Ms. albero decided to make juice to serve along with the pizza at the student government party. the directions said to mix 2 scoops of powdered drink mix with a half gallon of water to make each pitcher of juice. one of ms. albero’s students said she will mix 8 scoops with 2 gallons of water to make 4 pitchers. how can you use the concept of proportual relationship to decide whether the student is correct?

The student is correct.

Step-by-step explanation:

Consider the provided information.

The directions said to mix 2 scoops of powdered drink mix with a half gallon of water to make each pitcher of juice.

This can be written as:

2 scoops = 1/2 gallons of water

Multiply both side by 2

2×2 scoops = 2×1/2 gallons of water

4 scoops = 1 gallons of water

That means Ms. Albero wants 4 scoops for each gallons of water.

Albero’s students said she will mix 8 scoops with 2 gallons of water to make 4 pitchers.

This can be written as:

8 scoops = 2 gallons of water

Divide both side by 2.

8/2 scoops = 2/2 gallons of water

4 scoops = 1 gallons of water

That means Albero’s students used 4 scoops for each gallons of water, which is the same quantity of scoops per gallons as suggested by the Ms. Albero.

Hence, the student is correct.

they will manufacture 8496 cars

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'.