Answer:
(5 - y) ^3 = 125 - 75y + 15y^2 - y^3
Step-by-step explanation:
Binomial expression
1
1. 1
1. 2. 1
1. 3. 3. 1 --------power of 3
( 5 - y) ^3
( 5 - y) (5 - y) (5 - y)
( a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3
a = 5
b = -y
( 5 - y) ^2 = ( 5 - y) (5 - y)
= 5( 5 - y) - y(5 - y)
= 25 - 5y - 5y + y^2
=(25-10y+y^2)
( 25 - 10y + y^2)( 5 - y)
= 5(25 - 10y + y^2) - y( 25 - 10y + y^2)
= 125 - 50y + 5y^2 - 25y + 10y^2 - y^3
Collect the like terms
= 125 - 50y - 25y + 5y^2 + 10y^2 - y^3
= 125 - 75y + 15y^2 - y^3
Answer:
Kate's possible hourly rate of pay: $34.75
Hours of overtime: 100
Step-by-step explanation:
In order to find Kate's hourly wage, we can set up an equation based on the number of hours she works per week and the estimated number of overtime hours to equal her total pay for the year. If Kate works 36 hours/week and there are 52 weeks in a year, her total hours for one year are: 36 x 52 = 1872. Setting up an equation based on her total earnings of $72,000:
1872x + 100(2x) = 72000, where 'x' is the hourly rate and '2x' is her overtime rate which is double time.
Combine like terms: 1872x + 200x = 72000 or 2072x = 72000
Divide both sides by 2072: 2072x/2072 = 72000/2072
Solve for x: x = $34.75
Kate's hourly rate is estimated at $34.75. We can check to see if this is correct by putting this value back into our original equation:
1872(34.75) + 100(2)(34.75) = 65052 + 6950 = 72002
The answer of $72,002 is very close to $72,000 and the best estimate of Kate's hourly wage and overtime hours.
Answer:
13.7142857143
Step-by-step explanation:
If you need to round then do so, or i will comment the rounded version if needed.
So if Ann is a, then Tim has 11a brushes, and together they have a+11a=12a brushes.
if 12a=60, then a=60/12=5
o Ann has 5 brushes!
Whenever a problem says "one number" and "another number" we can substitute x and y. for this we have x=2y+1 and xy=1. since we know the value of x (2y+1) we can substitute it for the other equation to get (2y+1)y=10. simplify to get 2y^2+y=10. from here you can do a few methods to solve this, but the simplest in my opinion is by factoring.
In order to factor it must be equal to 0, so we have 2y^2+y-10=0. We factor this and get y=5 (we also get y=-4 but it is an extraneous root). now we can plug that into either equation and find that x=2.
this means our two numbers are 5 and 2
