You have 50 ft of fencing and want to fence in a rectangular area of 144 ft^2. What are going to
be the dimensions of the rectangular area?
Quadratic equation

Answers

Answer 1

Answer:

16 by 9 feet.

Step-by-step explanation:

We have 50 feet of fencing in total.

Therefore, the perimeter of our area is 50. Perimeter is given by:

[tex]P=2(\ell+w)[/tex]

Substituting 50 for P yields:

[tex]50=2(\ell+w)[/tex]

And dividing both sides by 2 yields:

[tex]\ell+w=25[/tex]

The area of a rectangular is given by:

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

Where [tex]\ell[/tex] is the length and [tex]w[/tex] is the width.

We want to enclose 144 feet squared. So, A=144:

[tex]144=\ell w[/tex]

By the perimeter equation, we can subtract a variable, say [tex]\ell[/tex] from both sides. Hence:

[tex]w=25-\ell[/tex]

Now, we can substitute this into our area equation. Therefore:

[tex]144=\ell(25-\ell)[/tex]

Distribute:

[tex]144=25\ell-\ell^2[/tex]

Subtract 144 from both sides:

[tex]-\ell^2+25\ell-144=0[/tex]

Divide everything by -1:

[tex]\ell^2-25\ell +144=0[/tex]

Factor:

[tex](\ell-9)(\ell-16)=0[/tex]

Zero Product Property:

[tex]\ell_1=9\text{ or } \ell_2=16[/tex]

Then it follows that:

[tex]w_1=25-(\ell_1)=25-9=16[/tex]

Or:

[tex]w_2=25-(\ell_2)=25-(16)=9[/tex]

Regardless, the dimensions of the rectangular area will be 16 by 9 feet.

Answer 2

Answer:

p = 2(l +w)

l= p÷2 -w = l= 25 -w

A= l x w =( 25 -W)W= 144

-w^2 +25w-144 =0

-w^2 +9w+16w- 144=0

(-w^2+9w) +(16w- 144) =0

-w(w - 9) + 16(w - 9) =0

(-w +16) = 0 or w - 9 =0

w = 9 or w = 16

so l = 25 - 9 = 16

or l = 25 - 16 = 9

therefore l = 16ft and w= 9ft


Related Questions

In a class of 25 students, 9 play an instrument and 18 play a sport. There are 3
students who do not play an instrument or a sport. What is the probability that a
student who plays an instrument also plays a sport?

Answers

Answer: 0.2592

Step-by-step explanation:

This is conditional probability because the events are dependent on one another. You use multiplication rule 2(for dependent events) to solve this problem. The rule goes as follows: “When two events are dependent, the probability of both occurring is: p(A and B) = p(A) * p(B|A)” So all you would do is plug in. p(Sports and Instruments) = p(sports) * p(instruments)

p(Sports and Instruments) = (18/25) * (9/25) = 162/625 = 0.2592

The probability that a student who plays an instrument also plays a sport is 0.2592

How to determine the probability?

The given parameters are:

Total = 25

Instrument = 9

Sport= 18

None = 3

The probability that a student plays a sport is:

P(Sport) = 18/25

The probability that a student plays an instrument is:

P(Instrument) = 9/25

The required probability is:

P = 18/25 * 9/25

Evaluate

P = 0.2592

Hence, the probability is 0.2592

Read more about probabiity at:

https://brainly.com/question/251701

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Find the zeros of f(x)=x^2+10x

Answers

The roots should be 0,-10

how Prove that if n is odd then 3n+5 is even.

Answers

Because 3 is a lower number then 5 and that would be negative if it were 5+3 it would be Positive

What is the y-intercept of the line with the equation y =4x+2

-2
4
2
-1/2

Answers

Y intercept: when x = 0
Y = 4(0) + 2
Y = 0 + 2
Solution: the y intercept is 2

How do I find the domain and range of this

Answers

Domain is the x values from the lowest x to the highest x values used.

Range is the y values from the lowest y to the highest y values used.

Domain : (-4,5)

Range: (0,4)

PLEASE PLEASE PLEASE HELP MEE!!!!!!!

Answers

Answer:

its b

Step-by-step explanation:

hi! pls help , i’ll give brainliest to the correct answer . you get reported if you scam!

Answers

Answer:

10.55 is the answer

Step-by-step explanation:

7.2 + 6.5/2

=> 7.2 + 3.25

=> 10.55

Hope this helps!    :3

plz mark as brainliest!

Please helppppppp!! Asap!!

Answers

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

i will give brainlist,
Unit #3 - Lesson #2 Erit Ticket: If /(x) = 5x – 2 then what is the value of $ (8) ? Show how you found your answer and place it in the answer box.​

Answers

Answer:

f(8) = 38

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = 5x - 2

f(8) is x = 8

Step 2: Evaluate

Substitute in x:                    f(8) = 5(8) - 2Multiply:                               f(8) = 40 - 2Subtract:                              f(8) = 38

Can some one help me with this please I don’t understand it

Answers

Answer:

its b

Step-by-step explanation:

so we know that all te angles in a trangle add up to 180 do the last angle has to be 50

no now we have 140+150+x=180 cuz, self explanitory the two angles make a line,

we get 190 +x=180 so x =-10

8.) On the first visit to the veterinarian's office, Cora's kitten weighed 550
grams. On the second visit, the kitten weighed 900 grams. What is the
percent increase since the first visit in the kitten's weight rounded to the
nearest percent?

Answers

Answer:

55/900=x/100 x=6 1/9%

Step-by-step explanation:

Karita had 138.72 in her checking account she wrote checks to take out 45.23 and 18.00 and then made a deposit of 75.85into her account how much does karita have in her account now

Answers

Answer:

$151.34

Step-by-step explanation:

You would do 138.72 minus 45.23.

138.72 minus 45.23 is 93.49.

Then, you would do 93.49 minus 18.

93.49 minus 18 is 75.49.

Now, you would add 75.49 and 75.85 together to get the answer.

75.49 + 75.85 = 151.34


Working as a salesman, James visits 5 cities per week. At this rate, about how many cities would he visit in
one year?
Use the following conversion to help you solve:
1 year = 52 weeks

This are the answer options:

1820 cities
60 cities
260 cities
57 cities

Answers

Answer:

260 cities

Step-by-step explanation:

Multiple 5 and 52

James would visit 260 cities in one year.

What is multiplication?

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

1 year = 52 weeks

James visits 5 cities per week.

To find the number of cities in e one year:

Multiply by 52

52 x 5

= 260 cities.

Therefore, he would visit 260 cities.

To learn more about the multiplication;

https://brainly.com/question/19634536

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Can y’all help me on question 10 please?

Answers

The correct answer is y=0x7+5

Answer:

[tex]\huge\boxed{\sf 16}[/tex]

Step-by-step explanation:

The fraction of the L.H.S is [tex]\sf 1 \frac{8}{9}[/tex]

The fraction of the R.H.S is [tex]\sf 1 \frac{?}{18}[/tex]

Since the denominator in L.H.S is multiplied by 2 to get 18, numerator will also be multiplied by 2 to get the result.

So,

8*2 = 16

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

Factor Quadratics
(10Point)
x² - 6x – 27
(x – 9) (x + 3)
(x - 2) (x - 3)
(x – 3) (x + 9)
(x – 9) (x – 3)

Answers

Answer:

Step-by-step explanation:

x^2 - 6x - 27

(x - 9)(x+3)

PLZ HELP PLZ PLZ IT MIGHT BE EASY for you

Answers

Answer:

step 1-  (3x2 +  h) +  2c

step 2- 2.1    Factoring    3x2 + h + 2c

Also, Try to factor this multi-variable trinomial using trial.

Therefor the expresion is -1

Step-by-step explanation:

Hopefuly this helped! :)

a triangle has two sides of length 6 and 3. what is the smallest possible whole number length for the third side?

Answers

Answer: 3
Explanation:

Please help due by 3

Answers

Answer:

im assuming its due now

Step-by-step explanation:

Answer:

If you're looking for the solution it would be where the two lines meet which is (1,3)

Step-by-step explanation:

find the slope of the line that passes through (10, 4) and (1, 3)​

Answers

Answer:

I hope it will be help full for u

Step-by-step explanation:

As we know that,

Two points slope formula,

slope=m=(Y2-Y1)/(X2-X1)

As given values

take,   (X1,Y1)=(10,4)

          (X2-Y2)=(1,3)

hence   X1=10  ,  Y1= 4   ,  X2=1  , Y2= 3

putt the values in the above equation of slope we get ,

m=(3-4)/(1-10)

m= -1/-9

m= 1/ 9  Ans

11. Use the distance formula to find the unknown value.
d = 480 mi, r = ?,1 = 3 h
a. 164 mi/h
b. 158 mi/h
c. 162 mi/h
d. 160 mi/h

Answers

Answer:

Torture

Step-by-step explanation:

Instant pain

which of the following is the correct factorization of the polynomial below?

Answers

Answer:

D.

Step-by-step explanation:

The polynomial cannot be factored with rational numbers.

Find the domain and the range of the following:


x y
3 2
5 7
1 4
9 2
3 7

Answers

Given:

The table of values.

To find:

The domain and range.

Solution:

The set of input values or x-values are known as domain.

In the given table, possible values of x are 1, 3, 5 and 9. So,

Domain = {1, 3, 5, 9}

The set of output values or y-values are known as range.

In the given table, possible values of y are 2, 4 and 7. So,

Range = {2, 4, 7}

Therefore, Domain = {1, 3, 5, 9} and Range = {2, 4, 7}.

Simply square root -20 using the imaginary number i

Answers

Answer:2i5

Step-by-step explanation:

Answer:

4.4721...

Step-by-step explanation:

the dots means it keeps going on

Solve a-c=d-r for a

please help me :)

Answers

Answer:

a = d - r + c

Step-by-step explanation:

Simply switch the terms around a bit and you have the answer.

Hope this helped!

it is a-c=d-r = a=d-r+c

The average daily maximum temperature in Syracuse is 21.85°C, and the average daily minimum temperature is -4.7°C. The average daily maximum temperature is
°C higher than the average daily minimum temperature.

Answers

Answer: 26.55°C

Step-by-step explanation:

Average daily maximum temperature in Syracuse = 21.85°C

Average daily minimum temperature = -4.7°C

In order to solve the question, we calculate the difference between the two temperature given. This will be:

= 21.85°C - (-4.7°C)

= 21.85°C + 4.7°C

= 26.55°C

It rains 2 out of 9 days in Austin, Texas. What is the probability that it rains two days in a row?​

Answers

Answer:

2/9 x 2/9 = 4/81

The probability that it rains two days in a row is 4/81 or 4.93% if it rains 2 out of 9 days in Austin, Texas.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

We have:

It rains 2 out of 9 days in Austin, Texas.

P(r) = 2/9

So the probability that it rains two days in a row = (2/9)(2/9)

= 4/81

= 4.93%

Thus, the probability that it rains two days in a row is 4/81 or 4.93% if it rains 2 out of 9 days in Austin, Texas.

Learn more about the probability here:

brainly.com/question/11234923

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Juan states that Andy is constructing the circumscribed circle of triangle ABC, and Kayla states that Andy is constructing the inscribed crcle of triangle
ABC. Who is correct about the type of construction that Andy is creating?

Answers

Answer: Only Kayla

Step-by-step explanation: i took the test

Kayla states correct statement that Andy is constructing the inscribed circle of the triangle.

Constructing the circumscribed circle of triangle ABC,

So that would be a circle that touches vertices the three vertices of the triangle .

We can construct using it using a compass and a straight edge, or a virtual compass and a virtual straight edge .

So what we want to do is center the circle at the perpendicular bisectors of the sides or sometimes that's called the circumcenter of the triangle.

To construct where the perpendicular bisectors of the sides are ,So let me put a circle over here whose radius is longer than this side right over here .

Now let get one that has the same size so let make it the same size as the one i just did.

And allow to construct a perpendicular bisector. If go through that point and this point right over here, this bisect the side over here, and its at a right angle.

Now lets do that for the other sides,  if i move this over here and  I really just have to do it for one, of the other sides.

Because the intersection of two lines is going to give a point . so can do it for this side right over here.

So let me add a other straight edge right over here. so going to go through the point , so that's the perpendicular bisector. of the side right over here. and i could do the third side and it should intersect at that point .

I am not ultra , ultra precise but closing enough. and now i just have to center one of these circle .

And move the circle to the circumcenter and adjust its radius so that its get close to touching .

The three sides the three vertices of the triangle ABC .

Kayla state that Andy is constructing the inscribed circle of the triangle . This is the correct.

For more information about the Construction click the link given below.

https://brainly.com/question/10637236

A.f(x)=-3/4x+10
B.f(x)=3/4x-10
C.f(x)=4/3x+10
D.f(x)=-4/3x-10

Answers

Answer:

Step-by-step explanation:

Equation of a line giving 2 points is

y-y1=m(x-x1) where m is the slope and (x1,y1) is one of the points.

First we have to find the slope using formula

(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are the points given

Slope m is (4-13)/(8--4) =-9/12 = -3/4

Looking at the answer choices, the only slope intercept equation that use the slope -3/4 is answer choice A

need help now btw i am in middle school

Answers

Answer:

umm use internet?

Step-by-step explanation:

Answer:

can you further explain

Step-by-step explanation:

mark me brainiest please

What would be a line perpendicular to (2,3) (5,5)?

There aren’t any answer choices, I just need help understanding how to find a line that is perpendicular to (2,3) (5,5).

Answers

9514 1404 393

Answer:

  3x + 2y = 0   or   y = -3/2x

Step-by-step explanation:

The relationship between a line and its perpendicular is that their slopes are opposite reciprocals of each other. So, the thing you need to know about the line through the two given points is its slope. That is found using the slope formula:

  m = (y2 -y1)/(x2 -x1) . . . . . . where the two give points are (x1, y1) and (x2, y2)

Putting your point coordinates in this formula gives ...

  m = (5 -3)/(5 -2) = 2/3

Then the perpendicular line will have a slope that is the opposite reciprocal:

  slope of perpendicular = -1/m = -1/(2/3) = -3/2

You have not said whether the perpendicular line must meet any other requirement, so the simplest one we can write is ...

  y = mx + b . . . . . m is the slope and b is the y-intercept

  y = -3/2x . . . . . . has a y-intercept of 0 (goes through the origin)

Multiplying by 2 and adding 3x gives ...

  3x + 2y = 0 . . . . . standard form equation

_____

Comment on the attachment

The geometry program I used to create the attachment wrote the equation of the line through the given points as ...

 2x -3y = -5 . . . . . standard form equation

The equation of a perpendicular line can be created from this form by swapping the x- and y-coefficients and negating one of them. Simply swapping the coefficients would give ...

  -3x +2y = <something>

In standard form, we want the leading coefficient to be positive, so we can choose to negate the x-coefficient. The <something> can be zero to make the line go through the origin.

  3x +2y = 0 . . . . . a perpendicular in standard form

__

If you need to have the line go through a particular point, you can determine the constant value (on the right of the = sign) by putting the point coordinates in for x and y.

_____

Method summary:

find the slope of the given linedetermine its opposite reciprocal to find the slope of the perpendicular lineuse that new slope in an appropriate form to have the line go where you want it to go. (Point-Slope Form is often useful)
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