by graphing the system of constraints find the values of x and y that maximize the object function.
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Answer with Step-by-step explanation:
The solution of system of equations is all those values of x and y which satisfy both the inequalities or the points which lie in the region common between both the inequalities.
N=100x+40y
The optimal solution will be find from the points which lie on the extreme end of the region common between the inequalities i.e. (2,6), (0,8) or (5,0)
(x,y)=(2,6)
N=100×2+40×6
N= 200+240
N=440
(x,y)=(0,8)
N=100×0+40×8
N= 0+320
N=320
(x,y)=(5,0)
N=100×5+40×0
N= 500+0
N=500
Hence, optimal solution is:
(5,0)
Related Questions
Number 19. Answer to number 19) the figure shows a game...
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Can you show it?
Which of the following represents 6 x to the 3 fourths power in radical form?
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Answer:
[tex]\\ 6x^{\frac{3}{4}} = 6\sqrt[4]{x^{3}}[/tex]
Step-by-step explanation:
When a number is raised to a rational number like [tex]\\ {\frac{3}{4}}[/tex], that is, a fraction, the denominator represents the index of the radical (or commonly known as the root nth of the radical), and the numerator represents the number to which the radicand (the part of the expression inside the radical sign) is about to be raised.
Looking at [tex]\\ 6x^{\frac{3}{4}}[/tex], the index (root) of the radical is 4 and the numerator raises the value of x to the third power, that is, [tex]\\ x^{3}[/tex]. That explains the answer: six (6) times [tex]\\ \sqrt[4]{x^{3}}[/tex]. The six (6) only multiplies the expression.
Likewise, a radical of index 5, with a radicand [tex]\\ (x + 8)[/tex] raised to the ninth power is represented by [tex]\\ \sqrt[5]{(x + 8)^{9}}[/tex], which is equivalent to [tex]\\ (x+8)^{\frac{9}{5}}[/tex].
By the way, a particular case is when the index is 2, that is, [tex]\\ x^{\frac{1}{2}}[/tex]. Here, the number 2 is omitted from the radical symbol and is represented by [tex]\sqrt{x}[/tex].
Whats 0.87 repeating as a fraction?
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then we subtract the to equations
100x-10x=8.7-87.7
90x=79
x=79/90
then 0.87777.....=79/90
Jessica made 2 pounds of fudge. How many 1/6 -pound servings are in the 2 pounds of fudge?
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Using the knowledge of fractions, the number of 1/6-pound servings in 2 pounds of fudge is: 12.
What are Fractions?Fractions are numbers that represent part of a whole number. They have a denominator and a numerator.
The fraction of a pounds servings is given as 1/6.
Therefore, number of 1/6 pound servings in 2 pounds of fudge would be:
2 ÷ 1/6 = 2 × 6/1 = 12.
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What are the coordinates of the vertex of the graph of f(x)=−3|x−1|?
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Paul will pay for his new car in 36 monthly payments.if his car loan is for $19,061,then about how much paul will pat each month? Round your answer to the nearest cent if necessary.
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Paul will pay approximately $529.47 each month for his new car.
Explanation:To calculate how much Paul will pay each month for his new car, we need to divide the total car loan amount by the number of monthly payments. In this case, the car loan is $19,061 and the number of payments is 36. So, the monthly payment can be calculated as:
Monthly payment = Car loan amount / Number of payments
Substituting the given values, we get:
Monthly payment = $19,061 / 36
Running this calculation, we find that Paul will pay approximately $529.47 each month for his new car, rounded to the nearest cent.
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1. If you want to create a cone or cylinder by spinning a 2–dimensional shape about an axis of symmetry, what shapes would you need to use?
2. Describe how the volume formulas for a cone, cylinder and pyramid derived. What are the similarities between the volume of a cone and pyramid?
3. What is the relationship between mass, density and volume? Provide and example that involves calculating population density.
4. Manufacturers often alter different packages to save money and to grab customers attention. Explain using an example, how changes in the dimensions of common geometric shapes (prisms, cylinders, cones and spheres) will affect the volume of these shapes.
5. The concept of volume is something you experience everyday in your life. Provide a specific example in which you could solve a real-world application using volume
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2) The volume of a cone is the area of the base, multiplied by height, divided by 3. This means that the volume of a cone is 1/3 the volume of a cylinder of equal height and base area. The volume of a cylinder is the area of the base times height. The volume of a pyramid, similar to a cone, is the area of the base (length x width) times the height, divided by three.
3) One definition of density is mass/volume, or mass per unit of volume. For example, if a 5 kg object has a volume of 10 cm³, than the density would be 0.5kg/cm³. In population density, relative to our example, area takes the place of volume and population takes the place of mass. This means that population density is population/area. For example, if 10,000 people occupy an area of 5 square miles, then the population density is 2,000 people/ square mile.
4) As you are clearly learning in this class, the volume of an object is not only determined by its dimensions, such as base, width, and height, but its shape. Let's review the cone example. If a cone and a cylinder have the same base area and height, the cone has a volume of 1/3 that of the cylinder.
5) When might you want to use volume in your daily life? Here is a depressing example. Say your corporate job in the Accounting Department has you feeling blue, and your only break is your daily trip to the water cooler. The cups at the cooler are cone-shaped. Not only is this inconvenient because you can't stand them up without getting the rim dirty, but these cups contain 1/3 the water that a perfectly cylindrical cup of the same base/height could provide. You may tell your manager this, and earn yourself some fancy new cylindrical paper cups!
Answer: if a cone and a cylinder have the same base and same height then the volume of the cone is the volume of the cylinder.
Step-by-step explanation: its right edge 2021
fifteen more than half a number is 9
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If I could get Brainliest it would completely make my day cause I have a HUGE test coming up and I need points for answering questions :)
Find the value of the 100th and 1000th term in the sequence { 3,-5,7,-9,...}
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and the value of 1000th is 2001
If y varies inversely as x, and y = 10 as x = 7, find y for the x-value of 10.
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A small school has 55 students. if 10 of the students are boys what is the ratio of girls to boys
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Factor this expression completely and then place the factors in the proper location on the grid.
ab + 2a + 3b + 6
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Factor by Grouping.
[tex]ab+2a+3b+6[/tex]
[tex]a(b+2)+3(b+2)[/tex]
Find the GCF.
[tex](b+2)(a+3)[/tex]
Hope this helps.
-Benjamin
Answer:
This was a little confusing. I had trouble getting the right answer, but it is all there. It was (a+3) *(b+2) for me.
Thanks BenjaminG123
A line passes through (−1, 7) and (2, 10).
Which answer is the equation of the line?
−3x+y=4−3x+y=4
−3x+y=16−3x+y=16
−x+y=8−x+y=8
−x+y=12
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To get the slope or m, use this formula
(the second y minus the first y)/(the second x minus the first x)
Now set it up.
(10-7)/(2--1)
3/3=slope is 1.
y=1x+b
Insert one of the points for x and y.
i will do (-1,7)
7=1(-1)+b
7=-1+b
8=b
Insert this into the final equation:
y=1x+8
Try it out. If you're not sure, try both points. If it works, then you set it up correctly.
the length of a rectangle is 2 cm less than 7 times the width. the perimeter is 62 cm. find the length and width
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I hope this helped!
Inequalities:
The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour plus $55 for an assistant. The committee wants to keep the total cost under $555. What is the maximum amount of hours the DJ will play at the dance?
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Okay, subtract 55 from both sides.
125x < 500
Divide by 125 to isolate the x.
125x < 500
/125 /125
x < 4
The school can have the DJ for less than 4 hours, or for 4 hours. Hope that helps.
The maximum amount of hours the DJ will play at the dance is 4 hours.
Explanation:To find the maximum amount of hours the DJ will play at the dance, we need to set up an inequality. Let x represent the number of hours the DJ will play. The total cost is given by $125 per hour plus $55 for an assistant, so the cost function is C(x) = 125x + 55. We want the total cost to be less than or equal to $555, so the inequality is 125x + 55 ≤ 555.
To solve this inequality, we need to isolate x. First, subtract 55 from both sides to get 125x ≤ 500. Then, divide both sides by 125 to get x ≤ 4. Therefore, the maximum amount of hours the DJ will play at the dance is 4 hours.
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Type the domain and range values for the corresponding variables that make these relations inverses of each other.
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Answer:
The domain and range values are a) -3.8 b) -2.6 C) 1.7 D) 4.4 E) 1.0
Step-by-step explanation:
Consider the provided table:
The domain of the function becomes the range of the inverse function and the range of the function becomes the domain of the inverse function.
Now consider Figure 1:
The x value of table 1 becomes the y value of table 2 and the y value of table 1 becomes the x value of table 2.
Therefore, the domain and range values are a) -3.8 b) -2.6 C) 1.7 D) 4.4 E) 1.0
ramon has a rope that is 25 1/2 feet long. he wants to cut it into 6 pieces that are equal in length. how long will each piece be?
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Write an equation for a line perpendicular to y = 2 x + 5 y=2x+5 and passing through the point (-6,1)
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Which equation shows y = − 12x +4 in standard form?
A. x + 2y = 8
B. 2x + y = 8
C. x + 2y = − 8
D. 2x − y = 8
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Answer: The equation that shows y=-(1/2)x+4 is standard form is x+2y=8
Option A. x+2y=8
Solution:
y=-(1/2)x+4
Standard form of the equation Ax+By=C, with A, B, and C integer numbers
The coefficient of x is a fraction. To simplify the fraction, let's multiply both sides of the equation by 2:
2y=2 [ -(1/2)x+4]
2y=-2(1/2)x+2(4)
2y=-(2/1)(1/2)x+8
2y=-[(2*1)/(1*2)]x+8
2y=-(2/2)x+8
2y=-1x+8
2y=-x+8
The two variables must be on the left of the equation, then adding x both sides of the equation:
2y+x=-x+8+x
x+2y=8
This is you correct answer
If 5 people share 1 2 pound of jelly beans equally, what amount will each person receive?
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1/10.
Hope this helps!
Tati suffered severe stroke damage near the rear of both sides of her brain. She is now unable to perceive
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1) One equation of a system of equations is 5x + 2y = 10. What is the second equation such that the system is independent?
A) x = -2/5y + 2
B) y = -5/2x + 15
C) y = 5/2x + 5
D) y = -5/2x + 5
2) What is the equation of y = |x| translated 1 unit up and 6 units to the left?
A) y = |x + 6| + 1
B) y = |x – 1| + 6
C) y = |x – 6| + 1
D) y = |x + 1| + 6
3) Which statement describes the relationship between the graph of the equation
y=|x/2| and the graph of the equation y=|x/2| +4 ?
A) The graph of y=|x/2| was shifted 4 units to the right.
B) The graph of y=|x/2| was shifted 4 units to the left.
C) The graph of y=|x/2| was shifted 4 units up.
D) The graph of y=|x/2| was shifted 4 units down.
Answer all questions and please show work :)
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5x + 2y = 10
Start by subtracting 5x from both sides....
2y = - 5x + 10
Divide both sides by 2 to get y by its self...
y = - 5/2 + 5 is the answer
2) A) y = |x + 6| + 1
Because the graph moved 6 to the left and 1 up
3) The graph of y=|x/2| was shifted 4 units up
From y=|x/2| to the graph of the equation y=|x/2| +4
The formula is f(x) = a ( x - h ) + k
k represents y value .... In the coordinate plane y values go up and down..
h represents x value .... In the coordinate plane x values go right and left
For example ..... f(x) = a ( x - 5 ) + 4
Means that the graph moved 5 to the right and 4 units up..
GUYS PLEASE HELP QUICK I'M OFFERING 10 PTS AND BRAINLIEST ANSWER
the length of a rectangle is twice its width. The area of the rectangle is 32 square feet. what are the length and width? which equation models this problem?
A) 32w = 2w + w
B) w - 2w = 32
C) 2w x w = 32
D) 2w+w = 32
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area = 32
So, it is C.
The area of the rectangle is its width times length. The width is w and the length is 2w.
A 10 foot ladder reaches a window 8 feet above the ground, how far from the wall is the base of the ladder
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To find the distance from the wall to the base of the ladder, use the Pythagorean theorem. The distance is 6 feet.
Explanation:To find the distance from the wall to the base of the ladder, we can use the Pythagorean theorem. The ladder, the ground, and the wall form a right triangle. Let's call the distance from the wall to the base of the ladder x. According to the Pythagorean theorem, the square of the ladder's length (10 feet) is equal to the sum of the squares of the distances from the base of the ladder to the wall (x) and the height of the window (8 feet).
x^2 + 8^2 = 10^2
Simplifying the equation, we get:
x^2 + 64 = 100
Subtracting 64 from both sides:
x^2 = 36
Taking the square root of both sides:
x = 6
Therefore, the distance from the wall to the base of the ladder is 6 feet.
Write the following in scientific notation:
1) 12 756 =
2) 116 464 =
3) 142 984 =
4) 1 392 000 =
5) 59 770 000 =
6) 903 500 000 =
7) 2 644 800 000 =
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2) 1.16464 x 10^5
3) 1.42984 x 10^5
4) 1.392 x 10^6
5) 5.977 x 10^7
6) 9.035 x 10^8
7) 2.6448 x 10^9
1.16464 x 10⁵
1.42984 x 10⁵
1.392 x 10⁶
5.977 x 10⁷
9.035 x 10⁸
2.6448 x 10⁹
Hope this helpppped!!!! :D
Find the slope of the line.
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What are some prime numbers between 80 and 90?
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How would you solve 5x+3y=12 by graphing it?
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a "solution" or zero or root, is pretty much just an x-intercept, namely, what is the value of "x" when the graph touches the x-axis. Keeping in mind that y = 0 at that moment.
Boat takes 3 hours to go 6 miles upstream. it can go 18 miles downstream in the same time. find the rate of the current and the rate of the boat in still water
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So, 2mph
Speed of the boat - current = 2mph - > x - y = 2
Find the MPH of the boat going downstream... 3h / 18m = 1h / 6m
So, 6mph
x + y = 6
We now have a system of equation, let's solve it!
x - y = 2 -> x = y + 2
x + y = 6 - > (y + 2) + y = 6 -> 2y + 2 = 6 -> 2y = 4 -> y = 2
This is the speed of the current!
Subtitute y = 2 in the first equation:
x - 2 = 2
x = 4
This is the speed of the boat
Rate of the current = 2mph
Rate of the boat in still water = 4mph
How do you write algebraic expressions to model quantities?
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5($2x2)=x
(THIS IS JUST AN EXAMPLE)
Algebraic expressions to model quantities
A businessman produces x Biscuits made up of wheat and rice daily, and another Business person produces y Snacks made up of vegetables daily.There is another person who manufactures z , drinks daily.Find total number of Biscuit,snack and Drink produced after 8 days.
So, Algebraic Expression will be
=8 x+8y+8z
As, there are three terms,so we call it Trinomial Expression.