Have at a party. they decided to start a ranking system where first place votes get 3 points, second place votes get 2 points and third place votes get 1 point. all other places receive no points. the winning food was chips and dip with 23 points. if it received 5 first place votes and 4 third place votes, how many second place votes did it receive?

The chips and dip got two second place votes

Step-by-step explanation:

First step you would do is figure out the amount of first place votes the chips and dip received

Since we know each first place vote is worth 3 points and we know there is 5 first place votes you multiply 5 x 3

5 x 3 = 15

So we now have 15 votes

Next we figure out the amount of third place votes

We use the same concept but different numbers to figure this one out

We know that each third place vote is worth 1 point and we also know that 4 people voted third place. Since we are using the same concept we multiply 4 x 1

4 x 1 = 4

Now we have to ad 15 + 4 to figure out how many votes there is so far

15 + 4 = 19

So as of right now the chips and dip has 19 votes

In order to get 23 it needs 4 more votes

19 + 4 = 23

We know each second place vote is worth 2 points. So now we have to figure out what to multiply by 2 to make 4.

2 x 1 = 2

Therefore we know it isn't 1

2 x 2 = 4

The chips and dip needed 4 more points to equal 23

So, your answer is that the chips and dip received 2 second place votes

Hope this helps!

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.