Answer:
Malcom's family travel 15 miles per hour faster than Theo's
Step-by-step explanation:
<em>See attachment for complete question</em>
Given
Malcom's Family:

To determine the equation of Theo's family, we refer to the attached graph.
From the graph:


First, we determine the slope, m:




Next, we determine equation for Theo's family using:



Add 50 to both sides


So, we have the following:
--- For Malcom's family
This implies that Malcom's family travel at 65 miles per hour
--- For Theo's family
This implies that Theo's family travel at 50 miles per hour
The difference between this rates is:


<em>Which implies that Malcom's family travel 15 miles per hour faster than Theo's</em>
You should know that you can predict changes in coordinates after translations without a graph or anything like that.
(x, y) reflected over the x axis = (x, -y)
(x, y) reflected over the y axis = (-x, y)
(x, y) rotated 90 degrees around the origin = (y, -x)
(x, y) rotated 180 degrees around the origin = (-x, -y)
(x, y) rotated 270 degrees around the origin - (-x, y)
So here's our set of points.
A(1, 2), B(4, 6), C(4, 6)
Here's those points reflected over the x axis.
A'(1, -2), B'(4, -6), C'(4, -6)
And here's <em>those</em> points rotated 180° around the origin.
A''(2, -1), B''(6, -4), C''(6, -4)
I think you made a mistake writing down the question, though, because B and C are the same yet you say ABC forms a triangle. You should be able to go through this process with whatever the coordinate was supposed to be.
Answe and Step-by-step explanation:
Looking at the question the way it was asked, it is easy because it said they have been labelled, so you don't have to stress yourself. Although, if what is intended is, the labelling got wrong along the way and how do you identify the correct one? Then this is what to do:
Go to the one labelled RB. Since I'm assuming that the labelling got wrong, if you pick a red, it means what we have should be a RR and if we picked a black, it means what we have is a BB and we can't have a RB because it was labelled wrongly.
Let's assume he saw a red,
We know that the BB box was labelled wrongly, and we already determined that the box with RB is a RR. Therefore, the box BB can never be RR(because we've seen it already) and it's certainly not BB (due to the fact that they were labelled wrongly). So we have only one option left which is it being RB and whatever we have left will be BB.
If we assume what was picked from the wrongly labelled RB is black.
We know that the RR box was labelled wrongly, and we already determined that the box with RB is a BB. Therefore, the box RR can never be BB and it's certainly not RR (due to the fact that they were labelled wrongly). So we have only one option left which is it being RB and whatever we have left will be RR.
I think it’s B. But if it’s not chose D