Answer:
(6,2)
Step-by-step explanation:
Variable Definitions:
x= the number of commercials
y= the number of movies
Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:
50x+150y=600
Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.
x=3y
Write System of Equations:
50x+150y=600
x=3y
Solve for y in each equation:
1) 50x+150y=600
150y=−50x+600
y=-1/3x+4
2) x=3y
y=1/3x
The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:
Emily's songs were played on 6 commercials and 2 movies.
Group first 2 and group last 2 and find factors and undistribute
(4x^3+x^2)+(-8x-2)
(x^2)(4x+1)+(-2)(4x+1)
x^2(4x+1)-2(4x+1)
answer is first one
270+26x is less than or equal to 1325
26x is less than or equal to 1055
x is less than or equal to 40
Answer:
14.85 feet & 18.85 feet
Step-by-step explanation:
This is a rectangle with area 10 * 14 = 140 sq. ft.
We want new rectangle to be DOUBLE this area, so that area would be:
140 * 2 = 280 sq. ft.
We will add same amount, x, to both length and width, to get 280. Lets do this and find x. [note: length * width = area]
Area = length * width
280 = (10+x)*(14+x)
280 = 140 + 10x + 14x + x^2
0 = -140 + 24x + x^2
We can solve this by using middle term factorization:
So, we need to add around 4.85 feet to both length and width
New dimensions are 14.85 feet & 18.85 feet
So to put this in terms, we are going to have the cost of the equipment is equal to, a fixed rate + (a daily rate * the amount of days the equipment is rented). Without the fixed rate and daily rate, it is difficult to create an equation, but it will look something like this:
y=w+mx
y=how much it costs to rent the gym equipment
w=the fixed rate
m=the daily rate
x=the amount of days the equipment is rented.
