When packing a sultcase for a trip, the optimal welght of the suttcase Is 40 pounds. You aim for this weight with every trip you take. But your
sultcase's actual welght tends to vary by at most a certain number of pounds.

Part A. Write an absolute value inequality that models this relationship.

Part B. If the suitcase weight can vary by at most 7.5 pounds,what inequality can be used to find the range of acceptable weights for your suitcase?

Part C. Use the inequality from part B to determine the range of acceptable weights for the suitcase.

Part E. How would the inequality in part B change if you wanted to know the rate of weights that are unacceptable for your suitcase? Explain.

Part F. What is the solution for the inequality you created in part E?

Part H. What comparisons can you make between the two inequalities?

Part I. Will there ever be an instance where there is no solution to an absolute inequality? If yes,then what would the inequality look like?

Answers

Answer 1

Answer:

|x − 40| ≤ 7.5.

Step-by-step explanation:

The absolute value inequality |x − 40| ≤ y models the relationship between the acceptable weights of the suitcase and the amount it can vary.

If the suitcase weight can vary up to 7.5 pounds, then 7.5 can be substituted for y in the inequality:

|x − 40| ≤ 7.5.

This inequality can be used to find the range of acceptable weights of the suitcase.


Related Questions

PLEASE HELP ITS DUE TODAY!!

Answers

Answer:

30

Step-by-step explanation:

Using the pythagorean theorem a^2+b^2=c^2

Answer:

30

78^2 = 72^2 + x^2 pythagoras theorem

x^2 = 900

x= 30

The distance a spring will stretch varies directly how much weight is attached to the spring if a spring stretches 6 inches with 80 pounds attached how far will it stretch with 55 pounds attached? Round to the nearest 10th of an inch

Answers

Answer:

The spring will stretch 4.1 inches

Step-by-step explanation:

Direct Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y = kx

Where k is the constant of proportionality.

Let's call:

y = distance a spring stretches

x = weight attached to the spring

We know when x=80 pounds, y=6 inches, thus:

6 = 80k

Solve for k:

[tex]k=\frac{6}{80}=\frac{3}{40}[/tex]

The equation is now:

[tex]\displaystyle y = \frac{3}{40}x[/tex]

When x=55 pounds are attached:

[tex]\displaystyle y = \frac{3}{40}\cdot 55[/tex]

Calculating:

y = 4.1 inches

The spring will stretch 4.1 inches

Best and correct answer gets BRAINLIEST!!!

Answers

Which line has a constant of proportionality between y and x (Slope) of 4/3?

4/3 = slope = rise over run

(Rephrase) Which line has a slope of 4/3? Go up 4 over 3

Answer: B

We could use all the help we can get. I can't find the Khan academy videos associated with my work and I'm struggling. any help is appreciatled

Answers

Answer:

#7.

The domain is {-3,0,4}

the range is {-5,0,1,7}

not a function

#8

D={3,6,12,18}

R={5,7,9,10}

not a function

Step-by-step explanation:

First, 7.

the domain is the all of the x values, in numerical order, listed once, even if it repeats.

D={-3,0,4} (notice how -3 is listed twice; despite that, we only list it once)  

the range is all of the y values, in numerical order, listed once, even if the numbers repeat

R={-5,0,1,7}

A function can have the range (y values) repeat, however, the domain (x values) cannot repeat.

Therefore, this is not a function, since -3 is listed twice.

For 8.

The domain, can be listed as

D={3,6,12,18}

And the range as

R={5,7,9,10}

Notice how it says that if 6 is the input (x), the output (y) can be 5 or 10. Since we said the domain CANNOT repeat, this isn't a function.

Hope this helps!

550 is 5% of what number?

Which statements are correct? Check all that apply.

Answers

Answer:

11000

Step-by-step explanation:

if we substitute the equation with 11000 550 is 5% of 11000

Measurement A equals 6X - 35°

Answers

Answer:

............the answer is 97

There are 60 seats on a train. 6 of the seats are empty. What percentage of the seats on the train are empty?

Answers

Answer:

10%

Step-by-step explanation:

Set up a proportion: [tex]\frac{6}{60} = \frac{x}{100}[/tex]  Cross multiply, then divide: 6 × 100 = 600, 600 ÷ 60 = 1010/100 = 10%

I hope this helps!

PLZ HELP

how long will it take 6 workers to complete a task, given that 4 workers can complete the same task in 12 days?

Answers

Answer:

I think 14 days

Step-by-step explanation:

If 4 workers can do the task in 12 days then I should be able to complete the task in 4 time's 12 days. 6 workers should be able to complete the task in 4 times 12 divided 6.

What is 2 1/2 - 3/8 as a fraction

Answers

Answer:

[tex]\frac{17}{8}[/tex] or [tex]2\frac{1}{8}[/tex]

Step-by-step explanation:

First we will convert the first term into an improper fraction. We multiply the whole number into the denominator and add the product to the numerator.

[tex]2\frac{1}{2}[/tex][tex]-\frac{3}{8}[/tex]

[tex]\frac{5}{2}[/tex][tex]-\frac{3}{8}[/tex]

Then we will multiply the first term by 4/4 to match the denominator of the second term..

[tex]\frac{5}{2}[/tex] * [tex]\frac{4}{4}[/tex] = [tex]\frac{20}{8}[/tex]

Finally we subtract.

[tex]\frac{20}{8}[/tex][tex]-\frac{3}{8}[/tex] = [tex]\frac{17}{8}[/tex]

The solution of the given fractional expression is 17/8.

What is a fraction?

A fraction is a numerical quantity that represents a part of a whole or a quotient of two quantities. It consists of a numerator (the top number) and a denominator (the bottom number), separated by a horizontal line.

The numerator represents the number of equal parts being considered, while the denominator represents the total number of parts that make up the whole.

First convert the mixed fraction into the whole fraction and solve further to get the final solution.

The given fractional expression will be solved as,

[tex]E = 2\dfrac{1}{2}-\dfrac{3}{8}\\\\E = \dfrac{5}{2}-\dfrac{3}{8}\\\\E = \dfrac{20-3}{8}\\\\E = \dfrac{17}{8}[/tex]

Hence, the solution will be 17/8.

To know more about fractions follow

https://brainly.com/question/12096281

#SPJ3

negative 4 divided by 3 as a fraction.

Answers

Answer:

-4/3

Step-by-step explanation:

Because 3 is a prime number, the answer can't be reduced furthermore making your answer -4/3.

Answer:

The answer is -1.333

Step-by-step explanation:

As a fraction it is 1 333

-----

1000

211 is 500% of what number

Answers

Answer: 42.2

Step-by-step explanation:

500/100 = 5

211/5 = 42.2

Answer:

It is 42.2!

Step-by-step explanation:

You divide 211 by 5 and get 42.2

So, 211 is 500% of 42.2! :D

Have a great day!

The ratio of Val's savings to Dan is 2:3 at first. After Dan spent P3000.00, Val's saving became 11/3 more of that Dan's remaining savings. What is the total amount of saving the two had at first

Answers

Answer:

P.7500.00

Step-by-step explanation:

We are told that:

The ratio of Val's savings to Dan is 2:3 at first.

Now, Dan spent P3000.00 and Val's saving became 1⅓ more of that Dan's remaining savings.

Let's say the total amount of savings they had at first was x.

Thus;

Val had: 2x/5

Dan had: 3x/5

Now, Dan spent P3000.00.

So amount Dan has left = (3x/5) - 3000

We are told Val's savings is now 1⅓ = 4/3 times that of Dan's remaining savings

Thus; 2x/5 = (4/3)((3x/5) - 3000)

2x/5 = 12x/15 - 4000

Multiply through by 15 to get;

6x = 12x - (3000 × 15)

6x = 12x - 45000

Rearranging, we have;

12x - 6x = 45000

6x = 45000

x = 45000/6

x = P.7500

Carlos completed x3 squats as part of his football workout. if x=5, how many squats did he complete?

Answers

3x

We need to substitute x with 5 because the question is asking how many squats Carlos has completed if he completed 5.

3 x 5 = 15

Therefore, Carlos completed 15 squats as part of his football workout.

By the way, this question is very simple and basic. I recommend reviewing Algebra for your benefit/

DOES ANYONE KNOW HOW TO FIND WHAT SLOPE REPRESENTS??? PLEASE HELP ME

Answers

Answer:

slope intercept form.

Step-by-step explanation:

heres the slope intercept form: y=mx+b.

this equation is what you will use to plot lines on graphs, points etc.

the letter b represents the y-intercept, where the line crosses a number on the y intercept on the graph. for example, an initial payment of 30 dollars.

the mx represents slope, or rate of change. for example, paying 5 dollars an hour.

you wouldn't plug a number to the x, but instead the m, because you'd multiply the m with the x.

Based on your question, I think you are asking what slope is. Slope is the rate of change.

Hope this helps!

Drag and drop the answers into the boxes to correctly convert between decimals, fractions, and percents.

Answers

Answer:

?

Step-by-step explanation:

There is no photo...

Ms. MacDonald raises rabbits. she starts with five rabbits after a few months she counts five times as many rabbits

Answers

Answer:

25 rabbits because 5 x 5 is 25

Answer: 25

Step-by-step explanation:

Given a Segment AB find the distance; B = 30 and A = 10

Answers

Answer:

use formula of distance ;

Step-by-step explanation:

d = distance

(x_1, y_1) = coordinates of the first point

(x_2, y_2) = coordinates of the second point

so d is √((x_2-x_1)²+(y_2-y_1)²)

to find the distance between any two points.

taking A as x coordinate and B as y coordinate ie

A= [10,0]; B= [0,30]

[10 is x1 ,0 is y1 ]; [0is x2 and 30 is y2]

putting values in distance formula

√(0-10)²+(30-0)²

= √( -10 )²+(30)²

=[tex]\sqrt[/tex] 100+900

=√1000

= 31.622

the distance between ab is 31.62 or√1000

You leave a pile of sand in your backyard on a windy day. Every minute the wind blows away 10 percent of the remaining sand. You started with five cubic feet of sand. What equation models the amount of sand after minutes?

Answers

Answer:

10% of the remaining sand You had 5 ft of sand So y=5(.10(x))

Answer:

the RIGHT answer is y = 5 x 0.90^x

Step-by-step explanation:

ten percent has already been blown away, so you only include the percentage of what hasn't been blown away in the equation. (also i just did the assignment and got 100% so you can trust this).

On the playground one for him of the students are on the jungle gym and 1/3 of the students are playing kickball what part of all the students on the playground is on the jungle gym or playing kickball use the tiles to complete the fraction strip model to show how you found your answer to fractions may be used more than once or not at all

Answers

1/4 + 1/3 = 7/12 of kids onjungle gym or playing kickball

Answer please! Find the answer to both questions

Answers

Answer:

APtₙ = (n-2)k² + (2n - 3)k + n

Step-by-step explanation:

Given sequence:

-k² - k + 1, k + 2, k² + 3k + 3, 2k² + 5k + 4, ...

We can see apart from the second term all terms are 2nd degree trinomial so it is not a GP.

Let's find the difference: to determine if it is a AP:

k + 2 - (-k² - k + 1) = k + 2 + k² + k -1 = k² + 2k + 1k² + 3k + 3 - (k + 2) =  k² + 3k + 3 - k - 2 = k² + 2k + 12k² + 5k + 4 - (k² + 3k + 3) = 2k² + 5k + 4 - k² - 3k - 3 = k² + 2k + 1

As we see the difference is common and it confirms the sequence is AP.

First term is

a₁= -k² - k + 1

Common difference is

d = k² + 2k + 1

nth term is:

tₙ = a₁ + (n-1)dtₙ = -k² - k + 1 + (n-1)(k² + 2k + 1) =-k² - k + 1 + (n-1)k² + (n-1)*2k + n-1 =(n-2)k² + (2n - 3)k + n

What is the slope of the line?
У
1
X Х

Answers

Answer:151500

Step-by-step explanation:the is the answer

which values of x are solutions to the eqaution below? 4x^2-30=34​

Answers

+4,-4 is your answer I hope :)

Andrew had $120. He gave one-third of that amount to charity. How much money did he give to charity? a. 40 c. 60 b. 90 d. 80 Please select the best answer from the choices provided A B C D

Answers

1/3. 120 x 1/3 = 40. it could also be written as 120/3. the answer is 40$ to charity

YALL I NEED HELP ASAP!!

Answers

Answer:

32

Step-by-step explanation:

You use angle chasing. Since a triangle's angle has to add up to 180, the other angle is 180-79-69. This gives 32. So angle E is 32 degrees. Since they are parallel, that means that E equals to D. That means that D is 32, so 32 is now the answer.

HAPPY NOW BRAINLY? I JUST DIDN'T ADD AN EXPLANATION ON THE OTHER ONE AND YOU DELETED IT! I GOT BRAINLIEST!  HE STILL GOT THE ANSWER ANYWAYS.

Select the expressions that are equivalent to 8(6m).

Answers

[tex]\textsf{Hey there!}[/tex]

[tex]\text{Select the expressions that are equicalent to 8(6m)}\downarrow[/tex]

[tex]\text{We DON'T have any like terms so we CAN'T pair them off!}[/tex]

[tex]\mathsf{8(6m) \rightarrow 8 \times 6 \times \ m}\\\mathsf{8\times 6 = 48}}\\\mathsf{48\times\ m = 48m}\\\\\\\boxed{\boxed{\mathsf{Answer: \bf{48m}}}}\checkmark[/tex]

[tex]\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\dfrac{\frak{LoveYourselfFirst}}{:)}[/tex]

What type of angles are <1 and <2 ?


I’m not sure if linear or complementary are the answer Bc Ik it’s not verticals

Answers

Answer:

it is linear pair

Step-by-step explanation:

it is not complementary because it doesn't add up to a sum of 90°. it is not vertical angles because that would mean they have the same degree. it's linear because they add up to 180°.

In an interval whose length is z seconds, a body moves (32z + 2z^ 2 ) ft. What is the average speed v of the body in this interval?

Answers

This question is incomplete, the complete question is;

In an interval whose length is z seconds, a body moves (32z + 2z²) ft.

What is the average speed v of the body in this interval?

Answer: the average speed v of the body in this interval is 32 + 2z ft/s

Step-by-step explanation:

Given that;

Length of travel = z seconds

also the body moves (32z + 2z²) ft

i.e

distance travelled = (32z + 2z²) ft

average speed v of the body in this interval = ?

Now to get the Average Speed

we simply say;

Average Speed V =  (32z + 2z²) / z

Average Speed V = 32 + 2z ft/s

Therefore the average speed v of the body in this interval is 32 + 2z ft/s

ANSWER THIS CORRECTLT SENDING PAYPAL WHEN YOU ANSWER INCLUDE YOUR PAYPAL IN THE ANSWER

Answers

Answer:

You will need Brainly Plus™ to view this answer!

Step-by-step explanation:

Answer:

I think its D. Not sure though.

Step-by-step explanation:

Sorry but if I get it right its okay. You keep ur money :)

what is 9,344 divided by 29

Answers

Answer:

322.2069

Step-by-step explanation:

s0 pretty much 322

A water tower that is 132 feet tall casts a 48-foot long shadow. If Shannon is 1 point
5'6" inches tall and standing near the tower, find the length of her shadow.

Answers

Answer:

2.03 ft

Step-by-step explanation:

132 divided by 48 is 2.75 and 5.6 divided by 2.75 is 2.03

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