Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?

A' (-1, 3)

Step-by-step explanation:

A shape has symmetry if we are unable to distinguish it from its transformed image. A shape has rotation symmetry if there exists a rotation less than 360° that carries the shape onto itself. Which means that if you can rotate a shape less than 360° about some point and the shape looks like it never moved, it has rotation symmetry.

A rectangle is an example of rotation symmetry because if we rotate a rectangle at 180° about its center, it looks exactly the same. However, the points diagonal with each other are exchanged.

So, when the given rectangle is rotated 180° , the tranformed rectangle has the point A' at the same location of point C of the orginal shape.

So coordinates of A' are (-1, 3)

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)