*No Links* Anton wants to plant a small orchard of apple trees and cherry trees in his backyard. He has a budget of $1,000, and
his plot has a maximum of 100 square feet. The apple trees he wants cost $40 each and require 5 square feet. The cherry trees he wants cost $50 each and require 4 square feet.
The following first-quadrant graph shows the system of inequalities that represents the situation,
5x+4y≤1005x+4y≤100
40x+50y≤100040x+50y≤1000
with the number of apple trees along the x-axis and the number of cherry trees along the y-axis.
Which combination of trees is a viable solution for this situation?
Group of answer choices There are more than one answer
A) 0 apple trees and 25 cherry trees
B) 24 apple trees and 0 cherry trees
C) 12 apple trees and 6 cherry trees
D) 20 apple trees and 4 cherry trees
E) 14 apple trees and 11 cherry trees
The following first-quadrant graph shows the system of inequalities that represents the situation,
5x+4y≤1005x+4y≤100
40x+50y≤100040x+50y≤1000
with the number of apple trees along the x-axis and the number of cherry trees along the y-axis.
Which combination of trees is a viable solution for this situation?
Group of answer choices There are more than one answer
A) 0 apple trees and 25 cherry trees
B) 24 apple trees and 0 cherry trees
C) 12 apple trees and 6 cherry trees
D) 20 apple trees and 4 cherry trees
E) 14 apple trees and 11 cherry trees
1 answer:
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The point of intersection is the point where lines intersect.
<em>There will be 595 intersections for 35 lines, where no 3 lines are concurrent.</em>
<em />
Given
<em /><em> --- the number of lines</em>
<em /><em> --- no three lines are concurrent</em>
<em />
When no three line are concurrent, it means that no three lines meet at the same point.
<u>So, the sequence of intersection is:</u>
- <em>0 intersection for 1 line</em>
- <em>1 intersection for 2 lines</em>
- <em>3 intersections for 3 lines</em>
- <em>6 intersections for 4 lines</em>
<em />
Following the above sequence, the number of intersections for n lines is:
In this case,
So, we have:
<em>Hence, there will be 595 intersections for 35 lines, where no 3 lines are concurrent.</em>
<em />
Read more about lines of intersections at:
