Whitney needs to paint her house so that she can sell it. she can choose between two different painters, george and henry. george will charge $90 for the paint, and then $40 per hour. henry will charge $120 for the paint and then $35 per hour. how long would both painters have to paint in order to charge whitney the same amount? how much would her bill be?

Charges of George and Henry would be same if they paint for 6 hours.

For 6 hours of work both the charges of Painter George and Henry would be same which is $330.

Step-by-step explanation:

Let the 'x' represents number of hours for work.

Also Let the 'y' represent the Total charge.

For Painter George:

Given:

Fixed charge = $90

Charge for each hour = $40

Amount of total charge is the sum of fixed charge and charge for each hour multiplied number of hours for work.

framing in equation form, we get;

For Painter Henry:

Given:

Fixed charge = $120

Charge of labor for each hour = $35

Amount of total charge is the sum of fixed charge and charge for each hour multiplied number of hours of work.

framing in equation form, we get;

Now to find the number of hours painter will work in order that they would charge the same, we will make both the equation equal we get;

Now we solve the equation,

Combining the like terms, we get;

Dividing both side by '5' using division property, we get;

Hence Charges of George and Henry would be same if they paint for 6 hours.

Charges of George after 6 hr =

Charges of Henry after 6 hr =

Hence For 6 hours of work both the charges of Painter George and Henry would be same which is $330.

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.