*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:
You might be interested in
Refer to the diagram shown below.
When x = 30 ft, the cable is at 15 ft, therefore y(30) = 15.
That is,
a(30 - h)² + k = 15 (1)
Also, because the distance between the supports is 90 ft, therefore
y(0) = 6 ft, and y(90) = 6 ft
That is,
a(-h)² + k = 6 (2)
a(90 - h)² + k = 6 (3)
From (2) and (3), obtain
a(90 - h)² = ah²
90² - 180h + h² = h²
180h = 90²
h = 45 ft.
From (1) and (2), obtain
225a + k = 15
2025a + k = 6
Therefore
1800a = -9
a = - 0.005
k = 15 - 225(-0.005) = 16.125 ft
Answer:
The equation for the cable is
y = - 0.005(x - 45)² + 16.125
A graph of the solution verifies that the solution is correct.
When x = 30 ft, the cable is at 15 ft, therefore y(30) = 15.
That is,
a(30 - h)² + k = 15 (1)
Also, because the distance between the supports is 90 ft, therefore
y(0) = 6 ft, and y(90) = 6 ft
That is,
a(-h)² + k = 6 (2)
a(90 - h)² + k = 6 (3)
From (2) and (3), obtain
a(90 - h)² = ah²
90² - 180h + h² = h²
180h = 90²
h = 45 ft.
From (1) and (2), obtain
225a + k = 15
2025a + k = 6
Therefore
1800a = -9
a = - 0.005
k = 15 - 225(-0.005) = 16.125 ft
Answer:
The equation for the cable is
y = - 0.005(x - 45)² + 16.125
A graph of the solution verifies that the solution is correct.