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ollegr [7]
3 years ago
15

Can I get help with this please

Mathematics
1 answer:
S_A_V [24]3 years ago
3 0

Answer:

Step-by-step explanation:

you want to multiply y by 2  or divide by 1/2  

? = 1/2  in this problem

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Universal Studios is looking to expand in Ontario. The new theme park will be located equidistant to
sukhopar [10]
<h3>Answer:  (2, 3)</h3>

===============================================

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

\begin{cases}y = x+1\\y = -3x+9\end{cases}

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.

7 0
2 years ago
How many times as great is the diameter of a pinhead as the diameter of a cloud-water droplet
Ulleksa [173]

Given:

The diameter of cloud-water droplet is

10^{-5}

The diameter of pinhead is 0.001.

Explanation:

Divide the dimater of cloud-water droplet by dimater of pinhead to determine the times as great is the diameter of a pinhead as the diameter of a cloud-water droplet .

\begin{gathered} a=\frac{0.001}{10^{-5}} \\ =0.001\cdot10^5 \\ =100 \end{gathered}

So diameter of a pin-head is 100 times the diameter of water-droplet.

5 0
1 year ago
2. Sandy made several investments. She bought 1000 shares of a company’s stock for $8.60/share, she bought a bond with a face va
vampirchik [111]
The stock price per share was $8.60
Number of shares bought 1000
Total price for the shares:
(Cost per share)*(Number of shares)
=8.60*1000
=$8600

The stock price after 1 year $9.15
Total number of shares is 1000
Current price=(current share price)*(number of shares)
9.15*1000
=$9150
current value=(Current price)-(buying price)
=9150-8600
=$550

Net Profit=(Current value)-(Expenses)
=550-14
=$536
6 0
3 years ago
Find slope given the graph of a line on a grid
Alborosie
Slope is rise over run or Y2 - Y1 divided X2 - X1. The X's and Y's are your coordinate points. It doesn't matter which Y you put down first but remember to choose the X in the same place. Your coordinate points are (0, -1) and (-4, 2)

Your equation will be:

-1 - 2 / 0 - (-4)
-3 / 0 + 4
-3 / 4
Your slope is negative 3/4
6 0
3 years ago
Which identity is shown below: 12 • 1/12 = 1? Select one: a. multiplicative identity b. additive inverse c. additive identity d.
lutik1710 [3]
What you're seeing here is 12 being multiplied by its reciprocal. 12 * 1/12 = 1. This is an example of a multiplicative inverse; a multiplicative inverse is when you multiply a number by its reciprocal (1 over the number).
3 0
3 years ago
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