Answer:
x=-5 y=2
Step-by-step explanation:
1) multiplying equation 1 by 4 and multiplying equation 2 by 2 .
2)adding them we get value of y.
3) replacing value of y in either of given equation
Answer:
C) 3x - 6
Step-by-step explanation:
Let the unknown number be represented by placeholder x.
Then the product of 3 and the number is represented by 3*x or 3x.
This value diminished by 6 corresponds to 3x-6.
So the expression representing the required overall construct mathematically is given by 3x-6
Option a, 6x-3 represents the difference of 6 times x and 3.
Option b, 3-6x represents the difference of 3 and (6 times x).
Option d, 6-3x represents the difference of 6 and (3 times x).
The questions for this problem would be:
1. What is the dimensions of the box that has the maximum volume?
2. What is the maximum volume of the box?
Volume of a rectangular box = length x width x height
From the problem statement,
length = 12 - 2x
width = 9 - 2x
height = x
where x is the height of the box or the side of the equal squares from each corner and turning up the sides
V = (12-2x) (9-2x) (x)
V = (12 - 2x) (9x - 2x^2)
V = 108x - 24x^2 -18x^2 + 4x^3
V = 4x^3 - 42x^2 + 108x
To maximize the volume, we differentiate the expression of the volume and equate it to zero.
V = 4x^3 - 42x^2 + 108x
dV/dx = 12x^2 - 84x + 108
12x^2 - 84x + 108 = 0x^2 - 7x + 9 = 0
Solving for x,
x1 = 5.30 ; Volume = -11.872 (cannot be negative)
x2 = 1.70 ; Volume = 81.872
So, the answers are as follows:
1. What is the dimensions of the box that has the maximum volume?
length = 12 - 2x = 8.60
width = 9 - 2x = 5.60
height = x = 1.70
2. What is the maximum volume of the box?
Volume = 81.872
Answer:
Step-by-step explanation:
we know that
substitute
Answer:
Step-by-step explanation:
We need to match the slope of the function with the slope of the lines connecting the two points given. The slope of the lines are as follows:
Now,
the slope of the line BC matches with the slope of y=-3.5x-15.
the slope of the line DE matches with the slope of y=-0.5x-3.
the slope of the line HI matches with the slope of y=1.25x+4.
the slope of the line LM matches with the slope of y=5x+9.
and the slopes of the lines FG and JK do not match with any of the functions given.
Thus,
