nearest tenth-place value is
576.6.
Option A is the correct answer.
What is place value?The place value of a number is given as:
Example:
1234.567
1 = thousand place value
2 = hundred place value
3 = tens place value
4 = ones place value
5 = tenths place value
6 = hundredths place value
7 = thousandths place value
We have,
576.558
The number in the tenth place is 5 bolded underscore.
576.558
Now,
The next value is 5 which is greater or equal to 5 so we will change the tenth place value 5 into 6.
If the next value was 4 or less we will keep the tenth place value 5 as 5.
Now,
The value of 576.558 after rounding to the nearest tenth-place value is
576.6.
Thus,
The value of 576.558 after rounding to the nearest tenth-place value is
576.6.
Option A is the correct answer.
Learn more about place value here:
https://brainly.com/question/27734142
#SPJ2