Universal Studios is looking to expand in Ontario. The new theme park will be located equidistant to
Newmarket, N (2,8), Markham, M (7,3) and Vaughan, V (-2, 0). Determine the location of the new
theme park if it is located at the point of intersection of the perpendicular bisectors.
Answers
===============================================
Explanation:
For now, we're only going to consider Newmarket and Markham, which are points N and M respectively.
Let's find the slope of line NM through use of the slope formula.
m = (y2-y1)/(x2-x1)
m = (3-8)/(7-2)
m = -5/5
m = -1
Line NM has a slope of -1. Its perpendicular slope is +1 or just 1.
Rule: If the slopes multiply to -1, then the lines are perpendicular.
Or you can apply the negative reciprocal rule to go from -1 to 1.
We'll keep this perpendicular slope in mind for later.
----------------
Now let's find the midpoint of points N and M.
Add up the x coordinates and divide by 2: (x1+x2)/2 = (2+7)/2 = 4.5
Do the same for the y coordinates: (y1+y2)/2 = (8+3)/2 = 5.5
The midpoint of N and M is at (4.5, 5.5)
The perpendicular line must go through these two points. I'm going to skip a few steps here, but basically we go from y = mx+b to y = x+1 after plugging in those x,y values and the perpendicular m we found earlier.
--------------------
In short, the perpendicular bisector for line segment NM is the equation y = x+1.
If you follow the same steps as the previous two sections, but you apply them for points M and V instead, then you should find that the perpendicular bisector is y = -3x+9. I'm skipping steps here as well.
----------------------
At this point, we have the system of equations
[tex]\begin{cases}y = x+1\\y = -3x+9\end{cases}[/tex]
Let's use substitution to solve for x and y
y = x+1
-3x+9 = x+1
-3x-x = 1-9
-4x = -8
x = -8/(-4)
x = 2
y = x+1
y = 2+1
y = 3
So together, x = 2 and y = 3 pair up to get the ordered pair solution (x,y) = (2,3)
This is the location where the theme park should be placed. Let's say that C = (2,3). I'm using C for center.
You can use the distance formula to confirm that segments CN, CM and CV are all the same length, which would verify that point C is equidistant from all the other points. Furthermore, it means that points N, M and V are all on the same circle centered at C.
I know it says not to use a graph, but it still helps to see what's going on. Also, it's a handy way to confirm the answer. I used GeoGebra to make the graph. See the diagram below.
Side note: you only need 2 perpendicular bisectors to find point C. You could use three, but that's overkill since they all intersect at the same location.
Related Questions
ABCF AND EFGH ARE CONGRUENT PARALLELGRAMS. AD = 10cm, MC = 8cm, and the area of ABCD is 112cm^2. What is the number of centimeters in EN? Express your answer as a decimal to the nearest tenth
Answers
The image to the question is attached below.
Answer: The value of EN is 11.2 cm
Step-by-step explanation:
We are given:
The parallelograms ABCD and EFGH are congruent, which simply means
AB = EF
BC = FG
CD = GH and
AD = EH
Area of ABCD = area of EFGH
Also, opposite sides of a parallelogram are equal. Thus,
AB = EF = CD = GH
BC = FG = AD = EH
It is given:
[tex]AD=10cm=FG\\\\\text{Area of ABCD}=112cm^2=\text{Area of EFGH}[/tex]
To calculate the area of a parallelogram, we use the equation:
[tex]Area=b\times h[/tex]
where, for parallelogram EFGH
b = base = FG = 10 cm
h = height = EN = ?
Area = [tex]112cm^2[/tex]
Plugging values in above equation, we get:
[tex]112cm^2=10cm\times EN\\\\EN=\frac{112cm^2}{10cm}=11.2cm[/tex]
Hence, the value of EN is 11.2 cm
the ratio of games lost to games won by a cricket team is 2:3. the team has won 18 games.how many games did they lose?
Answers
Answer:
they lost 12 games
Step-by-step explanation:
18÷3=6
6×2=12
Step 1: ax2 + bx + c = 0 Step 2: ax2 + bx = −c Step 3: Step 4: Step 5: Step 6: Step 7: Step 8:
Answers
Solution :
Given a quadratic equation :
[tex]ax^2+bx+c = 0[/tex]
Step 1 : [tex]ax^2+bx+c = 0[/tex]
Step 2 : [tex]ax^2+bx=-c[/tex]
Step 3 : [tex]$x^2+\frac{b}{a}x = -\frac{c}{a}$[/tex]
Step 4 : [tex]$x^2+\left(\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 5 : [tex]$\left(x+\frac{b}{2a}\right)^2=\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 6 : [tex]$\left(x+\frac{b}{2a}\right)=\sqrt{\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)$[/tex]
Step 7 : [tex]$x=\sqrt{\left(\frac{b}{2a}\right)^2\left(\frac{-c}{a}\right)} - \frac{b}{2a}$[/tex]
Step 8 : [tex]$x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}$[/tex]
Thus the derivation for finding the roots of a quadratic equations.
Answer:
B D A C
Step-by-step explanation:
Edge 2021
please help me with my question
Answers
Answer:
14.3%
Step-by-step explanation:
subtract 320 with 280 which is 40. divide 40 with 280 and multiply that will 100. You get 14.3%
Answer:
14.28 %
Step-by-step explanation:
cost price of an umbrella = 280
selling price of an umbrella = 320
profit% = SP - CP / CP *100%
=320 - 280/280 * 100
=40/280 * 100
=4000/280
=14.28
Can somebody help I’ll give brainless
Answers
Answer:
194.51
Step-by-step explanation:
Find 6% of 183.50
183.50 * 6%
183.50 * .06
11.01
Add this to the original price
183.50+11.01
194.51
Two weeks in a row, the golf course hosts a group of golfers. The second week had 10 more golfers than the first week. Use the dot plots to choose the true statement.
dot plot titled Number of Golfers for Week 1 with number line labeled Age of Golfer, 1 dot at 62, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, and 2 dots at 89
dot plot titled Number of Golfers for Week 2 with number line labeled Age of Golfer, 2 dots at 62, 3 dots at 64, 3 dots at 68, 1 dot at 69, 2 dots at 70, 3 dots at 72, 2 dots at 75, 1 dot at 76, 2 dots at 78, 3 dots at 80, 2 dots at 85, 3 dots at 86, and 2 dots at 89
The range for Week 1 equals the range for Week 2.
The range for Week 1 is greater than the range for Week 2.
The median for Week 1 is less than the median for Week 2.
The mean for Week 1 is greater than the mean for Week 2.
Answers
Answer:
The median for Week 1 is less than the median for Week 2.
What would happen if you subtracted the equation for z from the equation for 10z?
Answers
Answer:9z
Step-by-step explanation:10z-1z=9z
Answer:
the answer would be 3
Step-by-step explanation:
9z = 3
If b = the number of boys, which algebraic expression represents the phrase
below?
the sum of the number of boys and 15 girls
A.
no
B. b + 15
O Ο Ο Ο
C. b- 15
D. b. 15
Answers
If b = the number of boys, which algebraic expression represents the phrase
below?
the sum of the number of boys and 15 girls
A.
no
What is the first step in solving the quadratic equation -5x2+8=133
Answers
Answer:
subtracting 8 from both sides of the equation
Step-by-step explanation:
You have to get rid of +8 before squaring both sides.
The first and second steps to solve the equation 3x/5+5=20 are shown below
Answers
Answer:
The solution of the equation is:
x = 25.Step-by-step explanation:
To solve the equation:
[tex]\frac{3x}{5}+5=20[/tex]First, you must add the terms 3x/5 and 5:
[tex]\frac{3x+25}{5}=20[/tex]Now, you pass the number that is dividing (5), to multiply to the other side of the equality and operate:
3x + 25 = 20 * 53x + 25 = 100Next, you pass the number that is adding (25), to subtract to the other side of the equality and operate:
3x = 100 - 253x = 75At last, you pass the number that is multiplying the unknown variable, to divide to the other side of the equality and operate:
[tex]x=\frac{75}{3}[/tex]x = 25If we use this value in the original equation, we can prove if it's the correct:
[tex]\frac{3x}{5}+5=20[/tex][tex]\frac{3*25}{5}+5=20[/tex][tex]\frac{75}{5}+5=20[/tex][tex]15+5=20[/tex]20 = 20As you can see, the result x = 25 is the correct.
Please help I’ll give brainliest
Answers
Answer:
$48
Step-by-step explanation:
$160 * 0.05 = $8
$8 * 6 = $48
Hope this helps
Answer:
48
Step-by-step explanation:
Please Mark me brainlist
PLSSS, NEED ANSWER. Find the midpoint of the line segment with end coordinates of (-2,-5 and 3,-2
). Give coordinates as decimals where apropriate
Answers
Answer:
1, -3.5
Step-by-step explanation:
Answer:(0.5,-3.5)
Step-by-step explanation:
(-2+3/2)/2, (-5-2)/2
0.5,-3.5
Which of the following are mathematical sentences? Check all that apply.
O A. 12
B. 2<4
O C. 10g
D. 8- d = 16
E. 6 + 4 = 10
F. 8-V
Answers
Answer:
A,D
Step-by-step explanation:
Answer:
Answers: A and E ✡
- - Why?
Well a mathematical sentence needs to have something to equal to.
In this case for a we have
=10 and for d =16.
Step-by-step explanation:
Please help me ASAP
Answers
Answer:
4. =3 ft
5. 2/1.25 lb
Answer:
4) 3 ft = 36in ⇔ [tex]\frac{36in}{12in}[/tex] = 3 inches
5) 2 lb = 32 oz ⇔ [tex]\frac{32oz}{20oz}[/tex] = 1.6 oz
A cylinder with 1/4 of a section removed has a radius of 4 cm for the base and a height of 10 cm.
Determine the approximate volume of the solid. Use 3.14 for pi. cm3
Answers
Answer:
Volume of the solid is 377 cm³.
Step-by-step explanation:
Volume of the cylinder = [tex]\pi r^{2}h[/tex]
Here, r = radius of the cylinder
h = Height of the cylinder
By substituting the values in the formula, (r = 4 cm and h = 10 cm)
Volume of the cylinder = [tex]\pi (4)^2(10)[/tex]
= 160π
Since one fourth of the cylinder is removed,
Volume of the remaining cylinder = 160π - [tex]\frac{160\pi }{4}[/tex]
= 160π - 40π
= 120π
= 120(3.14)
= 376.8 cm³
≈ 377 cm³
Volume of the solid is 377 cm³.
Use the graph to determine the input value for which f(x) equals G(x) is true x=0.5,x=1, x=1.5,x=2
Answers
Step-by-step explanation:
1.5 is the answer I just tried it and got it correct
Answer:
1.5 I just got the correct answer on edge
F
is directly proportional to
a
.
If
F
=
25
when
a
=
5
find,
F
when
a
=
8
Answers
Answer:
F= 40
Step-by-step explanation:
F=ka
25 = k 5
k = 5
F=5a
F=5*8
F= 40
Someone pls pls pls solve this!!!!!!! And pls explain how u solved it. I need this due rn ASAP!!!
Answers
Answer:
What's the question? Please post the full question
Answer:This angle is a 35 degree angle
Step-by-step explanation:
b) The marked price of a bicycle is Rs. 2000. If the shopkeeper allows some discount and a customer bought it for Rs. 1921 including 13% VAT, how much amount was given as the dis
count?
Answers
Answer:
Rs. 300
Step-by-step explanation:
The bicycle marked price = Rs. 2000
The amount the customer bought the bike given that there was some discount allowed by the shopkeeper including VAT = Rs. 1921
The VAT applied = 13%
The amount given as the discount = Required
The VAT is applied to the selling price
Let d represent the discount amount, we have;
The selling price = 2000 - d
The amount paid as VAT = (2,000 - d) × 13% = (2,000 - d) × 0.13
The amount the customer bought it including VAT = The selling price + The amount paid as VAT
The amount the customer bought it including VAT = Rs. 1921
∴ 1921 = 2000 - d + (2,000 - d) × 0.13 = 2,260 - 1.13·d
1.13·d = 2,260 - 1,921 = 339
d = 339/1.13 = 300
The amount given as discount, d = Rs. 300
What are the domain, range, and asymptote of h(x)=2x+4
Answers
Step-by-step explanation:
Domain = x € the real Numbers
Range = y € the real Numbers
No asymptotes
Put these numbers in order from greatest to least.
0.07,3/5, and 5/8
Answers
Answer:
From greatest to least: 5/8, 3/5, 0.07
Step-by-step explanation:
5/8 = 0.625
3/5 = 0.6
0.07 = 0.07
Hence, determine the length of AB. (Correct to TWO decimal places).
Answers
Answer:
sorry also maybe a diagram would have helped
structions: Drag and drop the correct name for each angle. Each angle has more than one name so be sure to identify all the correct names
Answers
Answer:
1) I, 4, HIJ
2) G, 1, HGF
3) J, 2, IJK
Step-by-step explanation:
The expected (mean) life of a particular type of light bulb is 1000 hours with a standard deviation of 50 hours. The life of this world is normally distributed what is the probability that a randomly selected bulb would last fewer than 940 hours?
Answers
Answer:
11.5%
Step-by-step explanation:
To solve this problem, we can use the knowledge that there are z score tables that calculate probabilities based on z scores. Thus, we must calculate the z score.
The z score formula is [tex]\frac{x- m}{s}[/tex] , where x is the value, m is the mean, and s is the standard deviation. We can then plug our values in to get [tex]\frac{940-1000}{50} = \frac{-60}{50} = -1.2[/tex] as our z score. Plugging this into a table where table values represent the area to the left of the z score (as we want to calculate everything under 940), we get 0.115, or 11.5% as our answer
The formula V=IR shows the relationship between voltage, current, and resistance. Solve this formula for R
Answers
Answer:
The formula is [tex]R =\frac {V}{I}[/tex]
Step-by-step explanation:
The formula V = I R shows the relationship between voltage, current, and resistance.
It is given by the Ohm's law.
According to this law, at constant temperature, the current flows in any conductor is directly proportional to the potential difference applied.
V = I R
where, V is the potential difference, I is the current and R is the resistance.
The resistance is given by
[tex]R = \frac{V}{I}[/tex]
Answer:
R = V over I
Step-by-step explanation:
Evaluate F(x) = x^2 + 1 for f(-1)
Answers
Answer:
2
Step-by-step explanation:
f(x) = x^2 + 1
f(-1) = (-1)^2 + 1
f(-1) = 2
Answer:
f(x)=x^2+1
f(-1)=(-1)^2+1
f(-1)=1+1
f(-1)=2
х
f(x)
18
6
What is the decay factor of the exponential function
represented by the table?
-1
0
1
2.
WINNO
o
O 2
O 2
O 6
Answers
Answer:
winno o 6
Step-by-step explanation:
Find the missing segment
Answers
Answer:
45
Mark me as brainlist
ok
what is the value of J
Answers
Answer:
Step-by-step explanation:
Since all 3 of these angle come off a straight line, they all add up to equal 180. Thus,
2j + 32 + 6j - 2 + 30 = 180 and
8j + 60 = 180 and
8j = 120 so
j = 15
WILL MARK BRAINLIEST!!!
given j(x)= 7x+5 and k(x)=2x+1
What is (j-k)(1)
Answers
Answer:
[tex]7 \times 1 + 5 - 2 \times 1 - 1 = 7 + 5 - 2 - 1 = 12 - 3 = 9[/tex]
Hope this helps