1)A farmer plans to create a rectangular garden that he will enclose with chicken wire. The garden can be no more than 30 ft wide. The farmer would like to use at most 180 ft. of chicken wire. Write a system of linear inequalities that models this situation.
2) Determine the solution of the system.
y = x + 6
y = 2x
3)Write an equation of a line whose graph is parallel to the graph of y = 3x – 10.
thank u!
2. Eq1: Y = x+6.
Eq2: Y = 2x.
In Eq1, replace Y with 2x and solve for X.
2x = x+6.
2x-x = 6
X = 6.
In Eq2, replace X with 6 and solve for Y.
Y = 2*6 = 12.
Solution Set: (x,y) = (6,12).
3. Y = 3x - 6.
23. Tom has a collection of 30 CDs and Nita has a collection of 18 CDs. Tom is adding 1 CD a month to his collection while Nita is adding 5 CDs a month to her collection. Find the number of months after which they will have the same number of CDs.
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1) To create a rectangular garden, we need to come up with a system of inequalities for the width and length of the garden, as well as the perimeter of the garden.
Let's assume the width of the garden is represented by "W" (in feet), and the length of the garden is represented by "L" (in feet).
The first inequality states that the width of the garden can be no more than 30 ft: W ≤ 30.
The second inequality states that the perimeter of the garden should be no more than 180 ft: 2W + 2L ≤ 180.
Therefore, the system of linear inequalities that models this situation is:
W ≤ 30
2W + 2L ≤ 180
2) To find the solution to the system of equations, we need to find the values of x and y that satisfy both equations.
Given the system:
y = x + 6
y = 2x
To find the solution, we can substitute the value of y from the second equation into the first equation:
2x = x + 6
We can solve this equation by subtracting x from both sides:
2x - x = 6
x = 6
Now, substitute the value of x back into either equation to find the value of y:
y = 2(6)
y = 12
Therefore, the solution to the system of equations is x = 6 and y = 12.
3) To find the equation of a line parallel to y = 3x - 10, we need to use the fact that parallel lines have the same slope.
In the given equation, the coefficient of x is 3, which represents the slope of the line. So, any line parallel to this will have the same slope.
Therefore, the equation of the line parallel to y = 3x - 10 is y = 3x + b, where "b" is the y-intercept of the new line. The y-intercept can be any real number.
Hence, the equation of a line parallel to y = 3x - 10 is y = 3x + b.