Answer: 3 hours
Step-by-step explanation:
Here is the correct question:
Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?
Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.
Karen can also paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
x = 9 - 6
x = 3
Karen working alone will paint a house in 3 hours.
Let f(x)= y = x3 - 6x2 + 11x - 6
X intercept means a point on the graph which intercepts the x axis
And Y-intercept mean a point on the graph which intercepts the y axis
Meaning at the x intercept the component of y is zero because there is no y on the x axis
And at the y intercept the x component of the coordinate is zero because on the y axis there is no x value
So in finding the y intercept of the graph wherever u see x place zero there (ie x= 0 on the y axis)
So with x = 0
y = (0)3- 6(0)2 + 11(0) - 6
y = -6
Therefore the y intercept is (0,-6) in coordinate form or -6
X-intercept
y = x3 - 6x2 + 11x - 6
After factorization and simplification
y = (x-1)(x-2)(x-3)
On the x axis y= 0
0= (x-1)(x-2)(x-3)
Either x-1=0
x=1
(1,0)
Or x-2=0
x=2
(2,0)
Or x-3=0
x=3 (3,0)
Therefore the x intercepts are 1,2 and 3
And they are expressed in coordinate form as (1,0) ,(2,0) and
(3,0)
30% of them were sponge cakes ( this is because 50% were party cakes and 20% were fruit cakes = 70% which left the sponge cakes, as they were the remainder, to be 30% of what she baked.)
-18 +(-29) = -47 + (-10) = -57
-24 + (-16) = -40 + (-28) = -68 +(-19) = -87
-151 - 253 = -404 - 34 = -438 - 17 = -455
:)
