The expression 1/3b-1/3 factored
1 answer:
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Answer:
(a)
(b) 7 hours.
Step-by-step explanation:
(a) Let x be the number of hours and y is the total cost.
We have been given that Beatrice and her friends charge $8 per hour of babysitting, so the charges for x hours of babysitting will be 8x.
As they also charge a mandatory $5 per day fee for each child for snacks, so the total charges for babysit each day will be charges for x hours of babysitting plus mandatory charge.
We can represent this information in an equation as:
Therefore, the equation represents the total cost of using Beatrice’s babysitting service each day.
(b) To find the number of hours Beatrice babysit the daughter, we will substitute y = 61 in our equation and solve for x.
Let us subtract 5 from both sides of our equation.
Let us divide both sides of our equation by 8.
Therefore, Beatrice babysit 7 hours the daughter.
Expression for part c is missing.
So first we solve for y in second equation
3x+y=4
y=4-3x
sub for y in first equiton
2x-(4-3x)^2=1
2x-(16-12x-12x+9x^2)=1
2x-(16-24x+9x^2)=1
2x-16+24x-9x^2=1
-9x^2+26x-16=1
times -1 both sides
9x^2-26x+16=-1
add 1 to both sides
9x^2-26x+17=0
factor
(x-1)(9x-17)=0
set each to zero
x-1=0
x=1
9x-17=0
9x=17
x=17/9
so sub back to find y
y=4-3x
y=4-3(1)
y=4-3
y=1
(1,1)
y=4-3x
y=4-3(17/9)
y=4-17/3
y=12/3-17/3
y=-5/3
(17/9,-5/3)
the 2 intersection points are
(1,1) and
3x+y=4
y=4-3x
sub for y in first equiton
2x-(4-3x)^2=1
2x-(16-12x-12x+9x^2)=1
2x-(16-24x+9x^2)=1
2x-16+24x-9x^2=1
-9x^2+26x-16=1
times -1 both sides
9x^2-26x+16=-1
add 1 to both sides
9x^2-26x+17=0
factor
(x-1)(9x-17)=0
set each to zero
x-1=0
x=1
9x-17=0
9x=17
x=17/9
so sub back to find y
y=4-3x
y=4-3(1)
y=4-3
y=1
(1,1)
y=4-3x
y=4-3(17/9)
y=4-17/3
y=12/3-17/3
y=-5/3
(17/9,-5/3)
the 2 intersection points are
(1,1) and