Answer:
7392
Step-by-step explanation:
just divide 5544÷.75 on a calculator however you want to do it than you will get 7392
The sum of the angles of a quadrilateral is 360 degrees. So P+Q+R is 206, 360 - 206 = 154 degrees, the measure of angle S.
The four triangles, AQB, BRC, CSD, and DPA are all isosceles. So angle QBA = angle BAQ, etc. We find QBA = (180-24)/2 or 78 degrees.
RBC = (180-114)/2 = 33 degrees.
180 - (78 + 33) is the measure of angle B: 69 degrees.
The student should be able to see how to calculate the missing information from this.
Answer:
27.2 ft
Step-by-step explanation:
Let's set up a ratio that represents the problem:
Object's Height (ft) : Shadow (ft)
Substitute with the dimensions of the 34 foot pole and its 30 foot shadow.
34 : 30
Find the unit rate:
The unit rate is when one number in a ratio is 1.
Let's make the Shadow equal to one by dividing by 30 on both sides.
Object's Height (ft) : Shadow (ft)
34 : 30
/30 /30
1.13 : 1
Now, let's multiply by 24 on both sides to find the height of the tree.
Multiply:
Object's Height (ft) : Shadow (ft)
1.13 : 1
x24 x24
27.2 : 24
Therefore, the tree is 27.2 feet tall.
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
