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.
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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.
Name five whole numbers that can be expressed as the difference of two perfect squares. Show the math!
Of the marbles in a bag, 4 are yellow , 4 are white , and 5 are green . Sandra will randomly choose one marble from the bag. Fill in the blanks in parts a and b. The probability that Sandra will choose a marble from the bag is
Answer:
Probability[Random choose marble is green] = 5 / 13
Step-by-step explanation:
Given:
Number of yellow marble in bag = 4
Number of white marble in bag = 4
Number of green marble in bag = 5
Find:
Probability[Random choose marble is green]
Computation:
Probability of an event = Number of favourable outcome / Number of total outcome
Probability[Random choose marble is green] = 5 / [4 + 4 + 5]
Probability[Random choose marble is green] = 5 / 13
Pleaseeeeee help meee
Answer:
Surface area of sphere = 1,344.8 m² (Approx)
Step-by-step explanation:
Given:
Volume of sphere = 1,476π m³
Find;
Surface area of sphere
Computation:
Volume of sphere = [4/3]πr³
1,476π = [4/3]πr³
1,476 = [4/3]r³
[1,476][3/4] = r³
1,107 = r³
r = 10.35 m (Approx.)
Surface area of sphere = 4πr²
Surface area of sphere = 4(3.14)(10.35)²
Surface area of sphere = 4(3.14)(107.1225)
Surface area of sphere = 1,345.45
Surface area of sphere = 1,344.8 m² (Approx)
a=v2/rSolve the formula for r.
Answer:
r =v2 /a
Step-by-step explanation:
a=v2/r
ra=v2
r =v2 /a
Answer:
r = [tex]\frac{v^2}{a}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{v^2}{r}[/tex] ( multiply both sides by r to clear the fraction )
ar = v² ( divide both sides by a )
r = [tex]\frac{v^2}{a}[/tex]
Which table of ordered pairs represents a proportional relationship?
х
-2
4
-6
y
4
16
36
х
-4
-6
-8
y
-8
-12
-18
o
х
-3
-5
-7
y
5
3
1
O
х
-3
-6
-9
y
12
24
36
Answer:
x=-3×-5×-7
-3×-5=15
15×-7=-105
=-105
Please answer quickly, simple geometry
OPTION C IS THE CORRECT ANSWER.
What is the range of the function?
O all real numbers
O all real numbers greater than 0
O all real number less than or equal to 0
O all real numbers greater than or equal to 0
Its due in 20 mins
Will mark brainliest
Answer:
a) 20 km away fro the starting point.
b) The bearing from P to R is 80°.
c) Q is 60 km North P.
d) Q is - 60 km west of P
Step-by-step explanation:
Stating Facts in the Question:
P to Q is 80 km and bearing 330°
It turned around, Q to R is 60 km and bearing 250°.
a) Picture a number line (Look at the first image)
You go 80 to the right. You turn around and go 60 to the left.
80 - 60 = 20
20 km away fro the starting point
b) Picture a number line (Look at the second image)
P to Q is bearing 330°
Q to R is 60 km is bearing 250°
P to Q is red
Q to R is blue
330° - 250° = 80°
The bearing from P to R is 80°
c) P to Q is 60 km
The plane went forward or North so the answer is 60 km.
Q is 60 km North P.
d) Q to P is 60 km
Q is not to the west of P
Q is - 60 km west of P
i need help fast in these questions.
Luke's tyre pressure gauge shows a reading which is 8% higher than the actual pressure.
What is the actual pressure when Sue's gauge shows 39.42?
Answer:
so for this we do
39.42*1.08=42.5736
Hope This Helps!!!
pls help will give brainiest !!!! pls hurry pls pls
Answer:
"D" (2,4), (-2,-4)
Step-by-step explanation:
How many solutions does this have?
y=5x+-2
y=5--2x
Answer:
one solution (2.333, 9.6666)
Step-by-step explanation:
The ys have to be equal for there to be 1 solution. Let's see if they are. Equate the ys. - -2x becomes 2x
5x +-2 = 2x + 5 Write the left with 1 sign
5x - 2 = 2x + 5 Subtract 2x from both sides
2x 2x
3x - 2 = 5 Add 2 to both sides
2 2
3x = 7 Divide by 3
x = 7/3
x = 2 1/3
y = 5x - 2
y = 5(2 1/3) - 2
y = 11 2/3 - 2
y = 9 2/3
(5^-4/4^-6) multiplied by 5^3
Step-by-step explanation:
(5^-4/4^-6) multiplied by 5^3
4⁶×5³/5⁴
4⁶/5
819.2
Answer:
[tex]{ \tt{ (\frac{ {5}^{ - 4} }{ {4}^{ - 6} } ) \times {5}^{3} }} \\ \\ = { \tt{ \frac{ {5}^{ - 4} . {5}^{3} }{ {4}^{ - 6} } }} \\ \\ { \tt{ = \frac{ {5}^{ - 1} }{ {4}^{ - 6} } }} \\ { \tt{ = \frac{ {4}^{6} }{ {5}^{1} } }} \\ = { \tt{ \frac{4096}{5} }} \\ \\ = 819.2[/tex]
Please help I’ll give branliest
Answer:
optin d) 8
Step-by-step explanation:
[tex]2 \times 2 \times 2 = 2^3[/tex] [tex]= 8[/tex]
This is for Algebra 2 please someone help T^T
Answer:
-(a)^2 + a - 11
Step-by-step explanation:
N - T = -3(a)^2 + 2a - 5 - (-2(a)^2 + a + 6)
= -3(a)^2 + 2a - 5 +2(a)^2 - a - 6
= -3(a)^2 + 2(a)^2 + 2a - a - 6 -5
= -(a)^2 + a - 11
a. 17.5
b. 20
c. 22.5
d. 25
Answer:
x = 22.5
Step-by-step explanation:
∠2 and ∠7 are known as alternate exterior angles. This makes them equal to each other.
100 = 4x + 10
90 = 4x
22.5 = x
Suppose y varies directly with x, and y = 45 when x = 3. What is the value of y when x = -6?
Answer:
y=-90
Step-by-step explanation:
y = kx
45 = k 3
k = 15
~~~~~~~~~~~~
y = 15*-6
y=-90
Answer:
36
We should write a formula for their relationship:
Y = x+42. <- this is what a direct varieation is I believe.
So, when x is -6, y is +42 aka 36
What percent is represented by the shaded area?
Answer:91%
Step-by-step explanation:
the slope of line (-1,1) (2,-5)?
Answer:
slope = 4/3
Step-by-step explanation:
(-1 , 1) = (x1 , y1)
(2 , 5) = (x2 , y2)
slope (m) = y2 - y1/x2 - x1
=5 - 1/2 - (-1)
=4 /2+1
=4/3
If 1=3
2=3
3=5
4=4
5=4
Then, 6=?
9514 1404 393
Answer:
3
Step-by-step explanation:
For "a = b" it appears that the intention is b = f(a). It appears that f(a) is the number of letters in the spelling of 'a'.
"One" has 3 letters
"Two" has 3 letters
"Three" has 5 letters
"Four" has 4 letters
"Five" has 4 letters
"Six" has 3 letters
so, 6 = 3.
_____
Additional comment
This appears to be a non-standard use of the equal sign, in which it has no relation to the usual meaning of "equals." Using standard symbols with non-standard meanings should generally be avoided, unless the intended meaning is explained.
help help help help help
Step-by-step explanation:
press the picture to see the answer I swear it has a solution too
logo y = x means: log base b of y equals x.
True
False
If you meant to write [tex]\log_{b}(y) = x[/tex] then the statement is true.
As a more concrete example, something like [tex]\log_3(81) = 4[/tex] would be read out as "log base 3 of 81 is equal to 4".
what is the simplist form of 240/1000
Divide by 100 to reduce it to 24/100
Now divide by 4 to get 6/25
The simplest form is 6/25
Mark rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total of 5.
21
1
Simplify:
(Enter answer as a reduced fraction.)
3
12
Submit Question
Step-by-step explanation:
21/1
When a denominator is equal to 1, the fraction might be simplified, using this formula:
a/1=a
21/1=21
3/12
Reduce fraction
3/12=3÷3/12÷3
=1/4 or 0.25
I need help in this (￣▽￣)
Answer:
Step-by-step explanation:
a=-2.9
b=-2 5/8=-21/8=-2.625
c=-7/3=-2.333333
Solve for x.
3x + 10
3x +
x = [?]
Answer: x = 28
Step-by-step explanation:
3x+10+3x+2=180
6x+12=180
6x=168
x = 28
Answer:
x=28
Step-by-step explanation:
Since both lines going up are parallel, we can label the angle to the left of the angle with the measure of 3x+10 3x+2. These angles are supplementary as they are on different sides of the same line. This means that:
(3x+10)+(3x+2)=180
6x+12=180
6x=168
x=28
Simplify -|-7 + 4|. please helppppp
Answer: -3
Step-by-step explanation:
-l-7+4l = -l-3l = - 3
ll means anything inside there is positive, so for example if -3 was in there, l-3l = 3
Answer:
- 3
Step-by-step explanation:
-|-7 + 4|
Simplify inside the absolute values first( like parentheses)
-|-3|
Take the nonnegative value for the absolute value
- 3
Convert the following decimal to fraction 3.04
Answer:
3 1/25
Step-by-step explanation:
3.04
Do the decimal part first
.04 = 4/100
Reduce - cancel out 4
1/25
Put back the whole number
3 1/25
Answer:
3 [tex]\frac{1}{25}[/tex]
Step-by-step explanation:
I agree with the previous answer :
You need to do it part by part.
0.04 is equal to [tex]\frac{4}{100}[/tex]
[tex]\frac{4}{100}[/tex] simplified (we divide by 4 with both the denomantor and the numerator.) =
[tex]\frac{1}{25}[/tex]
And we still have those 3 wholes that we had in the beginning.
Now we add.
3 + [tex]\frac{1}{25}[/tex] = 3 [tex]\frac{1}{25}[/tex]
