The length of a rectangle is 2 centimeters less than three times its width. Its area is 21 square centimeters. Find the dimensions of the rectangle. Use the​ formula, area=length*width.

Answers

Answer 1

Area = length x width

Area = 21 square cm

Width = x

Length = 3x + 2

21 = 3x+ 2 * x

21 = 3x ^2 + 2x

Subtract 21 from both sides:

3x^2 + 2x -21 = 0

Use the quadratic formula to solve for x:

-2 +/- sqrt(2^2-4*3(-21))/(2*3)

X = 7/3 and -3

A dimension can’t be a negative value so x needs to be 7/3

Width = x = 7/3 = 2 1/3 cm

Length = 3(7/3) + 2 = 9 cm

Check: 9 x 2 1/3 = 21

Dimensions: width 2 1/3 cm length 9 cm

Answer 2

Answer:

The dimensions of the rectangle are 7 by 3 centimeters.

Step-by-step explanation:

We are given that the length of a rectangle is two centimeters less than three times its width. In other words:

[tex]\displaystyle \ell = 3w-2[/tex]

Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.

Recall that the area of a rectangle is given by:

[tex]A= w\ell[/tex]

Substitute:

[tex](21)=w(3w-2)[/tex]

Solve foro the width. Distribute:

[tex]3w^2-2w=21[/tex]

Isolate the equation:

[tex]3w^2-2w-21=0[/tex]

Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.

-9 and 7 suffice. Hence:

[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]

Zero Product Property:

[tex]3w+7=0\text{ or } w-3=0[/tex]

Solve for each case. Hence:

[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]

Since width cannot be negative, we can ignore the first solution.

Therefore, our width is three centimeters.

And since the length is two less than three times the width, the length is:

[tex]\ell = 3(3) - 2 = 7[/tex]

The dimensions of the rectangle are 7 by 3 centimeters.


Related Questions

A popular beach erodes 4 inches per year on average.

An eroding beach.
A. How many years will it take for the coastline to erode one foot?

Answers

Answer:

3 years

Step-by-step explanation:

4 inches per year on average

1 foot = 12 inches

12 divided by 4 equals 3

therefore it is 3 years

Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and ∠PAL = 93°. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places.

Answers

The area bounded by a chord and arc it intercepts is known as a segment of a circle segment of a circle

The area of the circle enclosed by line PL and arc PL is approximately 37.62 square units

The reason the above value is correct is as follows:

The given parameters in the question are;

The radius of the circle, r = 11

The length of the chord PL = 16

The measure of angle ∠PAL = 93°

Required:

The area of part of the circle enclosed by chord PL and arc PL

Solution:

The shaded area of the given circle is the minor segment of the circle enclosed by line PL and arc PL

The area of a segment of a circle is given by the following formula;

Area of segment = Area of the sector - Area of the triangle

Area of segment = Area of minor sector APL - Area of triangle APL

Area of minor sector APL:

Area of a sector = (θ/360)×π·r²

Where;

r = The radius of the circle

θ = The angle of the sector of the circle

Plugging in the the values of r and θ, we get;

Area of the minor sector APL = (93°/360°) × π × 11² 98.2 square units

Area of Triangle APL:

Area of a triangle = (1/2) × Base length × Height

Therefore;

The area of ΔAPL = (1/2) × 16 × 11 × cos(93°/2) ≈ 60.58 square units

Required shaded area enclosed by line PL and arc PL:

Therefore, the area of shaded segment enclosed by line PL and arc PL is found as follows;

Area of the required segment PL (98.2 - 60.58) square units = 37.62 square units

The area of the circle enclosed by line PL and arc PL ≈ 37.62 square units

Learn more about the finding the area of a segment can be found here:

https://brainly.com/question/22599425

The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.

The calculation of the area between line segment PL and circle arc PL is described below:

1) Calculation of the area of the circle arc.

2) Calculation of the area of the triangle.

3) Subtracting the area found in 2) from the area found in 1).

Step 1:

The area of a circle arc is determined by the following formula:

[tex]A_{ca} = \frac{\alpha\cdot \pi\cdot r^{2}}{360}[/tex] (1)

Where:

[tex]A_{ca}[/tex] - Area of the circle arc.

[tex]\alpha[/tex] - Arc angle, in sexagesimal degrees.

[tex]r[/tex] - Radius.

If we know that [tex]\alpha = 93^{\circ}[/tex] and [tex]r = 11[/tex], then the area of the circle arc is:

[tex]A_{ca} = \frac{93\cdot \pi\cdot 11^{2}}{360}[/tex]

[tex]A_{ca} \approx 98.201[/tex]

Step 2:

The area of the triangle is determined by Heron's formula:

[tex]A_{t} = \sqrt{s\cdot (s-l)\cdot (s-r)^{2}}[/tex] (2)

[tex]s = \frac{l + 2\cdot r}{2}[/tex]

Where:

[tex]A_{t}[/tex] - Area of the triangle.

[tex]r[/tex] - Radius.

[tex]l[/tex] - Length of the line segment PL.

If we know that [tex]l = 16[/tex] and [tex]r = 11[/tex], then the area of the triangle is:

[tex]s = \frac{16+2\cdot (11)}{2}[/tex]

[tex]s = 19[/tex]

[tex]A_{t} = \sqrt{19\cdot (19-16)\cdot (19-11)^{2}}[/tex]

[tex]A_{t} \approx 60.399[/tex]

Step 3:

And the area between the line segment PL and the circle arc PL is:

[tex]A_{s} = A_{ca}-A_{t}[/tex]

[tex]A_{s} = 98.201 - 60.399[/tex]

[tex]A_{s} = 37.802[/tex]

The area of the circle enclosed by line segment PL and circle arc PL is 37.80 square units.

Factors and rewrite the expression 25x-15​

Answers

Answer:

5(5x-3)

Step-by-step explanation:

The common factor in this expression is 5 so divide 5 to all the values

25/5=5

-15/5= -3

Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis

5(5x-3)

Answer:

5(5x - 3)

Step-by-step explanation:

The greatest common factor here is 5. Divide each term by 5 and simplify.

25x/5 = 5x

15/5 = 3

Therefore, the answer is 5(5x - 3).

The number of hearing aids that needs to be produced and sold is??

Answers

Answer:

14.36 AND 9.89 ===> 14 or 10

Step-by-step explanation:

Y =  Ax2 Bx C

Enter coefficients here >>>  -4 97 -568

   

Standard Form: y = -4x²+97x-568    

-24.25 -12.125 147.015625 -588.0625 20.0625

Grouped  Form: No valid Grouping      

   

Graphing Form: y = -4(x-12.13)²+20.06    

     

Factored Form: PRIME    

   

Solution/X-Intercepts: 14.36 AND 9.89    

   

Discriminate =321 is positive, two real solutions    

   

VERTEX: (12.13,20.06)     Directrix: Y=20.13    

Give example to verify if the given statement is true or false
1) if two numbers are co-primes , at least one of them should be prime number.

Answers

Answer:

no

Step-by-step explanation:

if two numbers are co-prime that is not necessary that one of them must be a prime number

Start with the number 2380.
Divide by 10,
The 8 will end up in the _____ place.

Answers

Answer:

The 8 will end up in the ones place.

Step-by-step explanation:

If you want to divide 2380 by 10… sry gtg

The 8 will end up in the "ones place".

How can we interpret the division?

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.

We need to find the 8 will end up in which place

A negative divided by a negative is positive, then;

2380/ 10 = 238

Therefore, The 8 will end up in the _ ones_ place.

Learn more about division here:

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please helpppp i need it by tonight its very important

Answers

Answer:

m<1=145

m<2=35

m<3=35

Step-by-step explanation:

measure one is supplementary(the angles add to 180) to measure four.

so we do 180-35=145

measure 2 is congruent to measure four because they are corresponding angles

so measure 2=35

and measure 3 is also congruent to measure 4 because the are corresponding angles

so m<3=35

Shawn has 4 times as many candies as Jason, who has a third as many candies as
lan. If Shawn has 64 candies, how many candies does Ian have?

Answers

Ian has 48 candies. hope that helps!
Ian has 4 candies...........

factorize : ( p- q ) cube​

Answers

Answer:

[tex]( {p - q}^{3} ) \\ = {p}^{2} - 3 {p}^{2} q + 3p {q}^{2} - {q}^{3} [/tex]

Hope my answer helped u :)

PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.

Answers

Answer:

The answer is 82.2  

Step-by-step explanation

hope this helps

A factory used 99.19 kilograms of tomatoes to make 7 batches of pasta sauce. What quantity of tomatoes did the factory put in each batch?

Answers

Answer:

14.17 kilograms

Step-by-step explanation:

Find what quantity of tomatoes was in each batch by dividing the total amount of tomatoes by the number of batches:

99.19/7

= 14.17

So, the factory put 14.17 kilograms of tomatoes in each batch.

Round 5,821 to the nearest thousands place:

Answers

Answer:

6000 hope this helps

if the question is 5,422 then the round figure is 5000

but the question is 5,821 its above 5500 will be 6000

prove that 2^n+1>(n+2).sin(n)​

Answers

Step-by-step explanation:

F(n)=|sin(n)|+|sin(n+1)|

then

F(n+π)=|sin(n+π)|+|sin(n+π+1)|=|sin(n)|+|sin(n+1)|=F(n)

and

F(π−n)=|sin(π−n)|+|sin(π−n+1)|=|sinn|+|sin(n−1)|≠F(n)

so we must prove when n∈(0,π), have

F(n)>2sin12

when n∈(0,π−1),then

F(n)=sinn+sin(n+1)=sinn(1+cos1)+sin1cosn

and n∈(π−1,π),then

F(n)=sinn−sin(n+1)

How prove it this two case have F(n)>2sin12? Thank you

and I know this well know inequality

|sinx|+|sin(x+1)|+|sin(x−1)|≥2sin1,x∈R

HELP PLEASE!!!

Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t


Question:

Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.

Answers

The logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

-------------

We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.

-------------

The original function is:

[tex]y = f(x) = e^{0.4x}[/tex]

To find the inverse function, first, we exchange y and x, so:

[tex]e^{0.4y} = x[/tex]

Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So

[tex]\ln{e^{0.4y}} = \ln{x}[/tex]

[tex]0.4y = \ln{x}[/tex]

[tex]y = \frac{\ln{x}}{0.4}[/tex]

Thus, the logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

A similar question is given at https://brainly.com/question/24290183

After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:

Answers

9514 1404 393

Answer:

  19 years

Step-by-step explanation:

The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...

  A = P(1 +r/n)^(nt)

Solving for t, we get ...

  t = log(A/P)/(n·log(1 +r/n))

Using the given values, we find t to be ...

  t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000

The investment will be worth $213,022 after 19 years.

please help me with both questions

Answers

Answer:

(b) 829 seconds

(c) 13.8 minutes

Step-by-step explanation:

(b) 2.48×10⁸/2.99×10⁵ = 829 seconds

(c) 829/60 = 13.8 minutes

Helpp me plzzz im being timed

Answers

Above question
Slope = change in y / change in x
(2 different random point on the line)
Let’s point out 2 points: (0,3) and (6,0)
So slope = (3 - 0) / (0 - 6) = 3/(-6) = -1/2

Y-intercept is when x = 0, the line cross the y-axis at y = ?
So y = 3
Below question is farmiliar:
Slope = (30-50) / (0-6) = -20/(-6) = 10/3
Y-intercept = 30

17 x 35=56 over 76 hope it helps s

five brothers of 4, 9, 11, 13 and 16 years respectively, receive an inheritance of 1,500,000, the will stipulated that that amount must be shared by the heirs so that, placed the shares in a bank, they would result in equal capitalized amounts, when each one reached 21, could raise his share. Knowing that the bank charges an interest rate of 9% per year, what is the amount of each share?

Answers

9514 1404 393

Answer:

Youngest to oldest:

160,406.86246,805.83293,230.01348,386.58451,170.72

Step-by-step explanation:

At 9% interest per year, the present value of 1 at age 20 is ...

  p(a) = 1.09^(a-20)

Adding the present values for the different ages, we get a total of about 2.35528984846. Dividing the inheritance by that amount gives the multiplier for each of the present value numbers. The result is the list of shares shown above. At age 20, each brother will inherit about 636,864.29.

__

Additional comment

This is the sort of question that suggests the use of a graphing calculator or spreadsheet for doing the tedious number crunching.

(We assume the bank pays 9% per year, rather than charges 9% per year.)

Starting with a fresh bar of soap, you weigh the bar each day after you take a shower. Then you find the regression line for predicting weight from number of days elapsed. The slope of this line will be:__________.

Answers

Answer:

The slope will be negative

Step-by-step explanation:

The slope of the regression line tells us about the relationship or behavior of the dependent and independent variables. In the scenario above, where the weight is being compared with the number of days elapsed. What is expected of the weight and quantity of a bar soap each time it is used for a shower is that it will decrease in weight. Therefore, as the number of days increases, and hence, number of showers rise, the weight of soap will decrease. Hence, we'll obtain a negative slope, one in which the increase in a variable leads to decrease in the other.

Which graph matches the exponential function f(x) = (3)x?

Answers

It is C if you plug in any x value into the equation

The segments shown below could form a triangle.
A
C
7
9
12
B
А
a
A. True
B. False

Answers

Answer:

TRUE

Step-by-step explanation:

I SEEN SOME ONE ELSE WIT 5 STARS SAY SO(:

The given segment can form triangle. Therefore, the given statement is true.

What is triangle?

A polygon has three edges as well as three vertices is called a triangle. It's one of the fundamental geometric shapes. In Euclidean geometry, each and every three points that are not collinear produce a distinct triangle and a distinct plane. In other words, every triangle was contained in a plane, and there is only single plane that encompasses that triangle.

All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Unless when otherwise specified, this article discusses triangles within Euclidean geometry, namely the Euclidean plane. The given segment can form triangle.

Therefore, the given statement is true.

To know more about triangle, here:

https://brainly.com/question/14712269

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You measure 49 turtles' weights, and find they have a mean weight of 80 ounces. Assume the population standard deviation is 6.1 ounces. Based on this, construct a 99% confidence interval for the true population mean turtle weight. Round your answers to 2 decimal places.

Answers

Answer:

The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 2.575\frac{6.1}{\sqrt{49}} = 2.24[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 80 - 2.24 = 77.76 ounces.

The upper end of the interval is the sample mean added to M. So it is 80 + 2.24 = 82.24 ounces.

The 99% confidence interval for the true population mean turtle weight is between 77.76 and 82.24 ounces.

90units needed 8 units per case what's the #of cases & # of additional units

Answers

Answer:

# of cases: 11

Additional units: 2

Step-by-step explanation:

If each case can hold 8 units, and we want to find the total # number of cases, we have to divide the # of units (8) for one case by the total # units (90).

As you can see, after dividing by 8, we have a total of 11 cases and a remainder of 2 units. The remainder will be the # of additional units because we cannot have another case filled with 8 units.

write your answer as an integer or as a decimal rounded to the nearest tenth​

Answers

Answer:

FH ≈ 6.0

Step-by-step explanation:

Using the sine ratio in the right triangle

sin49° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{FH}{FG}[/tex] = [tex]\frac{FH}{8}[/tex] ( multiply both sides by 8 )

8 × sin49° = FH , then

FH ≈ 6.0 ( to the nearest tenth )

Answer:

6

Step-by-step explanation:

sin = opposite/hypotenuse

opposite = sin * hypotenuse

sin (49) = 0,75471

opposite = 0,75471 * 8 = 6,037677 = 6

Please help explanation if possible

Answers

Answer:

18.84 feet.  let me know if you have ay other questions.

Step-by-step explanation:

The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr.  or 2 times pi times the radius.  

Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.

The diameter of the circle is 2 times the radius, so that's why it is replaced.

the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center.  so it's the center to one end plus the center to another end.  or r+r which is also 2r.

So d = 2r, so in this problem d =6 feet.

So now the formula πd = 3.14*6 feet = 18.84 feet

look at the image below

Answers

Answer:

201.1 km²

Step-by-step explanation:

Surface area of a sphere= 4πr², where r = radius

so,

4πr²

= 4×π×4²

= 64π

= 201.1 km² (rounded to the nearest tenth)

The polygons in each pair are similar. Find the missing side length.

Answers

Let missing side be x

If both polygons are similar

[tex]\\ \sf\longmapsto \dfrac{3}{4}=\dfrac{18}{x}[/tex]

[tex]\\ \sf\longmapsto 3x=4(18)[/tex]

[tex]\\ \sf\longmapsto 3x=72[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{72}{3}[/tex]

[tex]\\ \sf\longmapsto x=24[/tex]

Venn diagrams: unions, intersections, and complements

Attached is the photo reference

Answers

Answer:

a) 0

b) 2,3,4,5,6,7

c)3,4,6,7

Step-by-step explanation:

kabura bought a piece of cloth 3 metres long. The material shrunk by 1% after washing. What was the new length of the cloth​

Answers

Answer:

2.97m

Step-by-step explanation:

1% of 3m =1/100×3=0.03

0.03m of cloth was shrunk,

So, New lenght : 3-0.03=2.97m

What is the simplified form of the following expression? Assume x > 0.
3
2x
16x
2x
4/24x²
2x
4/2443
16x4
124²

Answers

Answer:

fourth root of 24 x cubed/16x to the power four

Other Questions
Triangle ABL is an isosceles triangle in circle A with a radius of 11, PL = 16, and PAL = 93. Find the area of the circle enclosed by line PL and arc PL. Show all work and round your answer to two decimal places. In ________ organizational cultures, more individuality is shown through the organizations rules being less strictly applied. please i need urgent help. can someone please write a french composition about a big and nice house of 3 storeys. Your company buys a computer system from IBM for $3 million and pays IBM $200,000 to install the computer system. The $3 million is on credit and your company pays $100,000 of interest on the loan in the current year. The acquisition cost of the computer system at the end of the current year will be Fill in the blank:"Throughout time men havegiven their word, and theirhas bound them.'' -DrBA. stubbornnessB. pityC. arroganceD. honor Is water the only liquid? If not, name 5 more what is wanton--------------------------------------------------- I need help please slope Convert 0.450 to a proper fraction A car insurance company has determined that6% of all drivers were involved in a car accident last year. If14drivers are randomly selected, what is the probability of getting at most 3 who were involved in a car accidentlast year 4) Write an email to your friend about the Colombo International Book Fair to be organized next week at the BMICH. Invite him/her to visit that exhibition. Use about 75-100 words. from the perspective of an employee, the effective channeling of work related information and concerns Jacks backpack weighs 15 pounds. Fernandos backpack weighs less than Jacks. Which graph shows how much Fernandos backpack can weigh? Simplify the following expression Which was not a reason the colonist wanted to declare independence An equation for the period of a planet is 4 pie r/Gm where T is in secs, r is in meters, G is in m/kgs m is in kg, show that the equation is dimensionally correct. Can someone do #4 and #5 A new machine requires an investment of $630,000 and will generate $100,000 in cash inflows for 7 years, at which time the salvage value of the machine will be $130,000. Using a discount rate of 10%, the net present value of the machine is $_________ What is the difference between-5 and 2 Mt cc th ca mt loi sinh vt khi gim phn to giao t. Trong s giao t c sinh ra ngi ta nhn thy s loi giao t mang 2 NST c ngun gc t m l 6. Qu trnh gim phn din ra bnh thng, khng xy ra trao i cho.a. Xc nh b NST 2n ca loi v tn loi.b. Tnh t l loi giao t ni trn?Cho rng t l th tinh ca giao t c v ci u l 100%. Ton b cc hp t u pht trin thnh c th con.