1) Let f(x) be x^3+5x^2+2x+1
Since f(x) is divided by x+1,
R= f(-1) = (-1)^3 + 5(-1)^2+2(-1) + 1
= -1+5-2+1
= 3
2) Let f(x) be x^3 - 6x + 5x +2
Since f(x) is divided by x-5,
R= f(5) = x^3 - 6x^2 + 5x +2
= 5^3 - 6(5)^2 + 5(5) +2
= 125 - 150 + 25 + 2
= 2
The slope of the line 
is 
.
The line perpendicular to the above line has slope 
Its equation is 
. Since this line passes through, 
,
Thus the equation of the line in slope intercept form is 
To solve this problem we will start by calculating time needed for each of them to fill the pool.
We have formula:
Volume = rate * time
Or
time = volume / rate
Wilma:
time = 9900 / 900
time = 11h
Betty:
time = 9900 / 500
time = 19.8h
Now we substract these two numbers:
time_difference = 19.8 - 11 = 8.8h
Betty needs 8.8 hours more than Wilma to fill the pool.
Answer and Step-by-step explanation:
7. 70 - 180 = 110
8. 39 - 180 = 141
9. 81 - 180 = 99
10. 81 - 180 = 99
11. 115 - 180 = 65
12. 41+36 = 77 - 180 = 103
x = answer
Answer:5
Step-by-step explanation:5/3 x 3/1= 15/3= 5
