Use inductive reasoning to predict the next line in the pattern. 11 x 14 = 154 11 x 15 = 165 11 x 16= 176 the next line is__x__=

11 * 17 = 187.

Step-by-step explanation:

11 * 14 = 154

11 * 15 = 165

11 * 16 =  176

So we have the series 154, 165, 176  which has a common difference of 11.

so the next line is 11*17 = 176 + 11 = 187.

replace   with   27   and simplify.

10 , 27 , 10 , 70 , 10 , 35 , 10 , 48

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)