The points you found are the vertices of the feasible region. I agree with the first three points you got. However, the last point should be (25/11, 35/11). This point is at the of the intersection of the two lines 8x-y = 15 and 3x+y = 10
So the four vertex points are:
(1,9)
(1,7)
(3,9)
(25/11, 35/11)
Plug each of those points, one at a time, into the objective function z = 7x+2y. The goal is to find the largest value of z
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Plug in (x,y) = (1,9)
z = 7x+2y
z = 7(1)+2(9)
z = 7+18
z = 25
We'll use this value later.
So let's call it A. Let A = 25
Plug in (x,y) = (1,7)
z = 7x+2y
z = 7(1)+2(7)
z = 7+14
z = 21
Call this value B = 21 so we can refer to it later
Plug in (x,y) = (3,9)
z = 7x+2y
z = 7(3)+2(9)
z = 21+18
z = 39
Let C = 39 so we can use it later
Finally, plug in (x,y) = (25/11, 35/11)
z = 7x+2y
z = 7(25/11)+2(35/11)
z = 175/11 + 70/11
z = 245/11
z = 22.2727 which is approximate
Let D = 22.2727
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In summary, we found
A = 25
B = 21
C = 39
D = 22.2727
The value C = 39 is the largest of the four results. This value corresponded to (x,y) = (3,9)
Therefore the max value of z is z = 39 and it happens when (x,y) = (3,9)
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Final Answer: 39
The given graph is a straight line passing through points (-4, -3) and (1, 5)
Equation in point slope form is y + 3 = (5 - (-3))/(1 - (-4)) (x - (-4))
y + 3 = 8/5(x + 4)
y + 3 = 8/5x + 32/5
y = 8/5x + 32/5 - 3
y = 8/5x + 17/5
Multiplying through by 5 gives
5y = 8x + 17
-8x + 5y = 17
Options B and C are the correct answers.
905,154 rounded to the nearest ten thousand is 910,000. This is because the 5 in the thousands place is equal to 5, and when the number is 5 or more, you round up. That’s why when you round that number to the nearest ten thousand, it is 910,000.
Given: 
Find: 
Solution: The first step that we need to take is to plug the given values into the point-slope formula which would help us out since we have both the slope and a point. Using that we would then distribute on the right side of the expression and then subtract 4 from both sides which would isolate y.
<u>Plug in the values</u>
<u>Distribute</u>
<u>Subtract 4 from both sides</u>
Therefore, after plugging in the values and completing the rest of the steps we were able to determine that equation of the data provided would be 
.
The mean age of the frequency distribution for the ages of the residents of a town is 43 years.
Step-by-step explanation:
We are given with the following frequency distribution below;
