{9, 18, 27, 36} ∩ {9, 27} = {9, 18, 27, 36}

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)

the linear relationship that represents a variation in direct proportion is the linear function that varies according to the numbers of its domain, for example the cost of producing x number of items can be represented in direct proportion by f (x) = mx + b, where m is the constant of proportionality, x the number of articles produced and b the fixed cost

(x,y) it'll always be like that.

in this case x is grams and y is ounces.

if there were numbers there, like (5,3)

x would be 5 and y would be 3.

we are given polynomial 2x^2 +4x +7.

we need to determine the number of roots of the given polynomial using the fundamental theorem of algebra.

a) for the given polynomial 2x^2+4x+7, we have degree =2.

b) let us find the roots of the given polynomial.

2x^2+4x+7= 0