<span>Constraints (in slope-intercept form)
x≥0,
y≥0,
y≤1/3x+3,
y</span>≤ 5 - x
The vertices are the points of intersection between the constraints, or the outer bounds of the area that agrees with the constraints.
We know that x≥0 and y≥0, so there is one vertex at (0,0)
We find the other vertex on the y-axis, plug in 0 for x in the function:
y <span>≤ 1/3x+3
y </span><span>≤1/3(0)+3
y = 3.
There is another vertex at (0,3)
Find where the 2 inequalities intersect by setting them equal to each other
(1/3x+3) = 5-x Simplify Simplify Simplify
x = 3/2
Plugging in 3/2 into y = 5-x: 10/2 - 3/2 = 7/2
y=7/2
There is another vertex at (3/2, 7/2)
There is a final vertex where the line y=5-x crosses the x axis:
0 = 5 -x , x = 5
The final vertex is at point (5, 0)
Therefore, the vertices are:
(0,0), (0,3), (3/2, 7/2), (5, 0)
We want to maximize C = 6x - 4y.
Of all the vertices, we want the one with the largest x and smallest y. We might have to plug in a few to see which gives the greatest C value, but in this case, it's not necessary.
The point (5,0) has the largest x value of all vertices and lowest y value.
Maximum of the function:
C = 6(5) - 4(0)
C = 30</span>
Answer:
Dominic can ride a mile every 4 minutes so if total miles is represented by m, then the solution for how many minutes he's riding for a specific amount of time would be 4m (4 x m). For example, if you want to find out how many minutes it would take to ride 1 mile, substitute m for 1. It would be 4 x 1 = 4 so it takes a total of 4 minutes. If you want to find out how many minutes it took to ride 6 miles, substitute m for 6. It would be 4 x 6 = 24 so it would take a total of 24 minutes to ride 6 miles. If you want to find out how many minutes it took to ride 12 miles, substitute m for 12. It would be 4 x 12 = 48 so it would take a total of 48 minutes to ride 12 miles. I think you gave a lack of information so your question is incomplete but I hope this is applicable and helps anyways!
Answer:
2500
Step-by-step explanation:
Let the first square number be 
then the next square number is 
.
The difference between these two consecutive numbers is 99.
This implies that:
We expand to get:
Simplify:
Divide both sides by 2
Therefore the value of the larger perfect number is
.
Answer:
y= 3/2x- 4
Step-by-step explanation:
3/2 = mx
b= -4
y=mx+b
Answer:
x=
Step-by-step explanation:
If you would like an explanation, let me know.
