Shivani is making greeting cards, which she will sell by the box at an arts fair. She paid $20 for a booth at the fair, and the materials for each box of cards cost $5. She will sell the cards for $7 per box of cards. At some point, she will sell enough cards so that her sales cover her expenditures. How many cards will that take?

10 cards

Step-by-step explanation:

So to do this problem, you can make an equation where x is the number of cards sold, which would be:

7x - 20 - 5x = 0

This is because she makes $7 for every card she sells (so 7x), she paid $20 for the booth (so -20), it costs her $5 to make every card (so -5x), and you want to see how many cards it will take for her to cover everything she spent (so it would equal 0).

Then, solving:

combine like terms

add 20 to both sides

divide both sides by 2

This means the answer is 10 cards

f is the midpoint of

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'.