It's a linear program; the extrema will be at the corners.
Let's enumerate them. 4 choose 2 gives 6 possible meets of 4 lines. One pair are parallel, down to five to try.
4x-y=1 intersects x=0 at y=-1, outside the domain y≥0.
4x-y=1 intersects y=0 at x=1/4, (1/4, 0)
4x-y=1 intersects x=5 at y=19, (5,19)
(0,0) is outside the domain 4(0)-0=0 which isn't ≥1.
(5,0) is a valid corner.
It's a triangular domain. Three points to try,
C(1/4,0) = 6(1/4) + 2(0) = 3/2
C(5,19) = 6(5) + 2(19) = 68
C(5,0) = 6(5) + 2(0) = 30
Answer: Maximum C=68 at (x,y)=(5,19)
In order to solve you must find the value of the blank angle.
Here is your first equation.
126 + x = 180
Subtract 126 from both sides.
x = 54
So now add up all the angles.
x + (2x + 6) + 54 = 180
Combine like terms.
3x + 60 = 180
Subtract 60 from both sides.
3x = 120
Divide.
x = 40
Now check your answer.
40 + 2(40) + 6 + 54 = 180
40 + 80 + 6 + 54 = 180
120 + 60 = 180
180 = 180
There is a solution. The answer is 40.
I hope this helps love! :)
We know that the total number of students is 180, so 180 is the 100 precent of the students, now we can set up a proportion and solve
180/100=135/x
x=135 times 100 over 180
x=75%
x represents the number of lawns weeded by Gwen and y represents the number of dogs walked by Fabio.
Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog.
So, for x number of weeds, Gwen earned 12x and for y number of dogs walked, Fabio earned 9y.
They need at least $510 to purchase the new gaming station.
Therefore,
12x + 9y ≥ 510
Also, the number of dog walks that Fabio has scheduled should not be more than twice the number of yards Gwen has scheduled to weed.
Therefore,
y ≤ 2x
Also, Fabio will walk at least 25 dogs.
Therefore,
y ≥ 25
Hence, the constraints are:
12x + 9y ≥ 510
y ≤ 2x
y ≥ 25
Answer:
half of 2 is 1, half of 3 is 1.5,half of 4 is 2.
Step-by-step explanation:
