Answer:
(3, 1)
Step-by-step explanation:
Given the following constraints:
2x + 4y ≤ 10
x + 9y ≤ 12
x ≥ 0
y ≥ 0
We have to first graph the above constraints and secondly, we find the boundary points for the feasible region. This is done by plotting the graphs of 2x + 4y ≤ 10 and x + 9y ≤ 12.
From the graph, the following points satisfy the constraints:
(0,0)
, (3,1)
, (0,4/3)
, (5,0)
Given that:
P = x + 6y
For (0, 0): P = x + 6y = 0 + 6(0) = 0
For (3, 1): P = x + 6y = 3 + 6(1) = 9
For (0, 4/3) P = x + 6y = 0 + 6(4/3) = 8
For (5, 0) P = x + 6y = 5 + 6(0) = 5
This written out is:
2/5 + 4/3
------------
3/5
Roughly, now first we need to change the denominators to all match up in order to properly solve this problem.
Both 5 and 3 go into 15, 5 goes into 15 3 times and 3 goes into 15 5 times. With that said, multiply the individual numerators by 5 and 3.
2/5 -> 2*3/15 -> 6/15
4/3 -> 4*5/15 -> 20/15
3/5 -> 3*3/15 -> 9/15
With this, we then add the top numerator of the overall problem:
26/15
------- | With this we now cross-multiply.
9/15
26/15 * 15/9 = 390/135 | Now to simplify this.
135 goes into 390 twice, as 270. Subtract 390 by 270, leaving us with 120.
Meaning: 2 120/135 is the answer, but now to simplify. Divide 120 and 135 by 5 to lessen this.
24/27 | Divide this by 3 to get your most simplified answer.
8/9 | Leaving us with the answer of:
2 8/9
I hope this helps, have a great rest of your day! ^ ^
| | Ghostgate | |
Answer:
option-A
Step-by-step explanation:
we are given
divisor is
Dividend is
=x-2
so, we can use synthetic division
so, we can write our expression as
so,
option-A
Inequalities help us to compare two unequal expressions. The correct option is B.
<h3>What are inequalities?</h3>
Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality -6 ≤y + 2x < 15 can be broken into two small inequality, as shown below.
Now, if we plot the inequality as shown below, then the area in which both the shaded region overlap is the area of the this inequality.
Hence, the correct option is B.
Learn more about Inequality:
brainly.com/question/19491153
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