Answer:
10 and 15
Step-by-step explanation:
Let 'x' and 'y' are the numbers we need to find.
x + y = 25 (two numbers whose sum is 25)
(1/x) + (1/y) = 1/6 (the sum of whose reciprocals is 1/6)
The solutions of the this system of equations are the numbers we need to find.
x = 25 - y
1/(25 - y) + 1/y = 1/6 multiply both sides by 6(25-y)y
6y + 6(25-y) = (25-y)y
6y + 150 - 6y = 25y - (y^2)
y^2 - 25y + 150 = 0 quadratic equation has 2 solutions
y1 = 15
y2 = 10
Thus we have
:
First solution: for y = 15, x = 25 - 15 = 10
Second solution: for y = 10, x = 25 - 10 = 15
The first and the second solution are in fact the same one solution we are looking for: the two numbers are 10 and 15 (since the combination 10 and 15 is the same as 15 and 10).
So it took him 4/5 of an hour to paint 1/3
that means there is still 2/3 to go
so that means that he will have two times that time to paint the rest of the room
<u>4/5</u> = <u> ? </u>
1/3 2/3
using cross multiplication
(4/5)(2/3) = (1/3) (?)
8/15 = 1/3 ?
divide both sides by 1/3
so that will be 8/5
that means it will take 8/5 of an hour to complete the rest
or 12/5 total to do entire room
Hope this helps ;)
Use pythagorean theorem - a^2+ b^2 = c^2
a = 2ft, b = ?, c = 6ft
2 x 2 + b^2 = 6 x 6
4 + b^2 = 36
b^2 = 36 - 4 = 32
b = square root of 32
= 5.66ft
If i'm correct. it should be $10,022.40
