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).
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Related Questions
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-6, -4),A(−6,−4),A, left parenthesis, minus, 6, comma, minus, 4, right parenthesis, comma B(-4,-4)B(−4,−4)B, left parenthesis, minus, 4, comma, minus, 4, right parenthesis, C(-4, -2)C(−4,−2)C, left parenthesis, minus, 4, comma, minus, 2, right parenthesis, and D(-6, -2)D(−6,−2)D, left parenthesis, minus, 6, comma, minus, 2, right parenthesis.
What is the perimeter of rectangle ABCDABCDA, B, C, D?
units
Answers
The perimeter of the rectangle is 8 units
The coordinates of the rectangle is given as:
[tex]A = (-6,-4)[/tex]
[tex]B = (-4,-4)[/tex]
[tex]C = (-4,-2)[/tex]
[tex]D = (-6,-2)[/tex]
Start by calculating the distance between the vertices using the following distance formula
[tex]d=\sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]AB=\sqrt{(-6 --4)^2 + (-4 --4)^2}[/tex]
[tex]AB=\sqrt{4}[/tex]
[tex]AB=2[/tex]
[tex]BC=\sqrt{(-4 --4)^2 + (-4 --2)^2}[/tex]
[tex]BC=\sqrt{4}[/tex]
[tex]BC=2[/tex]
[tex]CD=\sqrt{(-4 --6)^2 + (-2 --2)^2}[/tex]
[tex]CD=\sqrt{4}[/tex]
[tex]CD=2[/tex]
[tex]DA=\sqrt{(-6 --6)^2 + (-2 --4)^2}[/tex]
[tex]DA=\sqrt{4}[/tex]
[tex]DA = 2[/tex]
So, the perimeter of the rectangle is:
[tex]P =AB + BC + CD + DA[/tex]
This gives
[tex]P= 2 + 2+2+2[/tex]
[tex]P= 8[/tex]
Hence, the perimeter of the rectangle is 8 units
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The lines shown below are perpendicular. If the green line has a slope of
2/5 , what is the slope of the red line?
Answers
Answer:
-5/2
Step-by-step explanation:
for perpendicularity;
[tex]m1 = \frac{ - 1}{m2} [/tex]
where m1 is first slope
and m2 is second slope
so here, let m1 be green line slope
and m2 be red line slope
thus,
[tex]m2 = \frac{ - 1}{m1} [/tex]
[tex]m2 = \frac{ - 1}{ \frac{2}{5} } = - 1 \div \frac{2}{5} [/tex]
[tex] = - 1 \times \frac{5}{2} = \frac{ - 5}{2} [/tex]
PLS HELP ME I SUCK AT MATH
Answers
Question 3
Move the center of the circle vertically so it lies above and then below the x-axis. How does the equation of the circle change as the center crosses
the x-axis?
Answers
Answer:
The variable k changes as the focal point of the circle moves vertically.
Step-by-step explanation:
Answer: The variable k changes as the center of the circle moves vertically. The sign of k is positive when the center is below the x-axis and negative when it is above the x-axis. The sign of the variable k flips when the center moves across the x-axis.
Step-by-step explanation: plato/edmentum answer!
hope this helps! :)
Derek tried to dilate the isosceles trapezoid ABDC with the center of dilation at the origin with a scale factor of 2. Check his work and complete the statements. The slope of AC is . The slope of EG is . The polygons are not dilations of each other because .
Answers
Answer: the slope of AC is 4
the slope of EG is 2
the polygons are not dilations of eachother because the corresponding sides are not parallel
Answer:
D, D, C
Step-by-step explanation:
Match each equation to a step that will help solve the equation.
Eqautions: Numbers:
1) Multiply each side by 5.
2) Multiply each side by -5.
3) Multiply each side by 1/5.
4) Multiply each side by -1/5.
A) 5x= 0.4
B) x/5=8
C) 3 = -x/5
D) 7 = -5x
Answers
2 and C
3 and A
4 and D
B) x/5 = 8 — 1) Multiple by 5
C) 3 = -x/5 — 2) Multiple by -5
D) 7 = -5x — 4) Multiple by -1/5
Explanation:
A:
5x = 0.4
5x • 1/5 = 0.4 • 1/5
x = 2/25 or 0.08
B:
x/5 = 8
x/5 • 5 = 8 • 5
x = 40
C:
3 = -x/5
3 • -5 = -x/5 • -5
-15 = x
x = -15
D:
7 = -5x
7 • -1/5 = -5x • -1/5
-7/5 = x
x = -7/5 or -1.4
Hope it helps!
can anyone tell me what 3 1/4 looks like as a decimal
Answers
Answer:
3.25
Step-by-step explanation:
Step-by-Step-Explanation: I showed my work below and I hope that helps.
2/5 in Fraction form?
Answers
Answer:
2/5 is fraction form.
0.4 is decimal form btw.
At this pace, how many miles can she run in 88 minutes?
Answers
Answer:
What is her pace?
Step-by-step explanation:
Find her pace, then do 88/p to find how many miles she can run.
If her pace is 11 minute/mile, then she can run 8 miles.
8*11=88
anyone that's good at math please help <3
Answers
Answer:
i would try the first option,
Step-by-step explanation:
i'm not very good at math but i don't think the problem has exponents.
Briley has 347 marbles. Joey has 4 times as many as Briley. Carson has 799 fewer than Joey. How many marbles does Carson have?
Can somebody help me thank you? Show work please
Answers
Answer:
697 marbles
Step-by-step explanation:
We know:
Briley- 374 marbles
Joey- 374*4
Carson- (374*4)-799
Solve:
374*4= 1496 (This is how many Joey has)
1496-799= 697 (This is how many Carson has)
Hope this helps!
Which point is on the graph of the equation y=2x-5?
(3,-1)
(2,-1)
(4,2)
(2,-5)
Answers
Answer:
(2,-1)
Step-by-step explanation:
If you plug each answer into the equation, (2,-1) is the only answer that makes the equation true. Hope this helps!
Help me for brainliest ✅✅✅✅✅✅✅✅
Answers
Answer:
y=-2x-3
Step-by-step explanation:
Edwin has $50.00 in his bank. He starts spending $2.50 each week on snacks at lunch graph it
Answers
Answer: 50.00 - 2.50 each week
Answer:
Step-by-step explanation:
First label the x axis as "Time (Weeks)" and y axis as "money in the bank account". The x axis should go by 1. As in the squares being, 1,2,3, etc. The y axis should go by 5's and end at 50. Plant a dot at coordinates (0,50) and continue by subtracting $2.5 per week. So the next coordinates should be (1, 47.5). In the end, there should be $25 left in the account (after using all of the boxes).
please help mee!!! i will give u 5.0 starsss
Penny takes a taxi cab from the airport to her house. The distance is 4½ miles. The taxi costs $2.75 per mile. What is the cost of taking the taxi from the airport to her house? Round to the nearest cent.
Answers
Answer:
$12.38
Step-by-step explanation:
2.75 * 4.5 = 12.38
Answer:12.38
Step-by-step explanation:
Since the cost per mile is 2.75 even multiply that by the number of miles which would be 4.5 if you work that out it would get you 12.375 and you would round to 12.38 hope this helps.
Mia averages 16 goals for every 80 shots on goal. Abby averages 13 goals for every 52 shots.. Who has the greater goal rate?
Answers
Answer correctly
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0+0
Answers
Can someone explain this to me
Answers
Answer:
54°
Step-by-step explanation:
The angles inside of a triangle will equal a sum of 180. So you use the equation X= 180-(80+46)
please brainliest
Hope I helped :)
how do I write a polynomial when given the zeros
Answers
Given the zeros of a polynomial, you can very easily write it -- first in its factored form and then in the standard form. Subtract the first zero from x and enclose it in parentheses. This is the first factor. For example if a polynomial has a zero that is -1, the corresponding factor is x - (-1) = x + 1.
Answer:
Subtract the first zero from x and enclose it in parentheses. This is the first factor. For example if a polynomial has a zero that is -1, the corresponding factor is x - (-1) = x + 1.
Raise the factor to the power of the multiplicity. For instance, if the zero -1 in the example has a multiplicity of two, write the factor as (x +1)^2.
Repeat Steps 1 and 2 with the other zeros and add them as further factors. For instance, if the example polynomial has two more zeros, -2 and 3, both with multiplicity 1, two more factors -- (x +2) and (x -3) -- must be added to the polynomial. The final form of the polynomial is then ((x +1)^2)(x +2)(x -3).
Multiply out all the factors using the FOIL (First Outer Inner Last) method to get the polynomial in the standard form. In the example, first multiply (x + 2)(x - 3) to get x^2 + 2x - 3x - 6 = x^2 - x - 6. Then multiply this with another factor (x + 1) to get (x^2 - x - 6)(x + 1) = x^3 +x^2 - x^2 - x - 6x - 6 = x^3 - 7x - 6. Finally, multiply this with the last factor (x + 1) to get (x^3 - 7x - 6)(x + 1) =x^4+x^3-7x^2-7x-6x-6 = x^4 + x^3 - 7x^2 - 13x - 6. This is the standard form of the polynomial.
Geometry pls help me
Answers
Answer: 180
Step-by-step explanation:
When added together, Interior angles of a triangle are always equal to 180 degrees.
Answer:
∠FHG=120°
Step-by-step explanation:
first you calculate the angles of the triangle NGH
this is isoceles triangle, so there's 2 equal angles
and as shown, the 2 same angles are having 2 lines in each one, this 2 lines represents that the 2 angles are same
so both are 20°
any triangle has a sum of 180° of interior angles
so 180-(H+G)=the angle below N
180-(20+20)=140°
the angle below N is same as N because they're vertically opposite
140 is an exterior angle
and the exterior angle is equal to the 2 far angles
140=40+∠FHN
140-40=100°
so ∠FHN=100°
∠FHN+∠NHG=∠FHG
100+20=120°
so ∠FHG=120°
Use a product of two binomials to find a polynomial that represents the area of Roberto's plot.
Answers
Answer:
First, we know that the area of a rectangle of width W and length L is:
A = W*L
In the case of Roberto's plan, we can see that the length of the whole rectangle is:
L = 1.5ft + x + 1.5ft = 3 ft + x
And the width is:
W = 3ft + x + 3ft = 6ft + x
Then the area of the whole thing is:
A = (3ft + x)*(6ft + x)
This is what we wanted, a product of two polynomials that represents the area of Roberto's plot.
Now if we subtract the white square (is a square of sidelength x, then its area is A = x*x) we will get the area of the border;
The total area of Roberto's borders is:
Area of the border = (3ft + x)*(6ft + x) - x*x
= 3ft*6ft + 3ft*x + x*6ft + x^2 - x^2
= x*9ft + 18ft^2
OLEASE HELP I BEG YOU
Answers
Answer:1 is the remainder hope it helps
Answer:
This is pretty easy the dividend is 34,465 and the divisor is 6 and whatever the answer is will be the quotient
Step-by-step explanation:
hope this helps :>
Please helpppp will give brainliest
Answers
Answer: B it seems like
Answer:
A
Step-by-step explanation:
We can see that the y intercept is equal to 1
which means that we have the following equation
mx+1=y
We just need to solve for m at this point
We can use the ordered pair (-2,2) to help
We know that
-2m+1=2
Solve for m
-2m=1
m= -1/2
Put this together and we get
-1/2m+1=y which is A
Increase £490 by 11% give your answer rounded to 2 DP
Answers
Step-by-step explanation:
Given \:number (m) = £ 490Givennumber(m)=£490
Increase (g) = 11\%Increase(g)=11%
\begin{gathered} \red{ Required \:number } \\= m\Big( \frac{(100+g)}{100} \Big)\\= 490\Big(\frac{100+11}{100}\Big)\\= 490 \times \frac{111}{100} \\= 490 \times 1.11 \\= £ 543.9 \end{gathered}
Requirednumber
=m(
100
(100+g)
)
=490(
100
100+11
)
=490×
100
111
=490×1.11
=£543.9
Therefore.,
\red{ Required \:number }\green { = £ 543.9}Requirednumber=£543.9
•••♪
Answer:
£543.90
Step-by-step explanation:
You have to add 2 and nothing
27 to 32
What is the frequency between 27 to 32
Answers
Answer:
it has a frequency of 5
Step-by-step explanation:
At the beginning of a population study, city had 210,000 people. Each year since, the population has grown by 5.5%. Let t be the number of years since the start of the study. Let y  be the cities population. Write an exponential function showing the relationship between y and t. 
Y=
Answers
Answer:
y = 210,000(1.055)^t
Step-by-step explanation:
Initial population: p = 210,000
Annual growth rate: 5.5% = 0.055
Number of years: t
Population in year t: y
y = p(1 + r)^t
y = 210,000(1 + 0.055)^t
y = 210,000(1.055)^t
this is RAY MAK who knows him
Answers
1) someone help easy math question
Answers
Which one of these is NOT equivalent to 2/3?
1. 11/23
2. 12/18
3. 14/21
4. 6/9
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.
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