The length of a rectangle is 4FT less than three times the width, and the area of the rectangle is 55FT. Find the dimensions of the rectangle.

Answers

Answer 1

Answer:

The required dimensions of rectangle are 11 feet and 5 feet.

Step-by-step explanation:

Given, The length of a rectangle is 4 ft less than three times the width, and the area of the rectangle is 55 ft².

Let's assume width of rectangle be x feet and length be 3x - 4 feet. Using the formula of Area of rectangle we'll find the value of length and width.

[tex] \\ \dashrightarrow{ \red{ \underline{ \underline {\sf\: \:Area _{(rectangle)} = Length \times width}}}} \\ \\ [/tex]

Substituting the required values:

[tex]\dashrightarrow\: \: (3x - 4)(x) = 55 \\ [/tex]

[tex]\dashrightarrow\: \: 3x^2 - 4x = 55 \\ [/tex]

[tex]\dashrightarrow\: \: 3x^2 - 4x - 55 = 0 \\ [/tex]

[tex]\dashrightarrow\: \: 3x^2 + 11x - 15x - 55 = 0 \\ [/tex]

[tex]\dashrightarrow\: \: x(3x+11) -5(3x+11) = 0 \\ [/tex]

[tex]\dashrightarrow\: \: (x-5)(3x+11) = 0 \\ [/tex]

[tex] { \red{ \dashrightarrow\: \: { \underline{ \underline{ {x = 5 \: or \: \dfrac{-11}{3}}}}}}} \\ \\ [/tex]

Hence,

Length of rectangle = 3x - 4 = 3(5) -4 = 11 feet Breadth of rectangle= x = 5 feet

[tex]\therefore[/tex] The required dimensions of rectangle are 11 feet and 5 feet.


Related Questions

Anyone can help me with this? Kinda confusing. Thank you!

Answers

Answer:

14

Step-by-step explanation:

you can do 9 x 14 and get 126

I don't know how to do this (don't mind the 21)​

Answers

Answer:

The definition of alternate interior angles is that those two angles are the same.

Therefore because they are the same you can set them equal to eachother

3x + 24 = 78 is true

3x = 54

x = 18

Just know the definitions, for instance 3 and 4 are the same, 2 and 5 are the same, 1 and 6 are the same

Good people please don't leave me help!!! ​

Answers

Answer:

I hope it helped you

Step-by-step explanation:

Pls check the given attachment

I hope it helped you

Use the proof above to answer the question: What reason can be used to prove that the triangles are congruent?
A. AAS B. ASA C. AAA D. SAS E. SSS

Answers

Answer:

E. SSS

Step-by-step explanation:

AB=BC (Given)

AD=CD (Midpoint)

BD=BD (common)

Therefore answer is : SSS

For the point P(17,22) and Q(22,27), find the distance d(P,Q) and the coordinates of the midpoint M of the
segment PQ.

Answers

Step-by-step explanation:

[tex]x \: component = \frac{17 + 22}{2} \\ = 19.5 \\ y \: component = \frac{22 + 27}{2} \\ = 24.5 \\ (19.5...24.5)[/tex]

HELP PLEASE!!
Discuss the steps that you used
to create your tangent line.
What was the most important
step?
Give an example of tangents in
the real world that have not
been presented in this lesson.
Explain how you know the
tangent and the radius are
perpendicular.

Answers

Answer:

You need to have both the opposite and adjacent side of the right angled triangle. Tan = Opp/Adj

Step-by-step explanation:

Tangents are pretty much everywhere. A good example is maybe a slide at the playground. You’d need the tangent to figure out the angle of the slide and how it is.

The radius from the center of a circle to the point of tangency point shows that it would be perpendicular to the tangent line considering that anything with a radius is circular and the tangent line is… a line, making it impossible to be parallel.

A spinner is divided into 12 identical sectors and labeled 1 through 12.

How many spins are expected for a multiple of 5 to be spun 8 times?

Select from the drop-down menu to correctly complete the sentence.

The spinner is expected to have to spin approximately
times for a multiple of 5 has been spun 8 times.

Answers

Answer: The awnser is 48

Step-by-step explanation: I took the quiz

6.03 Quiz: Use Theoretical Probability to Predict

It is expected to take 48 spins for a multiple of 5 to be spun 8 times.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Since there are 12 sectors, the probability of landing on a multiple of 5 is 2/12 or 1/6.

The probability of not landing on a multiple of 5 is 5/6.

We can use the geometric distribution formula to find the expected number of spins:

E(X) = 1/p, where p is the probability of success.

As per the question, the probability of success is 1/6.

Therefore, E(X) = 1/(1/6) = 6.

We need to spin a multiple of 5 8 times, so we multiply the expected number of spins by 8:

6 x 8 = 48.

Therefore, we can expect to spin a multiple of 5-8 times after 48 spins.

Learn more about the probability here:

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I need help finding the surface area of this shape

Answers

Answer:

1030 [tex]yd^{2}[/tex]

Step-by-step explanation:

split it into 2 different rectangular prisms

first one is 27 yd by 8 yd by 9 yd

second is 10yd by 8 yd by 12 yd

Answer:

1494 [yd²].

Step-by-step explanation:

1) the required area can be calculated as (see the attached picture):
A=A1+A2+A3+A4+A5+A6+2*A7;

2) finally,

A=9*8+17*8+8*12+10*8+(12+9)*8+27*8+2*(27*9+12*10);

A=1494 [yd²].

Note, the suggested solution is not the shortest one.

Marlo uses 252 lb of gravel to cover a garden plot of 36 ft2.

Answers

Answer: 7lb

Step-by-step explanation:

The amount of gravel required cover each square feet of the garden obtained by dividing the total amount of gravel used and the total area of the garden is 7 lb

Total area of garden = 36 ft²

Total amount of gravel used = 252 lb

The amount of gravel used to cover each ft² of the garden can be calculated thus :

(Total amount of gravel used) ÷ (Total area of garden)

252 ÷ 36 = 7 lb

Therefore, the amount of gravel required to cover each square feet of the garden is 7 lb

Answer:

See below

Step-by-step explanation:

D o you want pounds / sq foot ?

252 lbs / 36 ft^2 =   7 pounds per square foot

£ 686 is shared out between David, Steve and Mike. Mike gets twice as much as Steve who gets twice as much as David. How much does Mike get?

Answers

Answer:

£ 392

Explanation

In Houston, 9 bats ate 50 grams of insects in one night. At this rate, how many grams of insects could 81 bats eat in one night?

Answers

Answer:

Step-by-step explanation:

Remark

Using Algebra, this is a proportion question. A proportion is 2 equal ratios

If the of the 2 ratio parts are known, it is possible to solve for the 4th one.

Formula

9_bats/50_grams::81_bats/x grams insects

Solution

Put the three knowns in and solve for the 4th which is not known

9 bats/ 50 insects = 81 bats /x insects.         Cross multiply

9 * x = 50 * 81                                                  Combine

9x = 4050                                                       Divide by 9

9x/9 = 4050/9

Answer: x = 450 grams

Martinez and grouse swimming pool is finally finished and all this left to do is fill it with water. Martinez family decides to fill their pool using their garden hose to save money even though they know it will take a really long time the swimming pool is 10 m long and 5 m wide and Martinez family wants to the water to be 2 m deep water from the garden holes flows at a rate of 2500 l or 2.5 m³ per hour how long will it take to fill the pool

Answers

Answer:

the answer ia true

Step-by-step explanation:

hope this helps

A sample of 36 people yielded the information about their health insurance in the table to the right.
Two people who provided information for the table were selected at​ random, without replacement. Find the probability that neither had traditional insurance.

Answers

The probability that neither of the two people selected have traditional insurance is 0.33.

What is the probability that neither had traditional insurance?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that neither of the two people selected have traditional insurance = (number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed x [(number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed - 1]

21/36 x 20/35 = 0.33

Please find attached the table. To learn more about probability, please check: https://brainly.com/question/13234031

A company paid ​$211.00 for an item. The original price was​ $299.20​, but this was marked down 40​%. If the operating expenses are 36​% of the​ cost, find the operating loss and the absolute loss.

1. What is the operating loss?
2. What is the absolute loss?

Answers

Answer:

If the operating expenses are 36% of the cost, find the operating loss and the absolute loss.

1. An operating loss occurs when a company's operating expenses exceed gross profits (or revenues in the case of a service-oriented company.

2. Mean absolute error (MAE) is a loss function used for regression. The loss is the mean overseen data of the absolute differences between true and predicted values, or writing it a formula.

Step-by-step explanation:

Find x in each triangle

Answers

Answer:

Applying Pythagoras we get x= 9

Answer:

using the relation,

h²=p²+b²:

15²=x²+12²

x=(225-144)^0.5

x=9

therefore x equal 9 meter.

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.

Answers

Answer:

x=5.09 seconds (times at max)

Step-by-step explanation:


If (x, 42) is a solution to the equation y = -6 (x – 15) – 3, find x

Answers

Put y and find x

y=-6(x-15)-342=-6(x-15)42+3=-6(x-15)45=-6x+90-6x=-45x=45/6x=15/2

Can someone help me? I'm pretty bad at math... But what is the number needed?
6 x ? x 3 = 90

Answers

The answer is 5 I’ll explain so when you multiply 6 times 3 it gives you 18 and 18 times 5 equals 90 hope it helps

Which set of angle measures could be the interior angles of a triangle?

Answers

Answer:

the three angles inside a triangle need to add up to 180 degrees

Step-by-step explanation:

For what value of k will the relation R = {(2k+1, 3), (3k−2, −6)} not be a function?

Answers

For the relation to not to be a function we need the same value of x in (x,y) that gives off different values (y).

2k+1= 3k-22k-3k = -2-1-k = -3k = 3

Now plugging in the value of k,

(2 x 3+1 ,3) =( 7,3)(3 x 3-2,-6) = (7,-6)

hence , the relation won't be function if k would be equal to 3

The value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.

What is a function?

In general terms, a function is a mathematical rule or relationship that maps one set of values (the input or domain) to another set of values (the output or range). In other words, it's a specific process that takes some input and produces a corresponding output.

For the given relation R to be a function, each input in the domain should have exactly one corresponding output in the range.

We can determine whether the relation R is a function by checking if both ordered pairs have the same first coordinate. If they do, then the relation is not a function.

Let's equate the first coordinate of the ordered pairs:

2k+1 = 3k-2

Solving for k, we get:

k = 3

If we substitute k = 3 into the relation, we get:

R = {(2(3)+1, 3), (3(3)−2, −6)}

R = {(7, 3), (7, -6)}

Since both ordered pairs have the same first coordinate of 7, the relation R is not a function.

Therefore, the value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.

To know more about function follow

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Given the function f(x) = 4 - 2x, find f(3r - 1).

Answers

Answer:

6 - 6r

Step-by-step explanation:

we just plug in 3r - 1 instead of x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= 6 - 6r

What is the area of the figure?
A. 18 yd
B. 54 yd
C. 72 yd
D. 90 yd​

Answers

The correct answer is C

I solved by multiplying 9 x 5 and 3 x 9 and adding them.

Hope this helps

The expression below is a sum of cubes.

125x^3 + 144

A. True

B. False

Answers

it would be false bc i just took it and it was right

Answer:

False

Step-by-step explanation:

Hey there!

If this is a sum of cubes, this means that both numbers have whole numbers as the cube root of that number

The cube root of 125 is 5

But the cube root for 144 is a decimal meaning this is not a sum of cubes

Decide whether it would be more convenient to solve the system of equations by substitution or elimination.
{−2x/3−15y=−6, 10x−6y=−4
Select the correct answer below:


elimination

substitution

Answers

Answer:

I would use elimination in this scenario. Because in both equations there is a coefficient on both variables, it would be difficult to isolate one variable and would leave the equation as a fraction. Instead, use elimination. Multiply the first equation by -15, which changes it to 10x + 225y = -90, and then subtract the second equation, thus cancelling out the 10x's and letting you solve for Y. Hope this helps!

!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

I believe it would be 9.

Step-by-step explanation:

Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9

solve system of equations can someone show step by step please
2x-6y=-12
x+2y=14

Answers

Answer:

x=6 y=4

Step-by-step explanation:

I hope this helps you and please mark me as brainlest!

What is the best way to describe the center of the data represented in this line plot?


Select from the drop-down menus to correctly complete the statement.


The Choose is Choose. your options are for the first one is Mean or Median then for the second one is 2 inches, 2.5 inches, 3 inches, or 3.2 inches

.

Answers

The best way to describe the center of the data represented in this line plot include the following: the median is 2.5 inches.

What is a median?

In Mathematics, a median refers to the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.

Since the data set representing the amount of rainfall has an outlier, the median would be best way to describe the center of the data represented in this line plot.

First of all, we would sort the 10 observations from the least to greatest as follows:

1, 1, 2, 2, 2, 3, 3, 5, 6, 7

Median = (2 + 3)/2

Median = 5/2

Median = 2.5 inches.

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In analysis of variance, then the term factor refers to_______
a) a dependent variable
b) a treatment total
c) an independent variable (or quasi-independent) variable
d) a treatment mean

Answers

C an independent variable

39 28. If y = (1 - 3x), find the value of dy! dx at x = -1.​

Answers

Answer:

the answer to this question is 52.18

Write an equation in slope-intercept form of the line that passes through ( 7,2 ) ( 2,12 )

Answers

Answer:

y = -2x + 16

Step-by-step explanation:

Slope-intercept form is:

y = mx + b

Where m = slope

b = y-intercept

To find the slope of the line containing (7,2) and (2,12), we have to find the slope, m.

m = (y2 - y1)/ (x2 - x1)= (12 - 2)/(2 - 7) = 10/-5 = -2

Now, to find the y-intercept (b), insert m = -2 into the equation and one of the given points:

y = -2x + b

let's use point (7,2) to find b:

2 = -2(7) + b2 = -14 + bb = 16

Now, we can find the equation of this line:

y = -2x + 16

Answer:

y=-2x+16

Step-by-step explanation:

First we should find the slope.

We can use the formula (y2-y1)/(x2-x1)


(12-2)/(2-7)=10/-5=-2

So, the slope is -2.

From there, we can plug in one of the points into the standard slope-intercept equation, y=mx+b, along with the slope we already found

y=-2x+b

12=-2(2)+b

12=-4+b

b=16

So, the slope-intercept equation is y=-2x+16

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