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Olenka [21]
3 years ago
11

A feasible region is bounded by the constraints:   20 20 4 5 0.25 y x y x y x            The objective function is P

= 3x + 5y.  (a) Graph the feasible region.
(b) Find the value of the objective function at each vertex of the feasible region.

(c) What is the minimum value of the objective function, P?

(d) At which vertex point does the minimum value occur?

Show all work. Answer: Math | Graded Assignment | Semester A Test, Part 2 © 2016 K12 Inc.

All rights reserved. Page 2 of 3 Copying or distributing without K12’s written consent is prohibited.  (Score for Question 3: ___ of 10 points)  2. In 2010, the population of a town was 8500.  The population decreased by 4.5% each year.

(a) Write an equation to find the population of the town t years after 2010.

(b) In what year will the population of the town be 7000?  Show your work. Answer:

Math | Graded Assignment | Semester A Test, Part 2 © 2016 K12 Inc. All rights reserved. Page 3 of 3 Copying or distributing without K12’s written consent is prohibited. (Score for Question 2: ___ of 10 points)

3. Consider the function       3 2 f x x x x 3 10 13 20 .

(a) Determine the x-intercepts of f x  .

(b) Determine the y-intercept of f x  .

(c) Identify a point in between each of the x-intercepts of f x  .

(d) Determine the end behavior of f x  .

(e) Use the points and end behavior from parts (a) – (d) to graph f x  . Label the scale of each axis.  Answer:
Mathematics
1 answer:
aev [14]3 years ago
3 0
I think it is C I am just guessing
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A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find
scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, O(0,0) in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

x^2=4ay\;\cdots(i)

where a is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is A(83, -40) and B(-83, -40).

There is only one constant in the equation of the parabola, so, use either of one point to find the value of a.

Putting A(83,-40) in the equation (i) we have

83^2=4a(-40)

\Rightarrow a=-43.05625

So, on putting the value of a in the equation (i), the equation of bridge is

x^2=-172.225y

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, x=\pm 10 feet, put this value in equation (i) to get the value of y.

(\pm10)^2=-172.225y

\Rightarrow y=-1.72225 feet.

The point P_1(10,-1.72225) and P_2(-10,-1.72225) represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is d=1.72225 feet and the distance of the base of the bridge from the x-axis is h=40 feet.

Hence, height from the base of the bridge at 10 feet from its center

= h-d

=40-1.72225=38.27775 feet.

8 0
2 years ago
2y + 3y -3y -6(y + 2) = -y + 6
irinina [24]
The answer is y= -6
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8 0
2 years ago
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Solve. <br> - 1/3b = 9<br><br> A. -3 <br> B. 3<br> C. - 27<br> D. 27
ruslelena [56]
-\dfrac{1}{3}b=9\ \ \ |multiply\ both\ sides\ by\ (-3)\\\\-3\cdot\left(-\dfrac{1}{3}b\right)=-3\cdot9\\\\\huge\boxed{b=-27}\leftarrow\boxed{C}
3 0
3 years ago
Read 2 more answers
Which point is the image of point R(4, -7) first reflected across the x-axis and then across the y-axis?
nasty-shy [4]

Answer:

(-4, 7)

Step-by-step explanation:

It would be the exact opposite of point R because it was rotated about 180 degrees from it's original location

6 0
2 years ago
1. Determine the following set of adjustments to the equation then draw the graph !!
suter [353]

Answer:

y = -1 and u = 3.333

Step-by-step explanation:

The given equations are :

3u + y = 9 ...(1)

3u-5y = 15 ...(2)

Subtract equation (2) from (1).

3u + y-( 3u-5y)= 9 -15

y+5y = -6

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y = -1

Put the value of y in equation (1).

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3u-1 = 9

3u = 10

u = 10/3

u = 3.333

The attached figure shows the graph for the above equations.

4 0
3 years ago
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