Modeling with systems of linear inequalities

Answers

Answer 1

Final answer:

Modeling with systems of linear inequalities involves using multiple linear inequalities to represent constraints and solve problems with multiple variables. We can graph the inequalities on a coordinate plane and find the feasible region, which represents all the solutions that satisfy the constraints.

Explanation:Modeling with systems of linear inequalities

Modeling with systems of linear inequalities is a mathematical concept that involves using multiple linear inequalities to represent constraints in a real-world situation. This allows us to model and solve problems involving multiple variables and constraints, such as optimizing profit or finding feasible solutions.

Here's an example:

Let's say we have two variables, x and y, representing the number of units of two products.We also have two inequalities, 2x + 3y <= 10 and x + y >= 4.These inequalities represent constraints on the production and sales of the products.To model this situation, we graph the two inequalities on a coordinate plane.The feasible region, the area where the shaded regions of both inequalities overlap, represents the set of solutions that satisfy all the constraints.We can then use this model to analyze and solve various problems, such as finding the maximum profit by maximizing a certain objective function within the feasible region.

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Related Questions

Kerry and Luke biked a total of 18 miles in one week. Kerry biked 4 miles more than Luke. Write a system of equations and solve it to find how far each boy biked

Answers

Let x = Kerry's distanceLet y = Luke's distance x + y = 18 eq1 x = y + 4x - y = 4 eq2 Our equations are: x + y = 18x - y = 4

PLEASE HELP! there are multiple answers. Juan has a budge of $20.00 for lunch each week. Choose one of the meals from the part b for juan's lunch on monday ( I chose hamburger which is $2.50). How much does he have left for the rest of the week? How many could he spend each remaining day, if he spends the same amount each day?

Answers

So he spends $12.50 a week since there is 5 days of school a week. He can spend $1.50 a day since there is 7.50 left from the week. So he can get a hamburger and use 1.50 every week and reach his budget of $20

Given the equation f(x) = (x + 3)2 – 8, fill in the blanks:

Answers

Solve for x:2 (x + 3) - 8 = 0
2 (x + 3) = 2 x + 6:
2 x + 6 - 8 = 0
Grouping like terms, 2 x - 8 + 6 = 2 x + (6 - 8):
2 x + (6 - 8) = 0
6 - 8 = -2:
2 x + -2 = 0
Add 2 to both sides:
2 x + (2 - 2) = 2
2 - 2 = 0:
2 x = 2
Divide both sides of 2 x = 2 by 2:
(2 x)/2 = 2/2
2/2 = 1:
x = 2/2
2/2 = 1:
Answer: x = 1

I need help I don't understand how to do this

Answers

What is the problem? Is there isn't a problem, do you just what help for a test?

On this you are really just trying to find the lowest number that both of the numbers go into. For example if you have the numbers 6 and 9, 18 would be the lowest common multiple because it is the smallest number that both the numbers go into. An example with fractions is 3/4 and 5/6, what they are trying to tell you is that you find a common denominator for the two fractions (here it would be 12, making them 9/12 and 10/12) and then you can add them together to get the least common multiple (for this problem it would be 19/12). This is a faster way that works for fractions, but would not work as well in my opinion for whole numbers.

Mr. Lyons is laying tile for the rectangular floor of a hotel lobby. The floor will be 38 tiles wide and 112 tiles long. He has a total of 4,400 tiles. Which explains whether or not he has enough tiles for the entire floor?
A. No, he does not have enough tiles. He needs 4,456 tiles, so he needs 56 more.
B. No, he does not have enough tiles. He needs 4,600 tiles, so he needs 200 more.
C. Yes, he has enough tiles. He needs only 4,146 tiles and will have 254 left over. D. Yes, he has enough tiles. He needs only 4,256 tiles a

Answers

D. Yes, he has enough tiles. He needs only 4,256 tiles and will have 144 left over.

Mr. Lyons has enough tiles he needs only 4,256 tiles A; option (D) Yes, he has enough tiles. He needs only 4,256 tiles and he will have 144 left over is correct.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Mr. Lyons is laying tile for the rectangular floor of a hotel lobby. The floor will be 38 tiles wide and 112 tiles long. He has a total of 4,400 tiles.

= 38x112

= 4256

= 4400 - 4256

= 144

Thus, Mr. Lyons has enough tiles he needs only 4,256 tiles A; option (D) Yes, he has enough tiles. He needs only 4,256 tiles and he will have 144 left over is correct.

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Can someone please solve this:

(a+b)2 - (a-b)2= (they are in square)

note: I know the formula but I don't understand hownu factorize it like why that way, if u want please explain it

Answers

(a+b)^2 – (a-b)^2

Since both are squares you end up with

(a+b +a-b) * (a+b –(a-b))

First set of parenthesis add the 2 a’s together to get 2a and subtract b from b

So you end you with 2a

Now you have

2a(a+b –(a-b))

Second set of parenthesis you subtract a from a and then have b+b left which equals 2b

So now you have 2a times 2b

Which equals 4ab

It takes Francisco 15 minutes to ride his bike 4 km, which is the distance from home to school. What is his average speed?

Answers

It takes francisco 15 minutes to ride his bicycle 4 km, which is the distance from home to school.

Answer:

The average speed is 16 km/hr.

Step-by-step explanation:

Given : It takes Francisco 15 minutes to ride his bike 4 km, which is the distance from home to school.

To find : What is his average speed?

Solution :

Distance covered from home to school is 4 km.

Time taken by bike to cover the distance is 15 minutes.

Converting minutes into hour,

1 hour = 60 minutes

1 minute = [tex]\frac{1}{60}[/tex] hours

15 minute = [tex]\frac{15}{60}[/tex] hours

15 minute = 0.25 hours

The speed formula is given by,

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Speed}=\frac{4}{0.25}[/tex]

[tex]\text{Speed}=16[/tex]

Therefore, The average speed is 16 km/hr.

What is the product in lowest terms?

1/4 x 3/5. ( / means fractions)

1.1/15
2.3/20
3.1/3
4.4/9

Answers

1/4 x 3/5 = 3/20

answer
2. 3/20

Okay, 0.25 x 0.6 is equivilant to 0.15.

3 divided by 20 is equivilant to 0.15 as well.
Your answer is number 2.

Hope this helped you.

math questions down below

Answers

= 5/3 x (-7/2)
= -35/6
= -5 5/6

answer A.
-5 5/6

Convert both mixed numbers to improper fractions:
5/3 and -7/2
Use the formula for multiplying fractions:
5*(-7)/ 3*2
-35/6
Convert to a mixed number.
The answer is (A) -5 5/6

Is 16% of 40 the same as 40% of 60? Explain your reasoning.

Answers

no 16% of 40 is 32/5 where 40%of 60 is 24.
Hope this helps.

16/100 * 40
.16*40=5.4
40/100 * 60 = 24 so no

Your local minor League baseball team has 120 ball caps 180 miniature baseball keychains and 240 glow-in-the-dark bracelets to give away to the children on opening day the items will be split into identical sets with no items left over each child will receive one set of items what is the greatest number of children that will receive a set of items on opening day please show all work due today

Answers

The answer will be 60.

Decompose all numbers into prime factors

Write all numbers as the product of its prime factors

Choose the common prime factors with the lowest exponent

Calculate the Greatest Common Factor or GCF

Final answer:

To find the greatest number of children that will receive a set of items on opening day, we can find the greatest common divisor of the quantities of ball caps, keychains, and bracelets.

Explanation:

To find the greatest number of children that will receive a set of items, we need to determine the number of identical sets that can be made from the available items. We can do this by finding the greatest common divisor (GCD) of the quantities of ball caps, keychains, and bracelets.

The GCD of 120, 180, and 240 is 60. This means that 60 sets of items can be made, with each set consisting of 2 ball caps, 3 miniature baseball keychains, and 4 glow-in-the-dark bracelets.

Therefore, the greatest number of children that will receive a set of items on opening day is 60.

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9d - 5 = 4d + 35
find what d equals.

Answers

9d - 5 = 4d + 35

9d (-4d) - 5 (+5) = 4d (-4d) + 35 (+5)

5d = 40

5d/5 = 40/5

d = 8

hope this helps

The answer is D = 8 . You have to subtract 4d from one side and what you do to one side you must do to the other. Then you end up with 5d-5=35. You would add 5 to both sides and get 5d=40. then you divide 5 into both sides and you would get 8 :D

help on homework due tomorrow

Answers

Solve for x by simplifying both sides of the equation, and then isolating the variable.

10. x = -1

12. x = 23/19

On morgans 3rd birthday, she weighed 45 pounds. On her 12th birthday, she weighed 105 pounds.Find the rate of change in her weight.

Answers

morgan gains 6.66666667 pounds every year

steve is 5 years older than his brother joe. in 4 years steve will be twice as old as joe will be then. how old is steve now?

Answers

Here is the answer with an explanation

Final answer:

The question requires the use of algebraic expressions to determine the ages of Steve and Joe. Solving the appropriate equation yields that Steve is 6 years old.

Explanation:

This problem can be solved using basic algebraic expressions. If we assume the current age of Joe to be 'x' years, then Steve, being 5 years older, is 'x + 5' years old. Now, in 4 years, Joe's age will be 'x + 4' and Steve's age will be '(x + 5) + 4' which equals 'x + 9'. According to the question, Steve will be twice as old as Joe in 4 years, so we can express this relation algebraically as '2(x + 4) = x + 9'. Solving this equation yields 'x = 1', which means that Joe is currently 1 year old, and thus, Steve is currently 1 + 5 = 6 years old.

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Together, two wildlife refuge tour guides lead nine 45-minute tours each day. The wildlife refuge needs to calculate the person-hours for the tours to allocate enough money in their budget to pay the tour guides. What is the number of person-hours per day for the tours? Bubble A. 27 Bubble B. 540 Bubble C. 13.5 Bubble D. 270

Answers

c 13.5 bubble id the best choice

what happens to a rational number in fractional form converts to a decimal

Answers

Suppose you started with the rational number 2/3. To convert this to a decimal fraction, we'd divide 3 into 2, obtaining 0.666666..... (repeating decimal).

The band sold 385 cases of fruit. There are 24 bags of fruit in each case. Which is the best estimate of the number of bags of fruit sold?
A. 900 bags of fruit
B. 1,000 bags of fruit
C. 6,000 bags of fruit
D. 10,000 bags of fruit

Answers

D, 385 times 24 equals 9,240

Answer:

it is 10,000

Step-by-step explanation:

The particle of dust has a mass of 7.53x10 to the-10 kilograms. Find the weight of 5 billion dust particles

Answers

It would be 3.765 pounds. You have to do 7.53 x 10 to the -10= 0.000000000753. Then do 0.000000000753 x 5 billion to get 3.765.

Final answer:

To find the weight of 5 billion dust particles, multiply the weight of one particle (determined by the mass of the particle times gravity) by 5 billion. The resulting weight of these dust particles is approximately 36.9 Newtons.

Explanation:

The weight of a particle can be determined using the formula weight = mass x gravity. Given that the mass of a dust particle is 7.53x10^-10 kilograms and assuming normal earth gravity which is approximately 9.8 meters per second squared, the weight of one dust particle is about 7.38x10^-9 Newtons. If we want to find the weight of 5 billion such particles, we'd multiply this single particle weight by 5 billion (5x10^9), resulting in a total weight of about 36.9 Newtons.

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I really need help on this one

17.) Rachel is planning a wedding for 100 to 250 people, depending on costs. She has hired a caterer that charges $20 per person, plus a flat fee of $200.

a.) Write an inequality in terms of p people that describes how many people Rachel plans to invite.

b.) Adjust that inequality to show how much the caterer will charge in terms of p.

c.) What is the range of catering fees that Rachel is considering?

Answers

Part A:

Given that Rachel is planning a wedding for 100 to 250 people, the inequality in terms of p people that describes how many people Rachel plans to invite is given by:

100 ≤ p ≤ 250

Part B:

Given that the caterer charges $20 per person, plus a flat fee of $200, the inequality that shows how much the caterer will charge in terms of p is given by:

20(100) + 200 ≤ 20p + 200 ≤ 20(250) + 200

Part C:

The range of catering fees (C) that Rachel is considering is given by:

20(100) + 200 ≤ 20p + 200 ≤ 20(250) + 200

2000 + 200 ≤ C ≤ 5000 + 200

2200 ≤ C ≤ 5200

Therefore, the range of catering fees Racheal is considering is from $2,200 to $5,200

Answer:

A ? B ? C ?

Step-by-step explanation:

triangles ABC and DEF are similar. what is the length of side EF

Answers

To find that out, we must find out how much larger <DEF is than <ABC
So we take the sides DE and divide it by AB
4.5/3=1.5
That means <DEF is 1.5 times larger than <ABC
So now, we take BC, and multiply it by 1.5
2 x 1.5 = 3
So EF=3
Hope this helps!

Each pitcher of power of smoothie that Ginger makes has two scoops of pineapple, three scoops of strawberries, one scoop of spinach, and one scoop of kale. If Ginger makes seven pitchers of power smoothies, how many scoops will she use in all? Write and evaluate a numerical expectation containing parentheses

Answers

Pineapple = P Strawberries =St Spinach = Sp Kale = K One Pitcher= (2P+3St+1Sp+1K) or 7 Scoops Seven Pitchers Pineapple = ((2P)x7) = 14 scoops Strawberries = ((3St)x7) = 21 Scoops Spinach = ((1Sp)x7) = 7 Scoops Kale = ((1K)x7) = 7 Scoops (((2P)x7)+((3St)x7)+((1Sp)x7)+((1K)x7))=49 Scoops

if the simple interest on $4,000 for 10 years is $3,200,then what is the interest rate

Answers

The. Interest rate would be 1.25.

Choose all the answers that apply. Todd drops three balls made of different materials to see how high they will bounce. He drops each ball from a height of ten feet. All the balls are the same size. The independent variable is how high the balls bounce. The dependent variable is the height the balls bounce. The independent variable is the type of material the balls are made from. The height the balls are dropped from is a control. The size of the balls is a control.

Answers

The independent variable is the type of material the balls are made from

Francine and Cheryl received equal scores on a test made up of multiple choice questions and an essay Francine got 34 multiple choice questions correct I received 14 points for her essay Cheryl got 30 multiple choice questions correct I received 22 point for her outside how many points with each multiple-choice?

Answers

the answer should be 2

You can solve this problem using this equation: 34x + 14 = 30x + 22. The x stands for how many points each multiple choice question is worth. 34x is the number of multiple choice questions Francine got correct multiplied by the currently unknown number each point is worth, while 14 represents the 14 points that Francine was given for her essay. 30x is the number of multiple choice questions Cheryl got correct multiplied by the currently unknown number each point is worth, while 22 represents the 22 points that Cheryl was given for her essay. To solve, we can subtract 30x from 34x on the left side of the equation, and subtract 14 from 22 on the right side of the equation. That leaves, 4x = 8. Next step would be dividing 4 from each side which gives us x = 2. In order for Francine and Cheryl to receive the same test score, each multiple choice questions would have to be worth 2 points.

Write 17/4 mixed number HELP PLEASE!!!!!

Answers

4 1/4
Hope this helps

The answer is: " 4 ¼ " .
________________________________________________
Note: Using long division:
________________________________________________

   4 R 1 ;
4 | 17
- 16
1

________________________________________________
So; we have: "4 R 1" {" 4 remainder 1"; the "4" is the "whole number" (in the "mixed number", the "1" is the numerator of the fraction in the "mixed number"; and the "divisor", "4", is the denominator of the fraction in the "mixed number.
________________________________________________
The answer is: " 4 ¼ " .
________________________________________________

Which one of the following letters is used as an abbreviation for electric current?

Answers

electric current is measured in Amps, which is abbreviated as the letter A

20-gallon gas tax can go 25 miles on 1 gallon if the tank is full at the beginning of a 725 miles trip how many times does the driver have to refill the gas tank

Answers

725/25 = 29

The driver will have to refill the gas tank 29 times during the 725 miles trip.

I hope this helped you! c:

the sum of two numbers is 15 and their difference is 7, What are the two numbers

Answers

These numbers are 11 and 4

11+4=15
11-4=7

Greetings!

Let x represent the first number
Let y represent the second number

Create a system of equations, representing the problem:
[tex] \left \{ {{x+y=15} \atop {x-y=7}} \right. [/tex]

Use elimination to solve:
[tex]+ \frac{\left \{ {{x+y=15} \atop {x-y=7}} \right. }{2x=22} [/tex]

Divide both sides by 2.
[tex]2x=22[/tex]
[tex] \frac{2x}{2}= \frac{22}{2} [/tex]
[tex]x=11[/tex]

Solve for the other variable:
[tex]x+y=15[/tex]
[tex]11+y=15[/tex]
Add -11 to both sides.
[tex](11+y)+(-11)=(15)+(-11)[/tex]
[tex]y=4[/tex]

The Solution to this Problem is:
[tex] \left[\begin{array}{ccc}x=11,y=4\end{array}\right] [/tex]

The numbers are 11 and 4.

Hope this helps.
-Benjamin

what is the square root of negative 100

Answers

What is the square root of negative 100
√-100 = 10i or -10i

Hello, let's say that a negative square root gives a result that is NOT a real number. A negative number is not a square (a negative number squared gives always a positive number).

Thus, they can be represented with an "i", the immaginary unit.

So, the solution would be -10i (because, as I said, there isn't a real negative number that squared gives -100).

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