The length of a postage stamp is 4 1/4 millimeters longer than its width. The perimeter of the stamp is 124 1/2 millimeters. Write the equation that represents the situation. What is the width of the postage stamp? What is the length of the postage stamp?

Answers

Answer 1

Answer:

- The equation is: [tex]\frac{249}{2}=2(x+\frac{17}{4})+2x[/tex]

- The width of the postage stamp is 29 milimeters.

- The length is 33.25 milimeters.

Step-by-step explanation:

1. The length ([tex]y[/tex]) is [tex]4^{\frac{1}{4} }mm=\frac{17}{4}mm[/tex] longer than the width ([tex]x[/tex]):

[tex]y=x+\frac{17}{4}[/tex]

2. The perimeter is [tex]124^{\frac{1}{2}}mm=\frac{249}{2}mm[/tex].

3. The perimeter of a rectangle is:

[tex]Perimeter=2Length+2Width[/tex]

4. Substitute values:

[tex]\frac{249}{2}=2(x+\frac{17}{4})+2x[/tex]

5. Solve for the width [tex]x[/tex]:

[tex]\frac{249}{2}=2x+\frac{34}{4}+2x\\x=\frac{116}{4}\\x=29[/tex]

6. Calculate the length:

[tex]y=x+\frac{17}{4}\\y=29+\frac{17}{4}\\y=33.25[/tex]

Answer 2
Final answer:

The width and length of the postage stamp are calculated by formulating and solving an equation based on the given perimeter and the relationship between the length and width. The width is found to be 29 mm, and the length is 33.25 mm.

Explanation:

The subject of this question is Mathematics and it's related to the concept of the perimeter of a rectangle. If we denote the width of the postage stamp as 'W' (in millimeters), then it's length will be 'W + 4.25' millimeters because it's stated in the problem that the length is 4.25 mm longer than the width.

The perimeter of a rectangle (which is the shape we can assume for a postage stamp) is calculated as follows: Perimeter = 2(Length + Width). Substituting the value for length that we've assigned, we get this equation:

124.5 = 2[(W + 4.25) + W]

Solving this equation step-by-step will lead you to the answer. First, distribute the 2 into the parentheses which gives: 124.5 = 2W + 8.5 + 2W. Combine like terms to simplify: 124.5 = 4W + 8.5. Then, subtract 8.5 from both sides of the equation: 116 = 4W. Lastly, divide by 4 to find 'W': W = 29 mm. Therefore, the width of the postage stamp is 29 mm, and the length is 29 mm + 4.25 mm = 33.25 mm.

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Related Questions

spent 305.43 on groceries she spent 213.20 in the first month how much did she spend in the second month

Answers

Total amount of money spent: 305.42

Money spent the first month: 213.20

Money spent on the second month: ??

Subtract 305.42 - 213.20= Amount of money spent the second month

Answer: 92.23

Final answer:

In Mathematics, the solution to this subtraction problem is to subtract the amount spent in the first month, $213.20, from the total amount spent on groceries, $305.43. The result is $92.23, the amount spent in the second month.

Explanation:

This appears to be a simple subtraction problem within the domain of Mathematics. If the total amount spent on groceries is $305.43 and she spent $213.20 in the first month, then to find out how much she spent in the second month, you need to subtract the amount spent in the first month from the total amount.

To solve this, you do the following calculation: $305.43 - $213.20 = $92.23.

Therefore, she spent $92.23 on groceries in the second month.

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you have 5/8 if a pepproni pizza. you divide the remaining pizza into 3 equal slices. what portion of the original pizza is each slice?

Answers

You have 5/8 remaining of a pizza. You want to divide it into 3 equal slices.

To find the answer, Divide 5/8 with 3, or multiply 5/8 x 1/3

5/8 x 1/3 = 5/24

Each portion is 5/24 of the original slice.

hope this helps

Kai is conducting a study about the percentage of students with jobs. His school has 2500 students. He asks everyone in his drama class to participate in a survey. He bases his findings on these results. Is this a valid study? Why or why not

Answers

No, he is only studying a small percentage out of 2500 kids. His study isn't large enough to count.

Answer:

not a valid study

Step-by-step explanation:

Given that

Kai is conducting a study about the percentage of students with jobs. His school has 2500 students. He asks everyone in his drama class to participate in a survey. He bases his findings on these results.

Just selecting only students in his drama class to form the sample will not give accurate results since samples are not drawn at random.  The sample done is convenient sample saving time, but failing to represent the entire student population with jobs.

THe best sample would be group the students with jobs and select from the group at random a sample size proportional to the population size.

17x-3y=4 2x-4y=1 the solution to the system of equations is

Answers

ANSWER

[tex]x=\frac{13}{62}[/tex]

and


[tex]y= \frac{-9}{62}[/tex]e have



EXPLANATION




[tex]17x-3y=4---(1)[/tex]


[tex]2x-4y=1[/tex]



Let us make y the subject and call it equation (2)


[tex]2x=1+4y[/tex]


[tex]x=\frac{1}{2}+2y--(2)[/tex]



We put equation (2) in to equation (1)




[tex]17(\frac{1}{2}+2y)-3y=4[/tex]


[tex]\frac{17}{2}+34y-3y=4[/tex]



[tex]34y-3y=4- \frac{17}{2} [/tex]


Simplify to get,



[tex]31y= \frac{8-17}{2} [/tex]



[tex]31y= \frac{-9}{2} [/tex]


Divide both sides by 31,



[tex]y= \frac{-9}{2} \div 31[/tex]



[tex]y= \frac{-9}{2} \times \frac{1}{31}[/tex]




[tex]y= \frac{-9}{62}[/tex]


We put this value in to equation (2) to get,



[tex]x=\frac{1}{2}+2\times -\frac{9}{62}[/tex]




[tex]x=\frac{1}{2} -\frac{18}{62}[/tex]


We collect LCM to obtain,



[tex]x=\frac{31-18}{62}[/tex]



[tex]x=\frac{13}{62}[/tex]








In the united states the speed limit signs are in Miles per hour. Unfortunately, your speedometer only reads in km/hour. How many fast are you allowed to go if the speed says 70 mph( round to the nearest hundredth) ?

Answers

Hello,

1mph = 1.60934kph

70 x 1.60934 = 112.6538

Answer:

70mph = 112.6538kph

What is 0.64 divided by 4 in standard algorithm

Answers

The answer to your is 0.16 hope this will help you.

The answer is 0.16 because 0.16 or . 16 times 4 equals 0.64 so that is your answer

i need help with this please??

Answers

*(Wednesday)*

1. Simply. Show your work.

[tex]9[/tex] · [tex]5+4[/tex]            Simplify The Exponents

[tex]45+4[/tex]                            Multiply [tex]9[/tex] to [tex]5[/tex]

[tex]49[/tex]                                Add [tex]45[/tex] to [tex]4[/tex]

*(Answer)*= [tex]49[/tex]

2. Model and Solve.

[tex]4[/tex] ÷ [tex]\frac{2}{3}=?[/tex]            Use the KCF strategy

[tex]4[/tex] ÷ [tex]\frac{2}{3}=?[/tex]            K = Keep the whole number or freaction on the left

[tex]4[/tex] · [tex]\frac{2}{3}=?[/tex]             C = Change the division sign to multiply sign

[tex]4[/tex] · [tex]\frac{3}{2}=?[/tex]            F = Flip the fraction or whole number

[tex]\frac{4}{1}[/tex] · [tex]\frac{3}{2}=?[/tex]        Make [tex]4[/tex] into a fraction

[tex]\frac{12}{2}[/tex]          Multiply the numerator to another and the denominator to another

[tex]6[/tex]                         Divide 12 to 2 to simplify the fraction

*(Answer)*= [tex]6[/tex]

3. Based on the diagram, describe how a parallelogram and rectangle are related.

They are the same is because the rectangle is the same as the parallelogram because it is same shade, however, sightly tilted.

4. Solve.

- [tex]\frac{5}{8}[/tex] · [tex]\frac{1}{2}= \frac{5}{16}[/tex]

- [tex]\frac{1}{4}[/tex] · [tex]\frac{4}{5}=\frac{4}{20}=\frac{1}{5}[/tex]


If you want than I can edit the answer to add Thursdays answer

Hope this helps

Person Who Answer: BangtanBoyScouts


Which choice is the closest estimate for the product? (5.4)⋅(3.8) A:18 B:15 C:24 D:20

Answers

(D:20) 3 times 5 is 15, but when you add the decimals it take the number up a few places

the function is decreasing for -3<x<1

Answers

Look at the picture.

138 in =____yd___ft___in

Answers

138/36 = 3 R 30

30/12 = 2 R 6

3 yds 2 ft 6 in

A recent survey of
300 juniors and seniors in physics in a certain high school had the following results: 160 males, 80 junior females, 130 seniors. Draw a vent diagram and label the data.

Answers

Answer:

The total number of students in a survey is 300.

Let the number of junior male(JM) be x and the number of senior males(SM) be y.

Let the number of junior female(JF) be p and the number of senior males(SF) be q.

It is given that there are 160 males, 80 junior females, 130 seniors.

Since number of males are 160. So the number of females are,

[tex]300-160=140[/tex]

Since number of junior females is 80.

[tex]JF+SF=140\\80+SF=140\\SF=60[/tex]

Since number of seniors are 130.

[tex]SM+SF=130\\SM+60=130\\SM=70[/tex]

Since number of males is 160.

[tex]JM+SM=160\\JM+70=160\\JM=90[/tex]

Therefore, the table and venn diagram is shown below.

Principal is ____.
A- the original amount invested
B- the total amount earned
C- interest plus original amount invested
D- interest on a loan

Answers

I think the answer is a

Help ASAP. Rt answer and explain pls. Thank you
Due 10/9/18

Answers

3-6+5 is equal to 2, as opposed to 3-5+6 which is 4. The commutative property is only applicable to positive numbers, in this case, Jerome could have done 5-6+3, which would still equal to 2.

The sign is part of the number.

The first term is +3, the second term is -6, and the third term is +5

In order to use the commutative property so that the -6 and +5 are switched, it would be rewritten as: 3 + 5 - 6

Answer: Jerome did not include the sign with the number when he used the commutative property.

What is four more than the number of weeks in a group of days

Answers

four more than the number of weeks in a group of days is broken down like this. weeks = (d/7)+4

The sentence 'four more than the number of weeks in a group of days' is converted into the equation is W = D/7 + 4.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Convert the sentence into an equation or expression.

The sentence is four more than the number of weeks in a group of days.

We know that in a week, there are 7 days. Then the equation will be

Week = (Days / 7) + 4

Simplify the equation, then the equation will be

W = D/7 + 4

The sentence 'four more than the number of weeks in a group of days' is converted into the equation is W = D/7 + 4.

More about the Algebra link is given below.

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what is the simplified expression of the following polynomial: xy4 + 5y7 - (6xy + 7y7) - x8y2 + (-3xy4)

Answers

This polynomial would simplified as: -2y^7-2xy^4-x^8y^2-6xy (I'm assuming you meant to square the answers)

If you didn't the answer would be: -30xy-14y

But I'm pretty sure you meant to put the first one!


Answer:

[tex](-2y^{7}-2xy^{4}-x^{8} y^{2}-6xy)[/tex]

Step-by-step explanation:

The given expression is  [tex]xy^{4}+5y^{7}-(6xy-7y^{7})-x^{8}y^{2}(-3xy^{4})[/tex]

We have to simplify the given expression.

[tex]xy^{4}+5y^{7}-6xy-7y^{7}-x^{8}y^{2}-3xy^{4}[/tex]

[tex](xy^{4} -3xy^{4})+(5y^{7}-7y^{7})-6xy-x^{8}y^{2}[/tex]

[tex]-2xy^{4}-2y^{7}-6xy-x^{8} y^{2}[/tex]

[tex]-2xy^{4}-2y^{7}-6xy-x^{8}y^{2}[/tex]

Therefore, simplified form of the expression will be

[tex](-2y^{7}-2xy^{4}-x^{8} y^{2}-6xy)[/tex]

Help please 10 minutes!!!!!!!!!

Answers

Substitute y = 2x - 15 to the second equation:

4x + 3(2x - 15) = -5      use distributive property

4x + (3)(2x) + (3)(-15) = -5

4x + 6x - 45 = -5       add 45 to both sides

10x = 40      divide both sides by 10

x = 4

Substitute the value of x to the equation y = 2x - 15:

y = 2(4) - 15 = 8 - 15 = -7

Answer: (4, -7)

Can you find the third angle measure in a triangle, if given the other two angle measures?

Answers

yes. there is an equation.

solve for x
21x+6
help please ?

Answers

subtract 6 from the 21x+6. Then divide by 21. The answer is going to be -6/21

If it equats to 0, then you send the six to where it equats as zro for it to bevome -6. It looks like this.
21x=-6.
Then send the 21 multiplied with the x to the other side. This time, it will act as division. This will look like this.
x=-6/21.
This simply means that x=-6/21.
Hope this helps.

the density of pure gold 1,204 pounds per cubic foot? how many cubic feet is 481.6lbs of pure gold?

Answers

Answer:

Volume of Gold = 0.4 cubic feet.

Step-by-step explanation:

First we have to make sure the units are same as the units the answer is required in.

Answer should be given in cubic feet.

Density is given in pounds per cubic foot. And Mass is given in pounds. So units are in order. Therefore, we can go ahead with the calculation.

The Density of Gold = [Mass of Gold/Volume of Gold]

By substituting values,

[tex]1204[/tex] ponds per cubic foot = [[tex]481.6[/tex] pounds / Volume of gold]

Making Volume of God the subject of the equation,

Volume of Gold = [[tex]481.6[/tex] pounds / tex]1204[/tex] ponds per cubic foot ]

Volume of Gold = 0.4 cubic feet.

please help.......if Frans fudge recipe calls for 2 1/2 cups of sugar and she increases it by 2/5 of a cup, how much sugar does she use?

Answers

For this you are adding two fractions together. You always want to make sure they are both improper or normal fractions and that they have a common denominator. To find a common denominator, you look at the denominators and look for a number (The smaller the better) that both can be multiplied by some number to get to. In this case, the common denominator is 10. To make the denominators the same you multiply by one so the value doesn't change. This is done by multiplying the numerator and denominator by the same number that results in the denominator becoming the common denominator.
2 1/2 = 5/2 × 5/5 = 25/10
2/5 × 2/2 = 4/10

When adding, the denominator remains the same and the numerators are added!
25 + 4 = 29
So the answer is 29/10 or 2 9/10 when converted back into a mixed number.
Hope this helped!

How many miles did I run

Answers

you do 4 3/4 times 5= 95/4-23 3/4

Answer: 23 3/4

One number is 3 1/3 larger than the other. The tripled sum of these numbers is 133.What is the largest number?

Answers

Let denote the two numbers with X and Y. n represent one number

Y=X + 3 1/3

The sum of the two numbers is: X+Y=X + X + 3 1/3

The triple sum is: 3(X + X + 3 1/3)

3(X + X + 3 1/3) = 133

3X + 3X + 10 = 133            

6X + 10 = 133                    

6X = 123                            

X = 12 1/2                  , Y= X+ 3 1/3 =  12 1/2 = 3 1/3 is the largest number

Answer:

[tex]23\frac{5}{6}[/tex]

Step-by-step explanation:

Let x be the smaller number,

Thus, according to the question,

Second number or larger number = [tex]x+ 3\frac{1}{3}[/tex]

Now, sum of these number = [tex]x+x+ 3\frac{1}{3}=2x+\frac{10}{3}[/tex]

Again according to the question,

[tex]3\times ( 2x + \frac{10}{3})= 133[/tex]

[tex]6x + 10 = 133[/tex]

[tex]6x = 123[/tex]

[tex]\implies x = \frac{123}{6}[/tex]

Thus, the larger number = [tex]\frac{123}{6}+3\frac{1}{3}=\frac{123}{6}+\frac{10}{3}=\frac{123+20}{6}=\frac{143}{6}=23\frac{5}{6}[/tex]

what is 990% rounded to ther nearest tenth percent.

Answers

Thats a whole number? It can't be rounded to the tenth percent if it doesn't even have a decimal point

But if you mean as a number and not a percent, it would be 9.9


That’s exactly right

If f(x)=x^2 and g(x)=6x+4, which value of x does (f+g)(x)=0

Answers

The answer is x  = −2

open the attachment to get the show the explaining.

pam has 3 times as many green beads as red beads and twice as many blue beads as green beads. She has 150 beads in total. How many blue beads are there?

Answers

25
[tex]150 \div 3 = [/tex]
answer

Identify the terms coefficients and constants in the expression 20x+13

Answers

Constant: 13

Coefficient: 20

The 20 before the X is the coefficient
and the 13 is a constant

Riding the bus,Jasmine uses 2/3 of her money for bus fare.What is this number as a decimal?


0.3*

0.6*

0.8*

1.5*

Help asap!!!!!

Answers

The answer is 0.666....

4 1/2 divide by 1 5/6

Answers

9/4 x 6/11= 27/22
That’s the answer.

3y squared + y squared +9y+3

Answers

3y² + y² + 9y  + 3

Simplify. Combine like terms.

(3y² + y²) = 4y²

4y² + 9y + 3 is your answer

hope this helps

~Rise Above the Ordinary

Fill in the Blank, 1.) 2t+8>-4(t+1). t>_____

Answers

Hey there!!  

Given equation :

... 2t + 8 > -4 ( t + 1 )

Using the distributive property :

... 2t + 8 > -4t - 4

Adding 4t on both sides :

... 6t + 8 > - 4

Subtracting 8 on both sides :

... 6t > - 12

Dividing by 6 on both sides :

... t > -2

Hence, the number in the blank is -2.

Hope my answer helps!!

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