Wolfrich lived in Portugal and Brazil for a total period of 141414 months in order to learn Portuguese. He learned an average of 130 new words per month when he lived in Portugal and an average of 150 new words per month when he lived in Brazil. In total, he learned 1920 new words. How long did Wolfrich live in Portugal, and how long did he live in Brazil?

The total period should be 14 months and not 141414 months.

Thus answer will be: number of months spent in Brazil is 5 months and he spent 9 months in Portugal.

Step-by-step explanation:

Let the number of months he lived in Portugal be X and the number of months he lived in Brazil be Y: Thus we have:

X  +  Y  = 14 months.

He learned an average of 130 new words per month when he lived in Portugal: 130 x number of months (X) = 130X

and an average of 150 new words per month when he lived in Brazil: 150 x number of months in Brazil (Y) = 150Y.

Thus we have 130X + 150Y  = 1920

Since X  +  Y = 14: make X subject of formula: X = 14 - Y. then substitute this for X in the equation below

130X + 150Y  = 1920

130(14-Y) + 150Y = 1920

1820 - 130Y + 150Y = 1920

150Y - 130Y = 1920 - 1820

 20Y = 100

    Y = 100/ 20 = 5 months

Thus number of months spent in Brazil is 5 months. To find the number of months spent in portugal, use the first equation:

    X  +  Y = 14 where Y is 5

   X = 14 - 5 = 9 months. Thus he spent 9 months in Portugal

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.