Select all of the characteristics that apply to each parallelogram.

a. rhombus
1. all sides are equal
2. diagonals are congruent
3. angles are 90 degrees
4. diagonals are perpendicular
5. diagonals are angle bisectors

b. rectangle
1. all sides are equal
2. diagonals are congruent
3. angles are 90 degrees
4. diagonals are perpendicular
5. diagonals are angle bisectors

c. square
1. all sides are equal
2. diagonals are congruent
3. angles are 90 degrees
4. diagonals are perpendicular
5. diagonals are angle bisectors

  see below

Step-by-step explanation:

A rhombus is a quadrilateral with equal-length sides, so each diagonal divides the figure into two isosceles triangles. The altitude of each triangle is both an angle bisector and part of the other diagonal. Hence the diagonals meet at right angles.

A rectangle is a quadrilateral with all right angles. Each diagonal divides the figure into congruent triangles, which are also congruent with the triangles created by the other diagonal. The diagonals bisect each other, but do not necessarily meet at right angles or bisect any angles.

A square is a rhombus that is a rectangle. So all of the applicable characteristics of each apply to the square.

step-by-step explanation:

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)