MODELING WITH SYSTEMS OF INEQUALITIES

There are many situations that arise in business and engineering that necessitate systems of linear inequalities. The region in the xy-plane that solves the systems often represents all of the viable solutions to the system, so being able to visualize this region can be extremely helpful. As always, with modeling, it is important to really read the problems and understand the physical quantities involved.


(a) If John works 14 hours mowing and 30 hours at the bakery, does this satisfy all of the problem’s constraints?


(b) If x represents the hours John spends mowing and y represents the hours he spends at the bakery, write a system of inequalities that describes this scenario.

Answers

Answer 1

The question is incomplete. The complete question is :

John mows yards for his father's landscaping business for $ 10 per hour and also at a bakery for $ 15 per hour. He can work at most 52 hours per weak during the summer. He needs to make at least $ 600 per week to cover his living expenses.

a) If John works 14 hours mowing and 30 hours at the bakery, does this satisfy all of the problem’s constraints?

(b) If x represents the hours John spends mowing and y represents the hours he spends at the bakery, write a system of inequalities that describes this scenario.

Answer:

a). No

b). 10x + 15y ≥ 600

Step-by-step explanation:

a). Number of hours John works mowing = 14 hours

    Number of hours John works at bakery = 30 hours

Therefore, according tot he question,

= 14($10) + 30($15)

= 140 + 450

= $ 590

This is not enough money. He needs to earn $ 600 per week.

b). Given :

    x = hours John spends mowing

    y = hours John spends at the bakery

Therefore, the inequalities which describes this situation is:

   x + y ≤ 52

  10x + 15y ≥ 600


Related Questions

The two triangles below are similar.
Also, m Z=20° and m Y= 100° as shown below.
Find m G, m H, and m 1..
Assume the triangles are accurately drawn.

Answers

I have a picture of the work for it but I don’t know how to upload it I can put a file maybe!

What is the value of 95 - 10 + +2(141 - 7)?​

Answers

Answer:

353

Step-by-step explanation:

95 - 10 + 2(141 - 7)

following PEMDAS we will do parenthesis first

95 - 10 + 2(134)

multiplication is next

95 - 10 + 268

addition and subtraction are interchangeable when using PEMDAS but you do whatever comes first. since it's subtraction first in this equation we will do 95 - 10.

85 + 268

now we are left with addition

85 + 268 = 353

Answer:

-3 4/5

Step-by-step explanation:

-9 1/5 - 10 + 2/5 + 2(14 1/2 - 7) =-9 1/5 - 10 + 2/5 + 2(7 1/2) = -9 1/5 - 10 + 2/5 + 15 = (- 9 - 10 + 15) + (- 1/5 + 2/5)- 4 + 1/5 = -3 4/5

Note. Solved as per your comment

Angel has $60 and his sister has $120. Angel saves $7 per week, and his sister saves $5 per week. Which equation and solution represent the number of weeks, w, it will take for the siblings to have the same amount of money?

A. 7w + 60 = 5w + 120; w = 30

B. 60w + 7 = 120w + 5; w = 30

C. Not here

D. 7w - 60 = 5w - 120; w = 30

Answers

Answer:

A. 7w + 60 = 5w + 120; w = 30

Step-by-step explanation:

60 + 7x = 120 + 5x7x - 5x = 120 - 602x = 60x = 30

Evaluate the expression, below, when a = 2 and b = 5.

(3 + a)² • (4 – b) + √36

Answers

Answer:

-19

Step-by-step explanation:

1) substitute a with 2 and b with 5

(3 + 2)^2 * (4-5) + √36

2) solve the brackets and the square root

(5^2) * (-1) + 6

3) solve the power

25 *(-1) + 6

4) solve the multiplication

-25 + 6

5) solve the sum

- 19

Answer:

-19

Step-by-step explanation:

i got the answer right

I need help with these. Click this to see the problems (if u don't know how to)

Answers

The ground is supplementary. That means it equals 180 degrees. (A circle is 360. The ground is half the circle)
So u set up the equation as
180=22x+14x
180=36x
/36 /36
5=x

But you need to find the 14x
14(5)
=70 degrees before the tree hits the ground

Find the total amount given the original price and tip rate. Round to the nearest cent if necessary. Original price: $41.32 Tip: 15%

Answers

Answer:

$6.20

Step-by-step explanation:

We can covert 15% to a decimal by moving the decimal point two places over.

15% = 0.15

41.32 X 0.15 = 6.198

6.198 ≈ $6.20

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Original price: $41.32

Tip: 15% = %6.189

Total amount = = Original price + Tip amount

The total amount is $47.509

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Original price: $41.32

Tip: 15%

Now,

The amount of the tip.

= 15% of 41.32

= 15/100 x 41.32

= $6.189

The total amount.

= Original price + Tip amount

= 41.32 + 6.189

= $47.509

Thus,

Original price: $41.32

Tip: 15% = %6.189

Total amount = = Original price + Tip amount

The total amount is $47.509

Learn more about percentages here:

https://brainly.com/question/11403063

#SPJ5

Please help soon, it's timed!!
What is the domain of the function shown in the graph?

Answers

Don’t believe the link^

what is 5/18 ÷ 2/6 pls answer as soon as possible

Answers

Answer:

Solution :-

[tex] \sf \dfrac{5}{18} \times \dfrac{6}{2} [/tex]

[tex] \sf \: \dfrac{5}{3} \times \dfrac{1}{2} [/tex]

[tex] \sf \: \dfrac{5}{6} [/tex]

Answer:

5/6

Step-by-step explanation:

solve for c
-38+-75c≥37

Answers

c= -1 because when you add 38 to the other side you are left with -75c=75 then divide by -75 and you are left with -1

the original price - $82 discount - 10% sale price - ?

Answers

Answer:

73.8 dollars.

Step-by-step explanation:

Answer:

$73.80

Step-by-step explanation:

$82.00 - 8.2% = $73.8

Move the decimal 2 spaces to the right --->

$73.80!! :D

Hope this helps!! Have a great day!! :DDD

Chris has scored the following points in his last five basketball games: 13,10,14,9,6
How many points must he have score in the next game to average 14 points per game?

PLEASE HELP! NO FILES THO! THEY DON'T WORK!

Answers

Answer:

he must score 32 points in the next game in order to average 14 points per game.

Step-by-step explanation:

14 x 6 = 84

84-(13+10+14+9+6)=32

checking:

32 + 13 + 10 + 14 + 9 + 6 = 84

84 divided by 6 = 14

HELPPP QUICK PLSS NO BOTS EITHER I WILL REPORT BUT PLS DONT IGNORE THIS HELP ME PLSS In the slope-intercept equation for a line the coefficient of the x-term gives the

Answers

Answer:

slope

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Since m is the coefficient of the x- term, then

The coefficient of the x- term gives the slope

A right cylinder has a height of 8 inches and a volume of 100 cubic inches. Which measurement is closest to the radius, in inches, of the cylinder? B. C. 16 D. 50​

Answers

Answer:

A

Step-by-step explanation:

volume of a cylinder:

[tex]V=\pi r^2h[/tex]

where r = radius and h = height

We are given the volume (V) and the height (h) and we need to find the radius (r).

To find the radius we are going to want to plug in the given values into the formula for volume of a cylinder and solve for r

so, * plug in given values *

[tex]400= \pi r^28[/tex]

Now we solve for r

step 1 take the square root of each side

[tex]\sqrt{400} =20\\\sqrt{\pi r^28} =\sqrt{\pi } 4*r\\[/tex]

now we have [tex]20=\sqrt{\pi } 4*r[/tex]

step 2 divide each side by sqrt (π) 4

[tex]\frac{20}{\sqrt{\pi } 4} =3.989 \\\\\frac{\sqrt{\pi } 4*r}{\sqrt{\pi } 4}=r\\[/tex]

we're left with r = 3.989

Finally we round to the nearest whole number and get that the answer is A.4

PLEASE HELP ME!!! ITS DUE TODAY!!!!!!! the file is down below!!!!!

Answers

Answer:

the first phot is correct becuase thh way she sets it up shows the right way to set up a number line.

Step-by-step explanation:

First pictures right the second picture is wrong u could really just look it up

surely help me with this question

Answers

Answer:

The area of the composite shape is:

122.50 [tex]cm^{2}[/tex]

Step-by-step explanation:

To find the area of composite shapes you can pull apart this in known shapes, in this case, a rectangle and a triangle. Taking into account this, we can find the rectangle area firstly:

Rectangle area = base * height

The base of the rectangle is the measure from down (14 cm) and the height is the measure in the left side (7 cm), with these values we can replace the formula:

Rectangle area = base * heightRectangle area = 14 cm * 7 cmRectangle area = 98 [tex]cm^{2}[/tex]

Now, to calculate the area of the remaining triangle, we must use the next formula:

Triangle area = [tex]\frac{base*height}{2}[/tex]

Where the base would be equal to the left side of the shape (7 cm) and the height is the difference between the measurement in the top side and the measurement in the bottom side:

Height of the triangle = top side - bottom sideHeight of the triangle = 21 cm - 14 cmHeight of the triangle = 7 cm

We can replace in the formula:

Triangle area = [tex]\frac{7 cm * 7cm}{2}[/tex]Triangle area =[tex]\frac{49cm^{2} }{2}[/tex]Triangle area = 24.5 [tex]cm^{2}[/tex]

By last, we must add the two values of the areas obtained:

Area of the composite shape = rectangle area + triangle area.Area of the composite shape = 98 [tex]cm^{2}[/tex] + 24.5 [tex]cm^{2}[/tex]Area of the composite shape = 122.5 [tex]cm^{2}[/tex]

What is the average rate of change of h over the interval (2,6) ?
Give an exact number.

Answers

Answer:

3

Step-by-step explanation:

2,6>>>1,3

the answer is

0.5

A line passes through the point (10, -6) and has a slope of -3/2 write an equation in slope-intercept form for this line

Answers

Answer:

y = -3/2x + 9

Step-by-step explanation:

As we already know the slope, we just need to find the y-intercept.

To find the y-intercept, you have to plug the values of x and y into the equation.

y = -3/2x + b

-6 = -3/2(10) +b

-6 = -15 + b

9 = b

The equation is y = -3/2x + 9


What is the base and height of this parallelogram? *
12.2 cm
8 cm
10 cm

Answers

Answer:

b=12.2 h=8

Step-by-step explanation:

dotted line vertical - always height

12 is under the height line vertically

3^4/3^2
8 grade mathematics edulastic

Answers

Answer:

9 or 81/9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

1. Simplify the exponents

3^4 = 3*3*3*3 = 9*9 = 81

3^2 = 3*3 = 9

81/9 = 9

what is the answer to this problem?

Answers

9 because it’s skip counting by 3 and 2
Answer

.

A = 9

B = 19

.

Explain

.

If median are getting from " ( a + b ) ÷ 2 " . So :

.

Find b :

.

(a + b) ÷ 2 = Median

(17 + b) ÷ 2 = 18

17 + b = 18 × 2

17 + b = 36

b = 36 - 17

b = 19

.

In conclusion, the value of b is 19

.

Find a :

[tex] \frac{7 + a + 12 + 15 + 17 + 19 + 20 + 22 + 24 + 25}{10} = 17[/tex]

[tex] \frac{161 + a}{10} = 17 \\ [/tex]

[tex]161 + a = 17 \times 10[/tex]

[tex]161 + a = 170[/tex]

[tex]a = 170 - 161[/tex]

[tex]a = 9[/tex]

.

In conclusion, the value of a is 9

.

.

#LearnWithBrainly

GAK BISA BAHASA INGGRIS :(

Answer the question above?

Answers

Mj is the right answer.
Je is the hypotenuse.
Em is the adjacent.

find y if the line through the points (-4,y) and (8,2) has a slope of -1/3

Answers

Step-by-step explanation:

hope this helps!!!!!!!!!!!

Which expression is equivalent to (a^2b^4c)^2(6a^3b)(2c^5)^3/4a^6b^12c^3

1) 3ac^7/b^5

2) 9ac^14/b^3

3) 12ac^14/b^3

4) 9ac^7/b^5​

Answers

Answer:

its c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

First of all we can simplify the the first therm because a property of power says that we can simplify a power of power by multiply the exponents

a^4b^8c^2

For the same property 2c^5 becomes 8c^15

now we have

(a^4b^8c^2)(6a^3b)(8c^15)/4a^6b^12c^3

if we simplify the numbers we can obtain

(a^4b^8c^2)(6a^3b)(2c^15)/a^6b^12c^3

If we simplify the parameters we can obtain

12ac^14/b^3

adding and subtracting polynomials. help?

Answers

mutiply the + sign to the second parenthesis, then combine the terms with the same variable and exponent. so, your answer would be B

Please, please help!

Answers

Answer:

y=-5x+19 is that what you're looking for bc I don't think you can solve for either variable

Notation and symbols for fractions cannot be introduced too soon .

Answers

Answer:

A fraction is a number consisting of one or more equal parts of a unit. It is denoted by the symbol a/b, where a and b≠0 are integers (cf. Integer). The numerator a of a/b denotes the number of parts taken of the unit; this is divided by the number of parts equal to the number appearing as the denominator b.

Step-by-step explanation:

Whats a equivalent expression to (3x^2+3)+(-2x^2+7)

Answers

Answer:

X^2+10

Step-by-step explanation:

Find the length of the third side. If necessary, round to the nearest
tenth.
20
28

Answers

Answer:

19.6

Step-by-step explanation:

missing side = a

a² + b² = c²

a² + 20² = 28²

a² + 400 = 784

a² = 384

[tex]\sqrt{a^2} =\sqrt{384}[/tex]

a = 19.59

Rounded to nearest tenth: 19.6

Answer:

34.4

Step-by-step explanation:

Here, we need to do 28·28 + 20·20

Then, we get 1,184 when we do that, then we square, which gives us 34.4

6 Kevin runs 2 km of a 20 km Journey, and
Walks the rest. How many km did he
walk? write an expression​

Answers

Answer:

walk for 20-2km

Step-by-step explanation:

18

Step-by-step explanation:

20-2=18 hope it helps

Determine the slope of the line that is perpendicular to the line shown in the picture below.

A. 3
B. 1/3
C. -3
D. 1/3

Answers

Answer:

-1/3 i think i might be wrong

Step-by-step explanation:

Answer:

-1/3 because 3/-1 = -3 and -3/3=-1

Step-by-step explanation:

Other Questions
Help!!!! 10 x 10 x 90 x 300000000000000000 Answer the question with a complete sentence using the cues provided.Qu'est-ce que vous prenez pour aller l'universit? (ma voiture) Manuel borrowed $1,500 from his bank and signed a contractto make monthly payments for two years at 4% interestcompounded annually, How much total interest will Manuelpay on this loan? Which type of energy resource is most dependent on weather conditions?A. Natural gasB. Tidal powerC. Wind energyD. Hydropower Match each verb of the sentence that completes that forms have to agree with that subjects 1) A sum of money is divided in the ratio 4:3.Ifthe larger part is $44 1) What is the small part?2) What is the total amount? * What will happen to Earth in the future if we continue to increase greenhouse gas emissions? Please SHOW YOUR WORK!Thanks In Advance, Will Mark Brainliest! (already asked this question before and wasted 20 points due to spammers. pls actually answer) Compare and Contrast four artist that did the "David" Sculpture who is Bernini, Donatello, Michelangelo, and Verrocchio? Do you think public school education for all would be a good example of equality of opportunity? Why or why not? Write your answer in one paragraph. Good night I will send you a picture who runs jonas's community is 1.41 _ 1.397equal, less than or more than?which one? please answer this right!! What was Adnan's job in Jessup Prison?Serial Podcast Season 1: Episode 9 5. What value of makes a true equivalent fraction statement.336 72 It was time to go home, but the bell refused to ring What kind of figurative language is this?? Investiga y en lista 10 ejemplos de vicios sintacticos del lenguaje is y=x^2-4 linear or non linear A sequence is given by the function an = 4an-1 . If a1= 3, what is the value of a6 ? Sabrina is making snack mix. She uses the items listed in the table below . Peanuts 5/6 chocolate chips 1/3 granola 1/2 raisins 3/4 what is the total weight of all the ingredients sabrina uses?