You are buying fabric to make a patio umbrella in the shape of a regular hexagon, as shown. the red fabric costs $3 per square yard and the white fabric costs $1.75 per square yard. you can only order whole numbers of square yards of fabric. what will be the cost of the fabric for this project?

$14.25

Step-by-step explanation:

This is a hexagon. Therefore all the angles are  60º.

4ft = 4/3 yd

Area of one triangle

= √3/4 (4/3)²

= √3/4 (16/9)

= (4√3)/9 yd²

Area of 3 triangles

=  (4√3)/9 x 3

= (4√3)/3 yd²

= 3 yd² (Next whole number)

Cost of red fabric = 3 x 3 = $9

Cost of white fabric = 3 x 1.75 = $5.25

Total cost = 9 + 5.25 = $14.25

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)