The product of two consecutive positive integers is 342. represent in the above situation in the form of quadratic equation. find the numbet also.

18 and 19

Step-by-step explanation:

Consecutive positive integers have a difference of 1 between them

let n and n + 1 be the 2 integers, then

n(n + 1) = 342, that is

n² + n = 342 ( subtract 342 from both sides )

n² + n - 342 = 0 ← quadratic equation in standard form

(n + 19)(n - 18) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 19 = 0 ⇒ n = - 19

n - 18 = 0 ⇒ n = 18

However, n > 0 ⇒ n = 18 and n + 1 = 18 + 1 = 19

The 2 integers are 18 and 19

150.6

all i did was i multiplied 5.02 by 30

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)