Mathematics Middle School

A rectangle has a perimeter of 34 cm in an area of 52 cm squared it's length is 5 more than twice its width write and solve the system of equations to find the dimensions of the rectangle

Answers

Answer 1
L+W=17 W=4 is the answer.
Answer 2

Let [tex] l [/tex] be the length and [tex] w [/tex] be the width of the rectangle.

Given perimeter of the rectangle

[tex] 2(l+w)=34 \; l+w=17[/tex]

Area of the rectangle is

[tex] lw=52 [/tex]

Also length is 5 more than twice its width,

[tex] l=2w+5 [/tex]

From the above equations

[tex] (l-w)^2=(l+w)^2-4lw=17^2-4*52=81\\
l-w=9,\; since \; l>w [/tex]

Now [tex] 2l=9+17=26\;,l=13,w=4 [/tex]

The dimensions of the rectangle are length [tex] l=13 [/tex], and width [tex] w=4 [/tex].


Related Questions

Based on the graph, what is the dependent variable, the equation relating the two variables, and how far will the dragonfly travel in 24 hours if it continues to fly at the same speed? (look at the image below)

The dependent variable is distance, the equation is x = 20y, and the dragonfly will travel 360 miles.
The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles.
The dependent variable is time, the equation is x = 20y, and the dragonfly will travel 360 miles.
The dependent variable is time, the equation is y = 20x, and the dragonfly will travel 480 miles.

Answers

40/2 = 20
so 
y = 20x

y = distance (miles) and x = time (hours)
so if x = 24 then y = 20x = 20(24) = 480

answer
The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles. 

Answer:

The dependent variable is distance, the equation is y = 20x, and the dragonfly will travel 480 miles.

Step-by-step explanation:

According to the graph, the dependent variable is Distance in miles, because it's on the vertical axis. Additionally, the independent variable is time in hours, because it's on the horizontal axis. However, you always put time as independent, because nothing affects time.

To find the equation, we just need to find the slope, using two points (0,0) and (2,40).

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }=\frac{40-0}{2-0}=20[/tex]

Therefore, the equation is [tex]y=20x[/tex], which shows a direct proportion between variables.

Now, in 24 hours, it would travel

[tex]y=20(24)=480[/tex]

It would travel 480 miles.

Therefore, the right answer is the second choice.

A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed. Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents of Mississippi would purchase the new product. Identify a problem with the study.

Answers

The sample size is too small. The company is trying to determine the percent of people in Mississippi that would purchase the product. To make a prediction for the entire state of Mississippi, they should survey more than just 24 people. A random survey should be created and given out across the state.

The conclusion is based on a small sample.

A rectangular bathtub is 5 1/2 feet long, 1 1/2feet wide, and 3 feet high. Daniel fills the tub to a depth of 2feet.What is the volume of the water in the tub?

Answers

To find the volume of the water that is in the tub, you will multiply the length by the wet by the height/depth of the water.

V = lwh
5 1/2 x 1 1/2 x 2
V = 16 1/2 ft.³

Plz show work and explain
Haley and Madison are arguing over a math problem. Haley insists that a square with a area of 196 square units is bigger than Madison’s square that has a perimeter of 196 units. Who is correct and why?

Answers

Perimeter of a square is:

4 * s

where s is the side length.

Area is:

s * s

So, we can set both of these values to 196.

4s = 196
s = 49

s * s = 196
s = 14

So, Madison is correct.

Hope this helped!

What are the answers to problem one and to WILL GIVE BRAINLEST AND SHOW YOUR WORK

Answers

The answer is: $19.56

4 * $4.89= $19.56

Which of the following graphs shows the solution of the inequality
x+1<5
?
A. Graph A
B. Graph B
C. Graph C
D. Graph D

Answers

[tex]x + 1 < 5 \\ x < 4[/tex]

Answer is C. Graph C

Hope this helps. - M

What is the volume of a 8 by 4.5 by 3.5 prism

Answers

Always for prisms like a rectangle you multiply all sides so 8 times 4.5 times 3.5 = 126, for a triangular prism  your have to divide by 2 .

Hope this was helpful
126squared becuawse you multiply the length,width,&height

Solve for x
X3=1/27
Solve in fraction simplest form

Answers

x³ = 1/27
x=³√1*1*1/3*3*3
x= 1/3
Factor using difference of cubes and set each factor equal to 0.

[tex]x= [/tex] [tex] \frac{1}{3} [/tex], [tex]- \frac{1-i \sqrt{3} }{6} [/tex],  [tex]- \frac{ 1+i \sqrt{3} }{6} [/tex]

Hope i was of some help ^.^

Hideki throws a baseball ball upward with an initial velocity of 12 meters/sec. When he throws the ball, it is two meters above the ground. How long will it take the ball to hit the ground?

Answers

For this case we have the following kinematic equation that models the problem:
 h (t) = (1/2) * (- 9.8) * t ^ 2 + 12 * t + 2
 Rewriting we have:
 h (t) = -4.9 * t ^ 2 + 12 * t + 2
 When the ball hits the ground we have:
 -4.9 * t ^ 2 + 12 * t + 2 = 0
 Solving the polynomial we have:
 t1 = -0.16
 t2 = 2.61
 We ignore the negative root because it is time.
 Answer:
 It will take the ball to hit the ground about:
 t = 2.61 sec

Answer:

-4.9^2 + 12t + 2 = 0

Step-by-step explanation:

Yo I just need to get this right so help me out

Answers

Answer:

1) yes--first term is -48, common ratio is -2

2) no--no common ratio

3) yes--first term is 3, common ratio is 3

4) yes--first term is 5, common ratio is 2

5) no--arithmetic sequence

6) no--arithmetic sequence

English has 6 letters that can be vowels. This includes Y, which can be either a consonant or a vowel; for this problem, we'll consider Y a vowel. The other 20 English letters are always consonants. How many two-letter "words" can we make from these letters if we are required to use at least one vowel? (We aren't limited to words that have an actual meaning in English. Thus, for this problem, we'll include nonsense "words" like QO, XY, and UZ.)

Answers

I think this should be posted in English instead of Math... but you can make lots of words.

as
my
he
we
me
by
hi
so
go
to

These are just a few.

In a '20% off' sale, a coat was £220. Work out the original price.

Answers

80% of p = 220 (We know this as the sale price is 20% off, so there is still 80%)

0.8p = 220

p = 220/0.8 (This is because we are making p the subject of the formula)

p = 275 (If you are not allowed to use a calculator for this, then: 220/0.8 is the same as 2200/8 because we are just simply multiplying both the numerator and denominator by 10. This can be simply worked out by long division)
80% is equal to 220

1) Set up a proportion:
80/100=220/x

2) Simplify:
4/5=220/x

3) Solve by cross-multiplying:
4x=1100
x=275

Original Price: 275

Jeremy is making a trail mix containing raisins and peanuts. Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound. Jeremy spends $10.50 to make 5 pounds of trail mix. He uses the table below to organize this information. Which equation can Jeremy use to determine the amount of raisins in the trail mix?
a.r + 1.50 = 1.5r
b. r + (5 – r) = 5
c. 1.5r + 2.5(5 – r) = 10.50
d. 1.5r + 2.5(5 – r) = 5

Answers

Answer:

Option C.

Step-by-step explanation:

Let Jeremy mixes "r" pounds of raisins to make a trail mix.

As the total weight of trial is = 5 pounds

So weight of peanuts in the trail mix will be = (5 - r )

Now cost per pound of raisins = $1.50

so cost of r pounds of raisins = $1.50(r)

Cost of the peanuts = $2.50 per pound

so cost of (5 - r) pounds peanuts = $2.50(5 - r)

Jeremy spends total amount = $10.50

So expression will be

Cost of Raisins + cost of peanuts = cost of trail.

1.5r + 2.5(5 - r) = 10.50

Option C. is the answer.

What is the angle of this triangle

Answers

[tex]A_\Delta=\dfrac{1}{2}\sin65^o\cdot8\cdot12=48\sin65^o\\\\\sin65^o=0.9063\\\\P_\Delta=48\cdot0.9063=43.5024\approx43.5\ cm^2[/tex]
[tex]\text{Given that the formula for Area is } \dfrac{1}{2} \text{ab} \sin(\text{c})[/tex]

[tex]\text{Area = } \dfrac{1}{2} \text{(12)(8)} \sin(\text{65}\textdegree)[/tex]

[tex]\text{Area = }43.5 \text{ cm}^2[/tex]

What is the measure of X

Answers

Answer:

we can know the answer by using phorem therom so

Step-by-step explanation:

all are 90 degree so x angle will also be 90 degree

now h^2 =p^2+b^2 so

79+b=159
b=
send help pls... :)

Answers

Subtract 79 from both sides to isolate variable b. 

b = 159 - 79
b = 80
B=80 simple as that

What must you do if you multiply one number in a ratio by n?

Answers

Hi there!

From what I know, when you multiply one number in a ratio, you must also multiply the other number by the same number. This allows for the ratio to stay the same, thus keeping it correct. If both terms were not multiplied by n, the ratio would no longer be the correct ratio.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

Find M angle P
The diagram is not a scale

Answers

Angle P is equal to 74. Do you need to know the working?

The answer would be angel M would be 74

NEED HELP ASAP!!! Susan makes $5 per hour babysitting and $7 per hour as a life guard. Her goal is to make at least $140. which of the following represents three possible solutions to the problem?

Answers

Number of hours Babysitting: x
Number of horus Lifeguard: y

Susan makes $5 per hour babysitting
Money she makes Babysitting: 5x

Susan makes $7 per hour as a life guard
Money she makes as a life guard: 7y

Total money she mahes: 5x+7y

Her goal is to make at least $140:
5x+7y>=140

Answer: First option
5x+7y>=140

What is the solution of the system? y = -8x - 2 and y = -6x + 4

A. (-3, 22)
B. (-8/3, 1/22)
C. (-14/3, 6/22)
D. (3/14, - 6/14)

Answers

Plug the x and y coordinates into those equations and whichever one makes sense for BOTH of the equations is a solution
Equation 1:  y = - 8x - 2    

Equation 2: y = - 6x + 4

Equation both equations, we get:

- 8x - 2= - 6x + 4

-8x + 6x = 4 + 2

-2x = 6

x = -3

Using the value of x in first equation, we get:

y= -8(-3) - 2 = 24 - 2 = 22

So, the solution to the given equations is (-3, 22)

So, the answer is option A

Write an inequality involving the variable x that describes the set of numbers graphed.

Answers

Since it does not include 0 in the inequality, nor does it include any numbers below 0, it must be [tex]\boxed{x\ \textgreater \ 0}[/tex]. 

Please help me!!!!!

Question: Kara and Steven are biking around a 1,800 kilometer path. They start biking from the same place, at the same time, and in the same direction. Kara bikes at a speed of 15 km/h and Steven bikes at a speed of 30 km/h. How long will it take before Steven and Kara will be at the same place of the path next time?

Answers

Answer: 120 hours

============================================================

Explanation:

The path is 1800 km. Kara's speed is 15 km/h. If this speed is held the same throughout the path, then it will take her d/r = 1800/15 = 120 hours to travel the entire path until she gets back to her starting point.

For Steven, it takes him d/r = 1800/30 = 60 hours to make the same journey.

The LCM of 60 and 120 is 120

Every 120 hours, both Kara and Steven will be back at the starting point together. 

Note: this is a very very large time value, and this is not considering the fact that the bikers slow down or stop to take a break. 

A hose fills a hot tub at a rate of 3.45 gallons per minute. How many hours will it take to fill a 280 ​-gallon hot​ tub?

Answers

For this case we must use the following definition:
 Q = V / t
 Where,
 Q: flow
 V: volume
 t: time
 Clearing the time we have:
 t = V / Q
 Substituting the values:
 t = (280) / (3.45)
 t = 81.16 minutes
 In hours we have:
 t = (81.16) * (1/60)
 t = 1.35 hours
 Answer:
 it will take to fill to 280 -gallon hot tub about:
 t = 1.35 hours

It will take approximately 1.35 hours to fill the 280-gallon hot tub.

We have,

A hose fills a hot tub at a rate of 3.45 gallons per minute.

This can be written as an expression:

3.45 gallons = 1 minute

Now,

Multiply 280/3.45 on both sides.

280/3.45 x 3.45 gallons = 280/3.45 minutes

280 gallons = 81.16 minutes

Now,

81.16 minutes can be converted into hours.

Divide 81.16 by 60.

So,

81.16/60 = 1.35 hours

Therefore,

It will take approximately 1.35 hours to fill the 280-gallon hot tub.

Learn more about expressions here:

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spining a spinner that has 5 equal section marked 1 through 5 and landing on an evean number

Answers

Judging on how the only even numbers between 1 and 5 are 2 and 4. You would use a calculator and do 2÷5 and it will come out as .40 meaning 40%! So there is a 40% chance of landing on a even number! Hope I helped!

2. Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months. Put the numbers in order from least to greatest. Show your work! City A: {4, 3.5, 5, 5.5, 4, 2} City B: {5, 6, 3.5, 5.5, 4, 6} (a) What is the mean monthly rainfall amount for each city? (b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth. (c) What is the median for each city? Answer: a) Mean of City A: 24 Mean of City B: 30 b) Find the MAD for each city. City A Absolute Deviation MAD for City A City B Absolute Deviation MAD for City B 4 5 3.5 6 5 3.5 5.5 5.5 4 4 2 6 c) Median of City A: 4 Median of City B: 5.25

Answers

City A: {2, 3.5, 4, 4, 5, 5.5}
City B: {3.5, 4, 5, 5.5, 6, 6}

Mean is the average.
Average of City A = 4 (2+3.5+4+4+5+5.5 = 24 and 24/6 = 4)
Average of City B = 5 (3.5+4+5+5.5+6+6 = 30 and 30/6 = 5)

Mean Absolute Deviation
Mean Absolute Deviation of City A = 0.8
Mean Absolute Deviation of City B = 0.8

Median is the middle (after putting it in order least to greatest)
Median of City A = 4
Median of City B = 5.25 (5+5.5 = 10.5 and 10.5/2 =5.25)

Food express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on the receipt so far 147 of the first 156 customers have not received a star in the receipts what is experimental probability of winning a free gallon of milk

Answers

Formula
P(nw) = no wins / total
no wins = 147
Total = 156 

Calculation for no wins 
P(nw) = 147 / 156 = 0.9423

Calculation for winners.
P(w) = 1 - 0.9423
P(w) = 0.05769

Another way.
You could calculate the winners from the total
156 - 147 = 9

P(w) = 9/156 = 0.05769 Same answer as before. Pick the method you like best.

what does it mean if the quotient times the divisor does not equal the dividend? What should you do?

Answers

say just for a example, that you have 400 divided by 20. The correct answer is 20. But say that you got ten. You would say how many times can 20 go into 40? The answer would be twice. Then, you would say, how many times can 20 go into zero. The correct answer would be 0. you should go back to your work and check and ask yourself those problems and see if they match. Hope this helps!

Final answer:

When the quotient times the divisor does not equal the dividend, it means there is a remainder. Depending on the context of the problem, you can round down, express the remainder as a fraction or decimal, or choose another appropriate method.

Explanation:

When the quotient times the divisor does not equal the dividend, it means that the division did not result in an exact whole number. This is called a remainder. For example, if you divide 15 by 4, the quotient is 3 and the remainder is 3. So, 3 times 4 does not equal 15.

If you encounter this situation, you can do a few things. You can round the quotient down to the nearest whole number, or you can express the remainder as a fraction or decimal. It depends on the context of the problem and what is required.

For example, if you are dividing cookies among friends, you may want to express the remainder as a fraction, saying each friend gets 3 and a half cookies. But if you are calculating the number of whole boxes needed, you may round down to 3 boxes.

A saving account pays 3.6% per annum simple interest Heidi puts £400 into the account, how much will she have in the account after 5 years?

Answers

One year:
0.036(400)+400
Because it is 5 years:
5(0.036(400))+400
0.18(400)+400
We can make it simpler:
1.18(400)
Multiply
472
SHE WILL HAVE £472
Final answer:

Using the simple interest formula, Heidi will gain £72 in interest on her initial £400 deposit over 5 years at an interest rate of 3.6%. Therefore, she will have a total of £472 in her account at the end of 5 years.

Explanation:

The subject of this question is simple interest calculation which is a topic in Mathematics. It's all about calculating the final amount Heidi will have in her account after 5 years, with a simple interest rate of 3.6% on her initial deposit of £400.

Given the simple interest formula, Interest = Principal × Interest rate × Time, here, the principal is £400, the interest rate is 3.6% (which is 0.036 as a decimal), and time is 5 years.

Using the formula: Interest = £400 × 0.036 × 5 = £72

So, Heidi earns £72 in interest over 5 years.

To find out how much money she will have after 5 years, we will need to add the interest to the initial deposit: Amount = Principal + Interest which gives: Amount = £400 + £72 = £472

So after 5 years, Heidi will have £472 in her account.

Learn more about Simple Interest Calculation here:

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A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?

Answers

8 pigs 4 ducks
8x4=32
2x2=4
32+4=36
there are 8 pigs and 2 ducks. 2 ducks equal 4 legs, and 8 pigs equal 32 legs. Then, you do simple math, so 32 plus 4 is 36 legs!

Sandra has four color cards: one blue, one red, one green, and one yellow. If she puts them in a box, in how many different orders could she draw them out?
A. 16
B. 24
C. 32
D. 64

Answers

A. 16 i don't know tho..
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