Write the coordinates of the vertices after a rotation 270° counterclockwise around the origin. U(-7,-4)
V(-7,-1)
W(-10,-2)

How to
U'( , ), V'( , ), W'( , )

The coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

U'(-4, 7), V'(-1, 7), W'(-2, 10)

Step-by-step explanation:

When a point P(x, y) is rotated 270° counterclockwise around the origin, we flip x and y and reverse the sign of x.

Thus,

The rule to rotate a point P(x, y)  after a rotation 270° counterclockwise around the origin is:

P(x, y) → P'(y, -x)

In our case, we have the points

U(-7,-4)

V(-7,-1)

W(-10,-2)

Thus, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

P(x, y)          →        P'(y, -x)

U(-7,-4)        →        U'(-4, 7)

V(-7, -1)        →        V'(-1, 7)

W(-10, -2)    →         W'(-2, 10)

Therefore, the coordinates of the vertices after a rotation 270° counterclockwise around the origin will be:

U'(-4, 7), V'(-1, 7), W'(-2, 10)

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)

49/6 is going to equal 8 1/6