Area = Area of rectangle + area of semicircle
Area of rectangle = 5 x 1 = 5 m^2
area of semicircle = πD²/8 = 3.14 x 5² / 8 = 9. 8125
Area = 5 + 9.8125 = 14.8125 m^2
Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
For f(x) to be a function, the value of x should not be repeated. That is no x value can be more then once.
So the required table is
And for g(x) , not to be a function, we have to repeat x value that is
Answer:
The approximate percentage is 25%.
Step-by-step explanation:
The initial population was = 12089 rounded off to 12000.
The final population is = 15025 rounded off to 15000.
Change in population = 
So, the approximate percent increase is =
= 25%.
Answer:
z = 4/5
Step-by-step explanation:
3(5z + 7) = 33
Divide each side by 3
3/3(5z + 7) = 33/3
5z+7 = 11
Subtract 7 from each side
5z+7-7 = 11-7
5z = 4
Divide by 5
5z/5 = 4/5
z = 4/5
